{ "schema": "architectureiq-public-evaluation-v1", "source_sha256": "d37f38466fc6746640dbca5571aff8b1d496cf54f1bf536c1074c2d6f8a1c3bb", "models": [ "gpt-6-luna", "gpt-6.1-sol", "claude-opus-5-5", "claude-haiku-5-5" ], "scoring": "Exact full ranking; API failures remain missing and are not counted as wrong.", "records": [ { "model": "gpt-6-luna", "question_id": "q_a9889bdd9a39a4c2caad00b528356fbd", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842901", "status": "complete", "gold_order": [ "A", "C", "B" ], "predicted_order": [ "B", "C", "A" ], "exact_order_correct": false, "public_content": "\nThe task requires comparing the locations of two objects across channels, not merely recognizing a local shape. Choice B’s patch transformer can attend across the image’s 36 spatial tokens, making it the most direct fit for learning a relationship between distant objects while retaining learned position information. Choice C has useful convolutional and spatial-pooling biases, but its two convolutional blocks have limited receptive fields; the final linear head receives pooled spatial features and may have difficulty combining distant locations into the required relation. Choice A preserves all pixel locations, so it can in principle represent the relation, but its large, unstructured MLP has less spatial inductive bias and must learn that structure from only 75 updates and 2,400 sampled examples.\n\nThus I predict B lower loss than C, and C lower loss than A. The margin and even the B–C ordering are uncertain: the training budget is short, and the CNN’s spatial pooling could make it easier to optimize than the transformer despite its weaker global interaction.\n\n{\"best_to_worst\":[\"B\",\"C\",\"A\"]}", "public_explanation": "The task requires comparing the locations of two objects across channels, not merely recognizing a local shape. Choice B’s patch transformer can attend across the image’s 36 spatial tokens, making it the most direct fit for learning a relationship between distant objects while retaining learned position information. Choice C has useful convolutional and spatial-pooling biases, but its two convolutional blocks have limited receptive fields; the final linear head receives pooled spatial features and may have difficulty combining distant locations into the required relation. Choice A preserves all pixel locations, so it can in principle represent the relation, but its large, unstructured MLP has less spatial inductive bias and must learn that structure from only 75 updates and 2,400 sampled examples.\n\nThus I predict B lower loss than C, and C lower loss than A. The margin and even the B–C ordering are uncertain: the training budget is short, and the CNN’s spatial pooling could make it easier to optimize than the transformer despite its weaker global interaction.", "model_identity_matches": true, "question_sha256": "d0c2b11985e3d2889f05611562f6d47b14afafeef088af0b5083eb72dfeb2bb1", "prompt_sha256": "fb3ce4370e766515d4851692e138003fc2a48d385264afe509bde9f56bfb1505" }, { "model": "gpt-6-luna", "question_id": "q_018f733cbf575236fbf126db4322c484", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_a9889bdd9a39a4c2caad00b528356fbd" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842901", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "A", "C", "B" ], "exact_order_correct": false, "public_content": "All three models see the same small, balanced dataset and receive only 75 updates, so useful inductive bias and optimization efficiency matter. The label depends on the relative locations of objects in separate channels, not merely on their local appearance.\n\nA is my predicted best: its convolutions exploit local shape structure, while the 3×3 spatial pooling retains coarse location information needed to compare the two objects. C comes next: learned positional embeddings and attention can represent relations across patches, but patching at size 4 may blur small objects and the model has limited width and training time. B is last: flattening gives direct access to spatial information, but the large unstructured input and dense MLP provide less useful image inductive bias under this short budget.\n\nThe A-versus-C ordering is uncertain: attention could be advantageous for global relations, while the CNN’s pooling may discard some precise location detail. I expect the CNN’s local bias and retained coarse spatial layout to win here. \n{\"best_to_worst\": [\"A\", \"C\", \"B\"]}", "public_explanation": "All three models see the same small, balanced dataset and receive only 75 updates, so useful inductive bias and optimization efficiency matter. The label depends on the relative locations of objects in separate channels, not merely on their local appearance.\n\nA is my predicted best: its convolutions exploit local shape structure, while the 3×3 spatial pooling retains coarse location information needed to compare the two objects. C comes next: learned positional embeddings and attention can represent relations across patches, but patching at size 4 may blur small objects and the model has limited width and training time. B is last: flattening gives direct access to spatial information, but the large unstructured input and dense MLP provide less useful image inductive bias under this short budget.\n\nThe A-versus-C ordering is uncertain: attention could be advantageous for global relations, while the CNN’s pooling may discard some precise location detail. I expect the CNN’s local bias and retained coarse spatial layout to win here.", "model_identity_matches": true, "question_sha256": "f1514b66e6151b6fceb6c4ae7168a41c6db186b9f7b42705569e764895c29113", "prompt_sha256": "7a0b3cc83d8eadcb682c289dc3eec30a046941fa0bb276ff0956c7875beefb09" }, { "model": "gpt-6-luna", "question_id": "q_f2e0f5463396043d48d5c5ae87bedb87", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_f41ad89255f54a110a6b78ac32e08910" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842902", "status": "complete", "gold_order": [ "B", "C", "A" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": false, "public_content": "Choice C is predicted to have the lowest loss: its convolutional features suit the compact rendered objects, and its 3×3 spatial pooling preserves coarse location information needed to compare the two channels’ object positions. Choice A is next: patch tokens retain spatial position and attention can relate distant regions, but 4×4 patching coarsens object boundaries and the small transformer must learn this relation from few updates. Choice B is last: flattening gives direct access to pixel locations, but its wider dense network has many more parameters and lacks the CNN’s spatial inductive bias, making reliable learning less likely in 75 updates. The C–A comparison is uncertain because the transformer’s global attention could help with the relation, while the CNN’s coarse pooling could discard useful detail.\n{\"best_to_worst\":[\"C\",\"A\",\"B\"]}", "public_explanation": "Choice C is predicted to have the lowest loss: its convolutional features suit the compact rendered objects, and its 3×3 spatial pooling preserves coarse location information needed to compare the two channels’ object positions. Choice A is next: patch tokens retain spatial position and attention can relate distant regions, but 4×4 patching coarsens object boundaries and the small transformer must learn this relation from few updates. Choice B is last: flattening gives direct access to pixel locations, but its wider dense network has many more parameters and lacks the CNN’s spatial inductive bias, making reliable learning less likely in 75 updates. The C–A comparison is uncertain because the transformer’s global attention could help with the relation, while the CNN’s coarse pooling could discard useful detail.", "model_identity_matches": true, "question_sha256": "e8c9cf5b5d874f791085a890e2df4b314527ca6f54efdedd47e4e42e9793bdb2", "prompt_sha256": "e5c9cd2df44039e83c370a64520fe53e9a14641a19cfcba002fbe51ef82e7bc4" }, { "model": "gpt-6-luna", "question_id": "q_2e828a18000b8cfc54065a359bf0ab04", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842903", "status": "complete", "gold_order": [ "A", "C", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": false, "public_content": "\nThe label depends on the relative centers of a circle and square, so preserving spatial information and combining evidence from both channels matter more than recognizing natural-image features. Choice C has the strongest spatial inductive bias: convolutions detect local object evidence, and its 3×3 spatial pooling retains coarse location information for the classifier. That makes it my predicted lowest-loss model, though its shallow depth and pooling may limit precision.\n\nFor C versus A, I favor C because A’s flattened MLP has no spatial weight sharing and must learn location-sensitive features from scratch. A nevertheless has a plausible advantage over B: its dense input-to-hidden layer can directly use fine-grained pixel locations, while B first compresses each 4×4 patch and must learn useful attention and positional interactions with only 75 updates. B’s learned positions and global attention are well suited to relations, so this comparison is uncertain; its transformer structure could overcome the small-data, short-training disadvantage.\n\n{\"best_to_worst\":[\"C\",\"A\",\"B\"]}", "public_explanation": "The label depends on the relative centers of a circle and square, so preserving spatial information and combining evidence from both channels matter more than recognizing natural-image features. Choice C has the strongest spatial inductive bias: convolutions detect local object evidence, and its 3×3 spatial pooling retains coarse location information for the classifier. That makes it my predicted lowest-loss model, though its shallow depth and pooling may limit precision.\n\nFor C versus A, I favor C because A’s flattened MLP has no spatial weight sharing and must learn location-sensitive features from scratch. A nevertheless has a plausible advantage over B: its dense input-to-hidden layer can directly use fine-grained pixel locations, while B first compresses each 4×4 patch and must learn useful attention and positional interactions with only 75 updates. B’s learned positions and global attention are well suited to relations, so this comparison is uncertain; its transformer structure could overcome the small-data, short-training disadvantage.", "model_identity_matches": true, "question_sha256": "a85d544f1c1d558a23b44ad1d97799e53d5321cee414365edda17ec6a862c69b", "prompt_sha256": "d9deece1f02ae57e194f40a57e3c91838fb98334d728674af4ebce39b043ea0f" }, { "model": "gpt-6-luna", "question_id": "q_89d77cd38238c082c9114a0773e6b261", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_2e828a18000b8cfc54065a359bf0ab04" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842903", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "A", "C", "B" ], "exact_order_correct": false, "public_content": "The task depends on comparing the locations of two channel-specific objects. Choice A’s convolutional features preserve spatial structure, and its 3×3 spatial pooling retains coarse location information for the final classifier, making the relation accessible with relatively few parameters. Choice C also preserves position and can compare image regions through attention, but its 4×4 patches reduce spatial detail and its small transformer must learn the relation within only 75 updates. Choice B’s flattened MLP can in principle learn the rule from pixels, but it lacks the CNN’s locality and the transformer’s explicit spatial interactions, so it is the least favorable under this short budget. Thus A is predicted to beat C, and C to beat B. There is material uncertainty: a sufficiently successful MLP can exploit the direct pixel layout, and outcomes may vary across seeds, especially with such limited training.\n{\"best_to_worst\":[\"A\",\"C\",\"B\"]}", "public_explanation": "The task depends on comparing the locations of two channel-specific objects. Choice A’s convolutional features preserve spatial structure, and its 3×3 spatial pooling retains coarse location information for the final classifier, making the relation accessible with relatively few parameters. Choice C also preserves position and can compare image regions through attention, but its 4×4 patches reduce spatial detail and its small transformer must learn the relation within only 75 updates. Choice B’s flattened MLP can in principle learn the rule from pixels, but it lacks the CNN’s locality and the transformer’s explicit spatial interactions, so it is the least favorable under this short budget. Thus A is predicted to beat C, and C to beat B. There is material uncertainty: a sufficiently successful MLP can exploit the direct pixel layout, and outcomes may vary across seeds, especially with such limited training.", "model_identity_matches": true, "question_sha256": "d7dca61949875a1cc3a4ea263e4e25148cb28e78133670ad99f56c761fa03571", "prompt_sha256": "893c63de1a94330af3befe0d4eb57e55c62e5a02cb08401764eb53805ea532ed" }, { "model": "gpt-6-luna", "question_id": "q_04b93ce5a8d08dcf6f6328205dd254ad", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842901", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "B", "A" ], "exact_order_correct": false, "public_content": "The local-shape task is most naturally solved by detecting local, translation-varying contours in channel 0 while ignoring the independently sampled channel-1 distractor. Choice C has the strongest inductive bias for this: dense convolutions preserve local shape structure and spatial pooling provides location tolerance. Its higher AdamW learning rate is somewhat aggressive, but the model is small, normalized, residual, and trained for 1200 updates with clipping, so it is likely to converge well.\n\nChoice B is next: the MLP has substantially more direct access to full-resolution pixels and more hidden width than the transformer, but lacks convolutional translation equivariance and must learn shape recognition across varying locations and distractors. Choice A is likely worst because 4×4 patchification and mean token pooling discard fine boundary detail, while the narrow two-block transformer has limited capacity for this small-object shape task. The main uncertainty is whether Choice C's 0.003 learning rate causes optimization noise or whether the transformer's global attention compensates for its patch resolution; these could make A and B relatively close, but C is the most likely best.\n{\"best_to_worst\":[\"C\",\"B\",\"A\"]}", "public_explanation": "The local-shape task is most naturally solved by detecting local, translation-varying contours in channel 0 while ignoring the independently sampled channel-1 distractor. Choice C has the strongest inductive bias for this: dense convolutions preserve local shape structure and spatial pooling provides location tolerance. Its higher AdamW learning rate is somewhat aggressive, but the model is small, normalized, residual, and trained for 1200 updates with clipping, so it is likely to converge well.\n\nChoice B is next: the MLP has substantially more direct access to full-resolution pixels and more hidden width than the transformer, but lacks convolutional translation equivariance and must learn shape recognition across varying locations and distractors. Choice A is likely worst because 4×4 patchification and mean token pooling discard fine boundary detail, while the narrow two-block transformer has limited capacity for this small-object shape task. The main uncertainty is whether Choice C's 0.003 learning rate causes optimization noise or whether the transformer's global attention compensates for its patch resolution; these could make A and B relatively close, but C is the most likely best.", "model_identity_matches": true, "question_sha256": "92a98eeec0d06b019e8e528487e1be9abc7074c7351968ae6fddb148646f2742", "prompt_sha256": "4a697beb14e725ce09fc114c5c0d23c756edb26da299573d36cdd87224e4a29c" }, { "model": "gpt-6-luna", "question_id": "q_7945972839e5ef8403e9a2edfb6ae39f", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_04b93ce5a8d08dcf6f6328205dd254ad" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842901", "status": "complete", "gold_order": [ "A", "B", "C" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": true, "public_content": "The main advantage is inductive bias for the local-shape task. Choice A uses dense 3×3 convolutions, residual blocks, and spatial pooling, so it can detect shape boundaries locally while tolerating the random object location; its larger learning rate should also make good use of the 1200 updates. Choice B's patch transformer can model spatial relationships, but 4×4 patchification is relatively coarse for objects only roughly 5–9 pixels across, and mean pooling with learned positional embeddings is less naturally translation-invariant. Choice C's MLP sees raw flattened pixels and therefore has to learn location invariance from data, making it the least sample-efficient despite its larger width.\n\nThus A is predicted better than B because its convolutional locality and spatial pooling match the rendered shapes; B is predicted better than C because patch tokens and attention provide some spatial sharing and relational modeling that the fully connected model lacks. The main uncertainty is the small-object/patch interaction: if 4×4 patch embeddings preserve enough shape information, B could approach A, while the higher learning rate in A could hurt if optimization becomes noisy, though clipping and the simple task make that less likely.\n{\"best_to_worst\":[\"A\",\"B\",\"C\"]}", "public_explanation": "The main advantage is inductive bias for the local-shape task. Choice A uses dense 3×3 convolutions, residual blocks, and spatial pooling, so it can detect shape boundaries locally while tolerating the random object location; its larger learning rate should also make good use of the 1200 updates. Choice B's patch transformer can model spatial relationships, but 4×4 patchification is relatively coarse for objects only roughly 5–9 pixels across, and mean pooling with learned positional embeddings is less naturally translation-invariant. Choice C's MLP sees raw flattened pixels and therefore has to learn location invariance from data, making it the least sample-efficient despite its larger width.\n\nThus A is predicted better than B because its convolutional locality and spatial pooling match the rendered shapes; B is predicted better than C because patch tokens and attention provide some spatial sharing and relational modeling that the fully connected model lacks. The main uncertainty is the small-object/patch interaction: if 4×4 patch embeddings preserve enough shape information, B could approach A, while the higher learning rate in A could hurt if optimization becomes noisy, though clipping and the simple task make that less likely.", "model_identity_matches": true, "question_sha256": "d469dca0be63dbd5af5b14a5cb27765ad59e93f694ca465bc9fdff7e6d3ba2cd", "prompt_sha256": "77c0870d6e36da370eeda582e896d1f06b35aec1588122ebcef3937c2052cb83" }, { "model": "gpt-6-luna", "question_id": "q_f2d7051e84a8d64012dfaf4f428f50e8", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_dc6a1198c1d2e494edd7b3618c36bf0b" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842902", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "B", "A" ], "exact_order_correct": false, "public_content": "The local-shape task rewards spatial locality and translation tolerance. Choice C has the strongest inductive bias: dense 3×3 convolutions preserve local boundaries, residual blocks and channel normalization stabilize optimization, and 3×3 spatial pooling retains enough structure to distinguish circle, square, diamond, and cross. Its higher AdamW learning rate is plausible for this smaller CNN and should make good use of the fixed 38,400-sample budget.\n\nChoice B's wide residual MLP has substantial capacity and can fit the task, but flattening destroys locality and translation sharing, making it less sample-efficient than C. It should nevertheless outperform A because its larger hidden width and direct pixel access avoid the patch-resolution bottleneck. Choice A uses 4×4 patchification, only 32-wide tokens, two attention blocks, and mean pooling; small antialiased shape distinctions can be blurred within patches, while the 1,024-image dataset and limited update budget provide little opportunity for the transformer to overcome that disadvantage. Thus the predicted order is C, B, A. The main uncertainty is B versus A: the MLP lacks spatial inductive bias, while the transformer can model relations across patches, but the small-data regime and coarse patching favor B.\n{\"best_to_worst\":[\"C\",\"B\",\"A\"]}", "public_explanation": "The local-shape task rewards spatial locality and translation tolerance. Choice C has the strongest inductive bias: dense 3×3 convolutions preserve local boundaries, residual blocks and channel normalization stabilize optimization, and 3×3 spatial pooling retains enough structure to distinguish circle, square, diamond, and cross. Its higher AdamW learning rate is plausible for this smaller CNN and should make good use of the fixed 38,400-sample budget.\n\nChoice B's wide residual MLP has substantial capacity and can fit the task, but flattening destroys locality and translation sharing, making it less sample-efficient than C. It should nevertheless outperform A because its larger hidden width and direct pixel access avoid the patch-resolution bottleneck. Choice A uses 4×4 patchification, only 32-wide tokens, two attention blocks, and mean pooling; small antialiased shape distinctions can be blurred within patches, while the 1,024-image dataset and limited update budget provide little opportunity for the transformer to overcome that disadvantage. Thus the predicted order is C, B, A. The main uncertainty is B versus A: the MLP lacks spatial inductive bias, while the transformer can model relations across patches, but the small-data regime and coarse patching favor B.", "model_identity_matches": true, "question_sha256": "c1dcd274e5bfe3fa29efdf9b1068dbba8f848a78ccec8ff6b76e3453f5ff750b", "prompt_sha256": "fe70cee8f13b0d073487d6679c19a1f3e01a0315d8718a0064aba562d7b10cb2" }, { "model": "gpt-6-luna", "question_id": "q_9d6e46a52044926788daa1beae022057", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_a03647bbfbcd65d2146723676eb79259" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842903", "status": "complete", "gold_order": [ "C", "B", "A" ], "predicted_order": [ "C", "B", "A" ], "exact_order_correct": true, "public_content": "\nThe CNN is favored because its convolutions directly capture the local boundaries that distinguish circles, squares, diamonds, and crosses, while spatial pooling retains some coarse location information. The transformer also has a useful image-specific inductive bias through its patch projection and attention, but its patch size of 4 may blur small shape-boundary details, and its learning rate is lower. The MLP sees all pixels without built-in locality or translation handling, which is a disadvantage with only 1,024 training images and randomly varying object positions.\n\nThus, I expect C to outperform B, and B to outperform A. The main uncertainty is that the CNN’s higher learning rate and the transformer’s global attention could change their relative outcomes across seeds; these are reasoned predictions, not measured results.\n\n{\"best_to_worst\":[\"C\",\"B\",\"A\"]}", "public_explanation": "The CNN is favored because its convolutions directly capture the local boundaries that distinguish circles, squares, diamonds, and crosses, while spatial pooling retains some coarse location information. The transformer also has a useful image-specific inductive bias through its patch projection and attention, but its patch size of 4 may blur small shape-boundary details, and its learning rate is lower. The MLP sees all pixels without built-in locality or translation handling, which is a disadvantage with only 1,024 training images and randomly varying object positions.\n\nThus, I expect C to outperform B, and B to outperform A. The main uncertainty is that the CNN’s higher learning rate and the transformer’s global attention could change their relative outcomes across seeds; these are reasoned predictions, not measured results.", "model_identity_matches": true, "question_sha256": "2bd9e2c73e99389ca37a213247435dfde05fcb94ad0d6da4ec71191b0f090cca", "prompt_sha256": "b233197f4130204277de0e1c8031551f9056e87969c65100ea9f3ad5065e90c1" }, { "model": "gpt-6-luna", "question_id": "q_5aa7514c54a69ed6cf080475ebf4304e", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842901", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "B", "A", "C" ], "exact_order_correct": true, "public_content": "The task requires comparing the channel-0 circle and channel-1 square geometrically, while the transformer has no positional embeddings and averages token outputs. Thus patch contents and the positional information implicitly encoded within each convolutional patch are crucial. Choice B's 12×12 patches produce only a 2×2 token grid, but each patch retains substantial within-patch coordinate information. Given that object centers lie mostly within the central 10.6-pixel span, those local coordinates can often distinguish the objects' global locations, and the larger receptive patch can contain both objects or substantial parts of them. This makes B the predicted best.\n\nChoice A's 6×6 patches provide finer spatial decomposition and more tokens, but the lack of token positions creates more translation/modulo-patch ambiguity; it is therefore predicted slightly worse than B, despite offering a useful compromise in resolution. Choice C's 3×3 patches creates 64 unpositioned tokens. Objects are fragmented across many patches, and their local coordinates are highly aliased modulo the small patch size. The model consequently loses much of the absolute and relational geometry and also has a harder optimization problem under only 300 updates, so C is predicted worst. The B-versus-A comparison is materially uncertain: if the learned patch representation does not robustly exploit within-patch coordinates, A's finer decomposition could win; the A-versus-C ordering is more confidently A better.\n{\"best_to_worst\":[\"B\",\"A\",\"C\"]}", "public_explanation": "The task requires comparing the channel-0 circle and channel-1 square geometrically, while the transformer has no positional embeddings and averages token outputs. Thus patch contents and the positional information implicitly encoded within each convolutional patch are crucial. Choice B's 12×12 patches produce only a 2×2 token grid, but each patch retains substantial within-patch coordinate information. Given that object centers lie mostly within the central 10.6-pixel span, those local coordinates can often distinguish the objects' global locations, and the larger receptive patch can contain both objects or substantial parts of them. This makes B the predicted best.\n\nChoice A's 6×6 patches provide finer spatial decomposition and more tokens, but the lack of token positions creates more translation/modulo-patch ambiguity; it is therefore predicted slightly worse than B, despite offering a useful compromise in resolution. Choice C's 3×3 patches creates 64 unpositioned tokens. Objects are fragmented across many patches, and their local coordinates are highly aliased modulo the small patch size. The model consequently loses much of the absolute and relational geometry and also has a harder optimization problem under only 300 updates, so C is predicted worst. The B-versus-A comparison is materially uncertain: if the learned patch representation does not robustly exploit within-patch coordinates, A's finer decomposition could win; the A-versus-C ordering is more confidently A better.", "model_identity_matches": true, "question_sha256": "7ed0219aec4b9051563488fa2c2790f13b55f7b44a251b85606dcfd34c3a502f", "prompt_sha256": "8b50362835072e3e6ec6df8405146d0f06e4026755e6cd55e1d5eeee9758fe64" }, { "model": "gpt-6-luna", "question_id": "q_7c4d6ba0c545202de44c8f79483454a8", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842902", "status": "complete", "gold_order": [ "C", "B", "A" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": false, "public_content": "All three choices use the same training budget and optimizer, so the main difference is spatial resolution in the patch embedding. The task depends on the relative locations of two channel-specific objects. Choice A’s 3×3 patches preserve the most local spatial detail and provide the largest token grid, giving its attention layers the best chance to extract location cues. Choice B’s 6×6 patches retain less detail, so I expect higher loss than A. Choice C’s 12×12 patches are coarsest, with only four tokens; that makes it hardest to preserve useful object-position detail, so I expect higher loss than B. A material uncertainty is that the transformer has no positional embeddings and mean-pools its tokens: it therefore lacks a direct representation of global token order, which limits all three models’ ability to solve a relative-position task and makes the predicted gaps uncertain.\n{\"best_to_worst\":[\"A\",\"B\",\"C\"]}", "public_explanation": "All three choices use the same training budget and optimizer, so the main difference is spatial resolution in the patch embedding. The task depends on the relative locations of two channel-specific objects. Choice A’s 3×3 patches preserve the most local spatial detail and provide the largest token grid, giving its attention layers the best chance to extract location cues. Choice B’s 6×6 patches retain less detail, so I expect higher loss than A. Choice C’s 12×12 patches are coarsest, with only four tokens; that makes it hardest to preserve useful object-position detail, so I expect higher loss than B. A material uncertainty is that the transformer has no positional embeddings and mean-pools its tokens: it therefore lacks a direct representation of global token order, which limits all three models’ ability to solve a relative-position task and makes the predicted gaps uncertain.", "model_identity_matches": true, "question_sha256": "c51f4fc9654aeccf18b9c0291212baf9c84872536be74d391e2f2fa11e711243", "prompt_sha256": "36003f34cf6c558f3bc65b4380aa27b0216aaad6c950d5ee4f4c399fc38c9dbc" }, { "model": "gpt-6-luna", "question_id": "q_c179b9eb52ffd8f3f234de5863020a7a", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_7c4d6ba0c545202de44c8f79483454a8" }, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842902", "status": "complete", "gold_order": [ "A", "C", "B" ], "predicted_order": [ "A", "C", "B" ], "exact_order_correct": true, "public_content": "The dominant issue is that the transformer has no positional embeddings and mean-pools tokens, making its representation permutation-invariant over patches. Thus it cannot generally compare the absolute locations of objects in different patches; performance depends heavily on whether both channel objects fall within a patch whose internal spatial layout can encode their relative displacement. Choice A's 12×12 patches most often provide a joint receptive field for the two objects, and its 32-dimensional projection should retain enough coarse geometry, so it is predicted to have the lowest loss. Choice C's 6×6 patches preserve finer local detail but are less able to contain both objects jointly, making it worse than A while still better than B. Choice B's 3×3 patches usually separate the objects across many tokens, so the position-free attention/mean-pooling stack loses the relation signal and should have the highest loss. The A-versus-C comparison is materially uncertain because 12×12 patch projections are coarser and may discard geometric detail; if that information bottleneck dominates, C could overtake A, but the larger joint context is expected to win here.\n{\"best_to_worst\":[\"A\",\"C\",\"B\"]}", "public_explanation": "The dominant issue is that the transformer has no positional embeddings and mean-pools tokens, making its representation permutation-invariant over patches. Thus it cannot generally compare the absolute locations of objects in different patches; performance depends heavily on whether both channel objects fall within a patch whose internal spatial layout can encode their relative displacement. Choice A's 12×12 patches most often provide a joint receptive field for the two objects, and its 32-dimensional projection should retain enough coarse geometry, so it is predicted to have the lowest loss. Choice C's 6×6 patches preserve finer local detail but are less able to contain both objects jointly, making it worse than A while still better than B. Choice B's 3×3 patches usually separate the objects across many tokens, so the position-free attention/mean-pooling stack loses the relation signal and should have the highest loss. The A-versus-C comparison is materially uncertain because 12×12 patch projections are coarser and may discard geometric detail; if that information bottleneck dominates, C could overtake A, but the larger joint context is expected to win here.", "model_identity_matches": true, "question_sha256": "4327fab3306887d72c21d9fbe2f5c301db6ab223eac36525743fd056e18528f9", "prompt_sha256": "c24266d7c88d813d3534d88aaed5c8b684604ff9d5ee731d7863c25fba7a9432" }, { "model": "gpt-6-luna", "question_id": "q_76cac3671eecb9ff4306d1b86e28b45c", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842903", "status": "complete", "gold_order": [ "B", "C", "A" ], "predicted_order": [ "B", "C", "A" ], "exact_order_correct": true, "public_content": "The dominant issue is that the transformer has no positional embeddings (`position: \"none\"`), while attention and token averaging are permutation-invariant. Thus, global patch order is unavailable and the relative-position task is intrinsically difficult for all three choices. Patch size nevertheless controls how much positional information is indirectly retained inside each patch. With 12×12 patches, object centers occupy distinctive within-patch regions because the rendered centers lie roughly in the central image area; this gives Choice B the strongest indirect cue about relative displacement. Choice C's 6×6 patches retain less useful absolute-within-patch information and require combining more tokens, so B is expected to have lower loss than C. Choice A's 3×3 patches mostly expose local shape fragments and discard displacement information modulo a very small patch, while also producing 64 nearly positionless tokens; it should therefore be closest to chance and worse than C. Material uncertainty remains substantial: because the architecture has no true positional encoding, all losses may be close, and the exact ordering depends on how effectively the patch projections exploit boundary and within-patch artifacts under only 300 AdamW updates.\n{\"best_to_worst\":[\"B\",\"C\",\"A\"]}", "public_explanation": "The dominant issue is that the transformer has no positional embeddings (`position: \"none\"`), while attention and token averaging are permutation-invariant. Thus, global patch order is unavailable and the relative-position task is intrinsically difficult for all three choices. Patch size nevertheless controls how much positional information is indirectly retained inside each patch. With 12×12 patches, object centers occupy distinctive within-patch regions because the rendered centers lie roughly in the central image area; this gives Choice B the strongest indirect cue about relative displacement. Choice C's 6×6 patches retain less useful absolute-within-patch information and require combining more tokens, so B is expected to have lower loss than C. Choice A's 3×3 patches mostly expose local shape fragments and discard displacement information modulo a very small patch, while also producing 64 nearly positionless tokens; it should therefore be closest to chance and worse than C. Material uncertainty remains substantial: because the architecture has no true positional encoding, all losses may be close, and the exact ordering depends on how effectively the patch projections exploit boundary and within-patch artifacts under only 300 AdamW updates.", "model_identity_matches": true, "question_sha256": "6b4fa08d1969fd32b3dd6aa13fe9c2ee0d4666d4e7cbcf203da570a32971d052", "prompt_sha256": "13573df98c8675006a14f0c15c929b41bdcdcb74b326cf53f235898480a567dc" }, { "model": "gpt-6-luna", "question_id": "q_21ca0ff91a02c38e27e1bebe5867c24d", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_76cac3671eecb9ff4306d1b86e28b45c" }, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842903", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": true, "public_content": "All choices use the same short training budget and differ only in patch size. The key limitation is that the task label depends on the relative locations of the channel-0 circle and channel-1 square, but these transformers have no positional embeddings and mean-pool their tokens. They therefore have little direct access to the objects’ arrangement across patches. Larger patches can preserve more within-patch spatial relationships: C (12×12) is most likely to retain useful relative-location cues when both objects fall in a patch, while A (6×6) offers less such context. B (3×3) splits objects and their relationship across many tokens, whose spatial order the model cannot use, so I expect the highest loss. Thus C should outperform A, and A should outperform B. This ordering is uncertain: useful within-patch co-occurrence may be uncommon, and seed variation or optimization could narrow or reverse the differences.\n{\"best_to_worst\":[\"C\",\"A\",\"B\"]}", "public_explanation": "All choices use the same short training budget and differ only in patch size. The key limitation is that the task label depends on the relative locations of the channel-0 circle and channel-1 square, but these transformers have no positional embeddings and mean-pool their tokens. They therefore have little direct access to the objects’ arrangement across patches. Larger patches can preserve more within-patch spatial relationships: C (12×12) is most likely to retain useful relative-location cues when both objects fall in a patch, while A (6×6) offers less such context. B (3×3) splits objects and their relationship across many tokens, whose spatial order the model cannot use, so I expect the highest loss. Thus C should outperform A, and A should outperform B. This ordering is uncertain: useful within-patch co-occurrence may be uncommon, and seed variation or optimization could narrow or reverse the differences.", "model_identity_matches": true, "question_sha256": "1ed74fdb24c4279febc8cc25695345ccb4178c002376e9f1e11c40ce1a5ae945", "prompt_sha256": "1b542c782593bec4e9a3b63caea8a34c2f95b491fcda8e2027d39985b3b21047" }, { "model": "gpt-6.1-sol", "question_id": "q_a9889bdd9a39a4c2caad00b528356fbd", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842901", "status": "complete", "gold_order": [ "A", "C", "B" ], "predicted_order": [ "A", "C", "B" ], "exact_order_correct": true, "public_content": "\nI predict **A → C → B** for the short, 75-update training budget.\n\n- **A over C:** The flattened MLP has direct access to absolute pixel locations and separate object channels. It can quickly learn spatial weighting patterns that approximate each object’s center and discriminate the four displacement directions. Residual blocks preserve this direct signal. C retains position through its 3×3 pooling grid, but spatial averaging compresses within-cell location information, and its convolutional features must first become useful for localization. That is a disadvantage with only 2,400 sampled training examples.\n- **C over B:** C’s spatial pooling gives the classifier an explicit, fixed spatial layout. B averages its patch tokens, so its positional discrimination depends on learning to combine the initially small learned position embeddings with object content through attention. Without those interactions, pooled patch features largely discard the spatial arrangement needed for this task. Learning them reliably is likely slower than exploiting C’s fixed spatial bins.\n\nThe main uncertainty is the A–C gap: C’s weight sharing and normalization could make it learn faster than expected, while A may fit position-specific patterns less robustly. Nevertheless, the target’s simple geometric rule and the very short training budget favor A’s direct spatial access. B is the strongest prediction for highest loss.\n\n{\"best_to_worst\": [\"A\", \"C\", \"B\"]}", "public_explanation": "I predict **A → C → B** for the short, 75-update training budget.\n\n- **A over C:** The flattened MLP has direct access to absolute pixel locations and separate object channels. It can quickly learn spatial weighting patterns that approximate each object’s center and discriminate the four displacement directions. Residual blocks preserve this direct signal. C retains position through its 3×3 pooling grid, but spatial averaging compresses within-cell location information, and its convolutional features must first become useful for localization. That is a disadvantage with only 2,400 sampled training examples.\n- **C over B:** C’s spatial pooling gives the classifier an explicit, fixed spatial layout. B averages its patch tokens, so its positional discrimination depends on learning to combine the initially small learned position embeddings with object content through attention. Without those interactions, pooled patch features largely discard the spatial arrangement needed for this task. Learning them reliably is likely slower than exploiting C’s fixed spatial bins.\n\nThe main uncertainty is the A–C gap: C’s weight sharing and normalization could make it learn faster than expected, while A may fit position-specific patterns less robustly. Nevertheless, the target’s simple geometric rule and the very short training budget favor A’s direct spatial access. B is the strongest prediction for highest loss.", "model_identity_matches": true, "question_sha256": "d0c2b11985e3d2889f05611562f6d47b14afafeef088af0b5083eb72dfeb2bb1", "prompt_sha256": "fb3ce4370e766515d4851692e138003fc2a48d385264afe509bde9f56bfb1505" }, { "model": "gpt-6.1-sol", "question_id": "q_018f733cbf575236fbf126db4322c484", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_a9889bdd9a39a4c2caad00b528356fbd" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842901", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "A", "C", "B" ], "exact_order_correct": false, "public_content": "The predicted order is A, C, B. Choice A has the strongest task-aligned inductive bias: its convolutions preserve local object structure and channel identity, while the 3×3 spatial pooling retains coarse location information for comparing the circle and square. The objects are several pixels wide, and the label is determined by signed displacement, which can be represented from spatially weighted channel responses. Thus A is expected to achieve lower loss than C, whose 4×4 patchification reduces positional resolution and whose width-32 attention model has less representational capacity, although its learned positions and global attention make it well suited to the relation task. C is expected to beat B because it retains spatial tokens, explicit positional embeddings, and global token interactions, whereas B must learn spatial structure from a flattened 1152-dimensional input through a width-96 bottleneck in only 75 updates. The main uncertainty is the A-versus-C comparison: attention may better implement the global pairwise relation, while CNN pooling may lose fine displacement information; the short budget and seed averaging could make that gap small. B could also benefit from directly learning centroid-like global pixel summaries, but lacks the stronger spatial inductive bias.\n{\"best_to_worst\":[\"A\",\"C\",\"B\"]}", "public_explanation": "The predicted order is A, C, B. Choice A has the strongest task-aligned inductive bias: its convolutions preserve local object structure and channel identity, while the 3×3 spatial pooling retains coarse location information for comparing the circle and square. The objects are several pixels wide, and the label is determined by signed displacement, which can be represented from spatially weighted channel responses. Thus A is expected to achieve lower loss than C, whose 4×4 patchification reduces positional resolution and whose width-32 attention model has less representational capacity, although its learned positions and global attention make it well suited to the relation task. C is expected to beat B because it retains spatial tokens, explicit positional embeddings, and global token interactions, whereas B must learn spatial structure from a flattened 1152-dimensional input through a width-96 bottleneck in only 75 updates. The main uncertainty is the A-versus-C comparison: attention may better implement the global pairwise relation, while CNN pooling may lose fine displacement information; the short budget and seed averaging could make that gap small. B could also benefit from directly learning centroid-like global pixel summaries, but lacks the stronger spatial inductive bias.", "model_identity_matches": true, "question_sha256": "f1514b66e6151b6fceb6c4ae7168a41c6db186b9f7b42705569e764895c29113", "prompt_sha256": "7a0b3cc83d8eadcb682c289dc3eec30a046941fa0bb276ff0956c7875beefb09" }, { "model": "gpt-6.1-sol", "question_id": "q_f41ad89255f54a110a6b78ac32e08910", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842902", "status": "complete", "gold_order": [ "A", "B", "C" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": true, "public_content": "\nI predict **A → B → C** for the short, 75-update training budget.\n\n- **A versus B:** A preserves absolute pixel positions through its flattened linear stem. Relative-position labels can be approximated efficiently using channel-specific spatial weight maps that compare the objects’ locations; mass normalization makes these signals more consistent across object sizes. Its residual MLP can refine that comparison. B retains useful location information through its 3×3 spatial pooling, but pooling compresses within-bin positions, and its local convolutional blocks must learn suitable features before the linear head can compare locations. I therefore expect A to reach lower cross entropy sooner.\n- **B versus C:** B has an explicit spatially indexed readout. C instead averages its patch tokens, so it must learn to bind object identity to the small learned positional embeddings and preserve that information through attention before averaging. With only 2,400 sampled training examples and 75 updates, this is likely substantially harder than exploiting B’s spatial bins.\n\nThe main uncertainty is **A versus B**: B’s shared filters and normalization could improve sample efficiency enough to narrow or reverse their gap. C’s global attention is expressive, but its positional learning burden makes it the clearest candidate for highest loss under this budget.\n\n{\"best_to_worst\": [\"A\", \"B\", \"C\"]}", "public_explanation": "I predict **A → B → C** for the short, 75-update training budget.\n\n- **A versus B:** A preserves absolute pixel positions through its flattened linear stem. Relative-position labels can be approximated efficiently using channel-specific spatial weight maps that compare the objects’ locations; mass normalization makes these signals more consistent across object sizes. Its residual MLP can refine that comparison. B retains useful location information through its 3×3 spatial pooling, but pooling compresses within-bin positions, and its local convolutional blocks must learn suitable features before the linear head can compare locations. I therefore expect A to reach lower cross entropy sooner.\n- **B versus C:** B has an explicit spatially indexed readout. C instead averages its patch tokens, so it must learn to bind object identity to the small learned positional embeddings and preserve that information through attention before averaging. With only 2,400 sampled training examples and 75 updates, this is likely substantially harder than exploiting B’s spatial bins.\n\nThe main uncertainty is **A versus B**: B’s shared filters and normalization could improve sample efficiency enough to narrow or reverse their gap. C’s global attention is expressive, but its positional learning burden makes it the clearest candidate for highest loss under this budget.", "model_identity_matches": true, "question_sha256": "265fcd17cb23554b617a57bfea7cb952934d1a4204aa69ba0b68f92abe28b48d", "prompt_sha256": "27654c0d84bd94e35c93f05379ff7f90c78d826947c7456eb743d2f2d16ebd40" }, { "model": "gpt-6.1-sol", "question_id": "q_89d77cd38238c082c9114a0773e6b261", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_2e828a18000b8cfc54065a359bf0ab04" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842903", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": false, "public_content": "The CNN (A) has the strongest inductive bias for this task: shared local filters can detect the two rendered objects across varying locations, while the 3×3 spatial pooling retains enough coarse positional information to compare their centers. Its convolutional weight sharing should also make the limited 75-update budget more efficient than the fully connected alternative. Thus A is favored over B, despite its smaller width.\n\nBetween B and C, the MLP retains all 24×24 pixel detail and has substantially greater hidden width, so it can learn the exact geometric relation given enough examples and updates. The patch transformer compresses the image into 4×4 patches before attention; this is useful for global interactions but can blur the small center displacements and dominance-axis boundary relevant to the labels. With only 75 AdamW updates, its lower width and patch quantization make C likely worse than B. The B/C ordering is materially uncertain because attention may learn the global comparison more efficiently, but the short budget and 4-pixel patches favor B.\n{\"best_to_worst\":[\"A\",\"B\",\"C\"]}", "public_explanation": "The CNN (A) has the strongest inductive bias for this task: shared local filters can detect the two rendered objects across varying locations, while the 3×3 spatial pooling retains enough coarse positional information to compare their centers. Its convolutional weight sharing should also make the limited 75-update budget more efficient than the fully connected alternative. Thus A is favored over B, despite its smaller width.\n\nBetween B and C, the MLP retains all 24×24 pixel detail and has substantially greater hidden width, so it can learn the exact geometric relation given enough examples and updates. The patch transformer compresses the image into 4×4 patches before attention; this is useful for global interactions but can blur the small center displacements and dominance-axis boundary relevant to the labels. With only 75 AdamW updates, its lower width and patch quantization make C likely worse than B. The B/C ordering is materially uncertain because attention may learn the global comparison more efficiently, but the short budget and 4-pixel patches favor B.", "model_identity_matches": true, "question_sha256": "d7dca61949875a1cc3a4ea263e4e25148cb28e78133670ad99f56c761fa03571", "prompt_sha256": "893c63de1a94330af3befe0d4eb57e55c62e5a02cb08401764eb53805ea532ed" }, { "model": "gpt-6.1-sol", "question_id": "q_04b93ce5a8d08dcf6f6328205dd254ad", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842901", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": true, "public_content": "The local-shape target is determined by a small channel-0 object, while channel 1 is an independent distractor and mass normalization removes a simple total-intensity cue. Choice C should perform best because its convolutional blocks preserve local boundary information and spatial pooling provides useful translation tolerance; its higher AdamW learning rate is plausible for this normalized CNN and 1200-update budget. Choice A is next: the patch transformer can aggregate shape evidence, but 4×4 patching and mean token pooling discard fine boundary detail, especially for small objects. Choice B is expected to be worst because the flattened MLP lacks locality and translation-equivariance, making it more reliant on learning many location-specific templates despite its larger width. Thus C beats A, and A beats B. The main uncertainty is the A/B comparison: the MLP has substantially more capacity and could exploit the simple synthetic task effectively, while the transformer has stronger spatial inductive structure but less fine-grained resolution.\n{\"best_to_worst\":[\"C\",\"A\",\"B\"]}", "public_explanation": "The local-shape target is determined by a small channel-0 object, while channel 1 is an independent distractor and mass normalization removes a simple total-intensity cue. Choice C should perform best because its convolutional blocks preserve local boundary information and spatial pooling provides useful translation tolerance; its higher AdamW learning rate is plausible for this normalized CNN and 1200-update budget. Choice A is next: the patch transformer can aggregate shape evidence, but 4×4 patching and mean token pooling discard fine boundary detail, especially for small objects. Choice B is expected to be worst because the flattened MLP lacks locality and translation-equivariance, making it more reliant on learning many location-specific templates despite its larger width. Thus C beats A, and A beats B. The main uncertainty is the A/B comparison: the MLP has substantially more capacity and could exploit the simple synthetic task effectively, while the transformer has stronger spatial inductive structure but less fine-grained resolution.", "model_identity_matches": true, "question_sha256": "92a98eeec0d06b019e8e528487e1be9abc7074c7351968ae6fddb148646f2742", "prompt_sha256": "4a697beb14e725ce09fc114c5c0d23c756edb26da299573d36cdd87224e4a29c" }, { "model": "gpt-6.1-sol", "question_id": "q_7945972839e5ef8403e9a2edfb6ae39f", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_04b93ce5a8d08dcf6f6328205dd254ad" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842901", "status": "complete", "gold_order": [ "A", "B", "C" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": true, "public_content": "The CNN (A) should achieve the lowest loss because the target is a translation-tolerant local shape, and its convolutional weight sharing directly captures local boundaries while spatial pooling preserves coarse location. Its higher AdamW learning rate may also accelerate fitting within the fixed budget, though it introduces some optimization uncertainty. The patch transformer (B) is next: patch embeddings and attention can aggregate shape evidence and handle the distractor channel, but 4×4 patching, learned absolute positions, low width, and only two blocks make it less naturally suited to small antialiased shapes than the CNN. The MLP (C) is likely worst because flattening discards translation inductive bias and requires learning equivalent shape detectors separately across positions, despite its larger width. The main uncertainty is B versus C: the MLP has substantially more capacity and could fit the simple synthetic task well, while the transformer’s patch representation may lose fine boundary information.\n{\"best_to_worst\":[\"A\",\"B\",\"C\"]}", "public_explanation": "The CNN (A) should achieve the lowest loss because the target is a translation-tolerant local shape, and its convolutional weight sharing directly captures local boundaries while spatial pooling preserves coarse location. Its higher AdamW learning rate may also accelerate fitting within the fixed budget, though it introduces some optimization uncertainty. The patch transformer (B) is next: patch embeddings and attention can aggregate shape evidence and handle the distractor channel, but 4×4 patching, learned absolute positions, low width, and only two blocks make it less naturally suited to small antialiased shapes than the CNN. The MLP (C) is likely worst because flattening discards translation inductive bias and requires learning equivalent shape detectors separately across positions, despite its larger width. The main uncertainty is B versus C: the MLP has substantially more capacity and could fit the simple synthetic task well, while the transformer’s patch representation may lose fine boundary information.", "model_identity_matches": true, "question_sha256": "d469dca0be63dbd5af5b14a5cb27765ad59e93f694ca465bc9fdff7e6d3ba2cd", "prompt_sha256": "77c0870d6e36da370eeda582e896d1f06b35aec1588122ebcef3937c2052cb83" }, { "model": "gpt-6.1-sol", "question_id": "q_dc6a1198c1d2e494edd7b3618c36bf0b", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842902", "status": "complete", "gold_order": [ "B", "C", "A" ], "predicted_order": [ "B", "A", "C" ], "exact_order_correct": false, "public_content": "The main advantage is matching the local-shape task: channel 0 contains the class-defining shape, while channel 1 is an independent distractor. Choice B has the strongest spatial inductive bias, using dense 3x3 convolutions, residual blocks, and spatial pooling, so it should learn shape boundaries while aggregating over position; its higher AdamW learning rate is also plausible for this normalized CNN. Thus B is expected to have lower loss than A. Choice A directly accesses all pixels and has substantially more hidden width, so it should still learn the four shapes, but its flattened MLP lacks locality and translation-friendly structure and must suppress the distractor through dense features. Choice C has useful patch locality and attention, but 4x4 patchification and mean pooling discard fine boundary detail for objects only roughly 2.5–4.5 pixels in radius; its narrower 32-wide, two-block model is consequently expected to trail the MLP. The closest and most uncertain comparison is A versus C: a favorable optimization outcome could reverse them, but the small shapes and patch aggregation favor A.\n{\"best_to_worst\":[\"B\",\"A\",\"C\"]}", "public_explanation": "The main advantage is matching the local-shape task: channel 0 contains the class-defining shape, while channel 1 is an independent distractor. Choice B has the strongest spatial inductive bias, using dense 3x3 convolutions, residual blocks, and spatial pooling, so it should learn shape boundaries while aggregating over position; its higher AdamW learning rate is also plausible for this normalized CNN. Thus B is expected to have lower loss than A. Choice A directly accesses all pixels and has substantially more hidden width, so it should still learn the four shapes, but its flattened MLP lacks locality and translation-friendly structure and must suppress the distractor through dense features. Choice C has useful patch locality and attention, but 4x4 patchification and mean pooling discard fine boundary detail for objects only roughly 2.5–4.5 pixels in radius; its narrower 32-wide, two-block model is consequently expected to trail the MLP. The closest and most uncertain comparison is A versus C: a favorable optimization outcome could reverse them, but the small shapes and patch aggregation favor A.", "model_identity_matches": true, "question_sha256": "d3b698eb2cbd3c0339d6fafe28333df4794a1062bfa8887fa1a3e7ba8ab27849", "prompt_sha256": "a7df13a151777eba77efe2a89ce0ae8420134f2cb76f07f44143945ea5a0322e" }, { "model": "gpt-6.1-sol", "question_id": "q_f2d7051e84a8d64012dfaf4f428f50e8", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_dc6a1198c1d2e494edd7b3618c36bf0b" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842902", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": true, "public_content": "\nMy predicted order is C, A, B.\n\n- **C over A:** Local shape recognition favors shared, fine-scale edge and corner detectors. C preserves full spatial resolution through its stem and two dense 3×3 convolutional blocks, allowing it to learn local boundary patterns before spatial pooling. Its channel normalization and higher AdamW learning rate (0.003) should also support rapid learning within 1,200 updates. A retains information through learned patch embeddings, but its nonoverlapping 4×4 patches make boundary features more sensitive to alignment and require attention to combine evidence across patches.\n- **A over B:** A shares its patch projection and attention computations across image locations, providing a useful inductive bias for shapes whose centers vary independently of class. B flattens the image and learns location-specific input weights; with only 1,024 training images, it is more likely to fit incidental location and distractor-channel patterns, yielding worse held-out cross entropy.\n\nThe main uncertainty is A versus B: B could learn effective global shape features quickly, while A may spend a substantial fraction of its budget learning to aggregate sparse foreground patches. Nevertheless, shared spatial processing makes A the stronger prediction. All three receive the same number of updates and examples, so the ranking primarily reflects architecture and optimization rather than budget.\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "My predicted order is C, A, B.\n\n- **C over A:** Local shape recognition favors shared, fine-scale edge and corner detectors. C preserves full spatial resolution through its stem and two dense 3×3 convolutional blocks, allowing it to learn local boundary patterns before spatial pooling. Its channel normalization and higher AdamW learning rate (0.003) should also support rapid learning within 1,200 updates. A retains information through learned patch embeddings, but its nonoverlapping 4×4 patches make boundary features more sensitive to alignment and require attention to combine evidence across patches.\n- **A over B:** A shares its patch projection and attention computations across image locations, providing a useful inductive bias for shapes whose centers vary independently of class. B flattens the image and learns location-specific input weights; with only 1,024 training images, it is more likely to fit incidental location and distractor-channel patterns, yielding worse held-out cross entropy.\n\nThe main uncertainty is A versus B: B could learn effective global shape features quickly, while A may spend a substantial fraction of its budget learning to aggregate sparse foreground patches. Nevertheless, shared spatial processing makes A the stronger prediction. All three receive the same number of updates and examples, so the ranking primarily reflects architecture and optimization rather than budget.", "model_identity_matches": true, "question_sha256": "c1dcd274e5bfe3fa29efdf9b1068dbba8f848a78ccec8ff6b76e3453f5ff750b", "prompt_sha256": "fe70cee8f13b0d073487d6679c19a1f3e01a0315d8718a0064aba562d7b10cb2" }, { "model": "gpt-6.1-sol", "question_id": "q_a03647bbfbcd65d2146723676eb79259", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842903", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "B", "A", "C" ], "exact_order_correct": true, "public_content": "\nMy predicted order is **B, A, C**.\n\n- **B over A:** The target is local shape in channel 0, with randomly varying position, radius, and intensity. B’s stride-1 convolutions preserve fine boundary structure and share edge/corner detectors across locations. Its two residual convolution blocks and spatial pooling are well suited to combining those cues. The higher AdamW learning rate (0.003 versus 0.001) also plausibly helps within the fixed 1,200-update budget. A instead partitions the image into nonoverlapping 4×4 patches, making boundary descriptions more dependent on alignment with the patch grid.\n- **A over C:** A retains spatially shared patch processing and can aggregate evidence across patches through attention. C must learn shape discrimination and tolerance to translation from flattened pixels, without convolutional or patch-level weight sharing. With only 1,024 distinct training examples, C is more likely to fit location-specific patterns and distractor variation rather than generalizable shape features.\n\nThe main uncertainty is the size of A’s advantage over C: the small transformer could learn patch-alignment-sensitive shortcuts, while the MLP may exploit consistent global shape statistics. B’s architectural match to local boundary recognition makes its first-place prediction more convincing, although its higher constant learning rate could introduce final-checkpoint variability.\n\n{\"best_to_worst\": [\"B\", \"A\", \"C\"]}", "public_explanation": "My predicted order is **B, A, C**.\n\n- **B over A:** The target is local shape in channel 0, with randomly varying position, radius, and intensity. B’s stride-1 convolutions preserve fine boundary structure and share edge/corner detectors across locations. Its two residual convolution blocks and spatial pooling are well suited to combining those cues. The higher AdamW learning rate (0.003 versus 0.001) also plausibly helps within the fixed 1,200-update budget. A instead partitions the image into nonoverlapping 4×4 patches, making boundary descriptions more dependent on alignment with the patch grid.\n- **A over C:** A retains spatially shared patch processing and can aggregate evidence across patches through attention. C must learn shape discrimination and tolerance to translation from flattened pixels, without convolutional or patch-level weight sharing. With only 1,024 distinct training examples, C is more likely to fit location-specific patterns and distractor variation rather than generalizable shape features.\n\nThe main uncertainty is the size of A’s advantage over C: the small transformer could learn patch-alignment-sensitive shortcuts, while the MLP may exploit consistent global shape statistics. B’s architectural match to local boundary recognition makes its first-place prediction more convincing, although its higher constant learning rate could introduce final-checkpoint variability.", "model_identity_matches": true, "question_sha256": "0dfb1c35252b1b32dd15e13d43053aee3c0821628464debf9c87fcdff5796c97", "prompt_sha256": "3a6f9497c20315f937936b5fd8b513050e2a0b99110e1c68fedf05e13ae98741" }, { "model": "gpt-6.1-sol", "question_id": "q_9d6e46a52044926788daa1beae022057", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_a03647bbfbcd65d2146723676eb79259" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842903", "status": "complete", "gold_order": [ "C", "B", "A" ], "predicted_order": [ "C", "B", "A" ], "exact_order_correct": true, "public_content": "The local_shape label depends on the channel-0 object's local geometry and is independent of absolute position; channel 1 is distractor. Choice C has the strongest matching inductive bias: dense convolutions preserve local shape features and provide translation-equivariant processing, while spatial pooling aggregates evidence across locations. Its higher AdamW learning rate should also allow effective progress within the fixed 38,400-sample budget. Thus C is expected to have lower loss than B, whose patch size 4 and learned positional embeddings can represent the shapes but introduce patch-boundary and position sensitivity; its mean token pooling and attention still make it substantially better suited than a position-specific flat MLP. B is expected to beat A because A must learn location invariance directly from flattened pixels, with no convolutional sharing or pooling, despite its larger width. Material uncertainty remains between C and B: the CNN's only two blocks and 3x3 spatial pooling may limit shape integration, while the transformer can globally combine patch evidence, and the differing learning rates affect finite-budget convergence.\n{\"best_to_worst\":[\"C\",\"B\",\"A\"]}", "public_explanation": "The local_shape label depends on the channel-0 object's local geometry and is independent of absolute position; channel 1 is distractor. Choice C has the strongest matching inductive bias: dense convolutions preserve local shape features and provide translation-equivariant processing, while spatial pooling aggregates evidence across locations. Its higher AdamW learning rate should also allow effective progress within the fixed 38,400-sample budget. Thus C is expected to have lower loss than B, whose patch size 4 and learned positional embeddings can represent the shapes but introduce patch-boundary and position sensitivity; its mean token pooling and attention still make it substantially better suited than a position-specific flat MLP. B is expected to beat A because A must learn location invariance directly from flattened pixels, with no convolutional sharing or pooling, despite its larger width. Material uncertainty remains between C and B: the CNN's only two blocks and 3x3 spatial pooling may limit shape integration, while the transformer can globally combine patch evidence, and the differing learning rates affect finite-budget convergence.", "model_identity_matches": true, "question_sha256": "2bd9e2c73e99389ca37a213247435dfde05fcb94ad0d6da4ec71191b0f090cca", "prompt_sha256": "b233197f4130204277de0e1c8031551f9056e87969c65100ea9f3ad5065e90c1" }, { "model": "gpt-6.1-sol", "question_id": "q_5aa7514c54a69ed6cf080475ebf4304e", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842901", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "A", "C", "B" ], "exact_order_correct": false, "public_content": "The predicted best choice is A because 6×6 patches provide a useful compromise: the objects span multiple patches, while the 16-token representation retains more local boundary and displacement information than the 12×12 alternative. The transformer has no positional embeddings, so all choices are permutation-invariant over patch tokens; this makes exact global arrangement difficult, but local object location within each patch and interactions among patch contents still provide signal.\n\nA is preferred to C because 3×3 patches produce 64 tokens, diluting object-level evidence through mean pooling and making the fixed 300-update budget less favorable, despite retaining fine detail. A is preferred to B because 12×12 patches yield only four very coarse tokens and frequently merge or poorly resolve the small objects, losing directional and boundary information. The main uncertainty is the absence of positional encoding: depending on how much relative-position signal is recoverable from patch-boundary effects and within-patch coordinates, C could approach or exceed A; nevertheless, B is most likely worst because of its coarse spatial discretization.\n{\"best_to_worst\":[\"A\",\"C\",\"B\"]}", "public_explanation": "The predicted best choice is A because 6×6 patches provide a useful compromise: the objects span multiple patches, while the 16-token representation retains more local boundary and displacement information than the 12×12 alternative. The transformer has no positional embeddings, so all choices are permutation-invariant over patch tokens; this makes exact global arrangement difficult, but local object location within each patch and interactions among patch contents still provide signal.\n\nA is preferred to C because 3×3 patches produce 64 tokens, diluting object-level evidence through mean pooling and making the fixed 300-update budget less favorable, despite retaining fine detail. A is preferred to B because 12×12 patches yield only four very coarse tokens and frequently merge or poorly resolve the small objects, losing directional and boundary information. The main uncertainty is the absence of positional encoding: depending on how much relative-position signal is recoverable from patch-boundary effects and within-patch coordinates, C could approach or exceed A; nevertheless, B is most likely worst because of its coarse spatial discretization.", "model_identity_matches": true, "question_sha256": "7ed0219aec4b9051563488fa2c2790f13b55f7b44a251b85606dcfd34c3a502f", "prompt_sha256": "8b50362835072e3e6ec6df8405146d0f06e4026755e6cd55e1d5eeee9758fe64" }, { "model": "gpt-6.1-sol", "question_id": "q_8da922eda3a7c018f59492bcb3c32238", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_5aa7514c54a69ed6cf080475ebf4304e" }, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842901", "status": "complete", "gold_order": [ "C", "B", "A" ], "predicted_order": [ "C", "B", "A" ], "exact_order_correct": true, "public_content": "\nAll three models omit positional embeddings and average their output tokens, so they are invariant to patch-token permutations. Consequently, smaller patches do not automatically help: this task requires relative location, and the models must infer it from within-patch coordinates, object fragments, and channel co-occurrence.\n\n**C over B:** With 12×12 patches, each token captures a substantial part of the image and often both objects or informative fragments. Given the restricted object-center range, within-patch coordinates and boundary crossings provide useful spatial cues. The 6×6 patches discard more of the objects’ global arrangement when treated as an unordered set.\n\n**B over A:** The 6×6 patches retain more object-scale structure and relative-placement evidence than 3×3 patches. A produces 64 unordered local tokens; many arrangements have similar local content despite different labels, making the missing positional information particularly damaging.\n\nThe shared optimizer and 300-update budget reinforce the advantage of directly accessible spatial evidence. There is material uncertainty about the size of these gaps because fragment patterns can reveal some location indirectly, and learning those cues may vary across seeds.\n\n{\"best_to_worst\": [\"C\", \"B\", \"A\"]}", "public_explanation": "All three models omit positional embeddings and average their output tokens, so they are invariant to patch-token permutations. Consequently, smaller patches do not automatically help: this task requires relative location, and the models must infer it from within-patch coordinates, object fragments, and channel co-occurrence.\n\n**C over B:** With 12×12 patches, each token captures a substantial part of the image and often both objects or informative fragments. Given the restricted object-center range, within-patch coordinates and boundary crossings provide useful spatial cues. The 6×6 patches discard more of the objects’ global arrangement when treated as an unordered set.\n\n**B over A:** The 6×6 patches retain more object-scale structure and relative-placement evidence than 3×3 patches. A produces 64 unordered local tokens; many arrangements have similar local content despite different labels, making the missing positional information particularly damaging.\n\nThe shared optimizer and 300-update budget reinforce the advantage of directly accessible spatial evidence. There is material uncertainty about the size of these gaps because fragment patterns can reveal some location indirectly, and learning those cues may vary across seeds.", "model_identity_matches": true, "question_sha256": "0a08c68af53658c387e61079f81eb5be48c7c13909e4eb29ece0078e92e70391", "prompt_sha256": "bc802d4b5fa52f58451c3101a14cef4d8ee97309ddcf03e147976e005a8cba0d" }, { "model": "gpt-6.1-sol", "question_id": "q_76cac3671eecb9ff4306d1b86e28b45c", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842903", "status": "complete", "gold_order": [ "B", "C", "A" ], "predicted_order": [ "B", "C", "A" ], "exact_order_correct": true, "public_content": "The dominant issue is that the transformer has no positional embeddings, so its mean-pooled token representation is permutation-invariant over patches. Relative left/right/above/below labels are therefore difficult when the two objects fall in separate patches; the model can mainly use cases where both objects and their relative geometry are visible within a single patch. Choice B (12×12 patches) maximizes that opportunity and makes the relation easier to encode in one patch, so it is expected to have the lowest loss. Choice C (6×6 patches) preserves more spatial detail but splits the two objects across tokens more often, making their global ordering unavailable; it should therefore trail B. Choice A (3×3 patches) produces many localized tokens and most often separates the objects, leaving the permutation-invariant model near a weak ceiling, so it is expected to have the highest loss. The B-versus-C margin is materially uncertain because patch embedding capacity and the exact distribution of object placements could offset the co-location advantage, but the no-position limitation makes A the least favorable.\n{\"best_to_worst\":[\"B\",\"C\",\"A\"]}", "public_explanation": "The dominant issue is that the transformer has no positional embeddings, so its mean-pooled token representation is permutation-invariant over patches. Relative left/right/above/below labels are therefore difficult when the two objects fall in separate patches; the model can mainly use cases where both objects and their relative geometry are visible within a single patch. Choice B (12×12 patches) maximizes that opportunity and makes the relation easier to encode in one patch, so it is expected to have the lowest loss. Choice C (6×6 patches) preserves more spatial detail but splits the two objects across tokens more often, making their global ordering unavailable; it should therefore trail B. Choice A (3×3 patches) produces many localized tokens and most often separates the objects, leaving the permutation-invariant model near a weak ceiling, so it is expected to have the highest loss. The B-versus-C margin is materially uncertain because patch embedding capacity and the exact distribution of object placements could offset the co-location advantage, but the no-position limitation makes A the least favorable.", "model_identity_matches": true, "question_sha256": "6b4fa08d1969fd32b3dd6aa13fe9c2ee0d4666d4e7cbcf203da570a32971d052", "prompt_sha256": "13573df98c8675006a14f0c15c929b41bdcdcb74b326cf53f235898480a567dc" }, { "model": "gpt-6.1-sol", "question_id": "q_21ca0ff91a02c38e27e1bebe5867c24d", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_76cac3671eecb9ff4306d1b86e28b45c" }, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842903", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": true, "public_content": "\nThe key difference is patch size: C uses 12×12 patches, A uses 6×6, and B uses 3×3. All three omit positional embeddings and average token outputs, so their predictions are invariant to patch-token permutations. This limits recovery of the global spatial relation, but each patch projection still preserves information about positions *within* a patch.\n\n**C over A:** C’s larger patches capture more of each object and more joint circle–square geometry. With only four patches, and object centers constrained away from image edges, within-patch locations and boundary truncations also provide useful implicit spatial cues. A fragments these cues across more tokens without supplying their global positions.\n\n**A over B:** A’s patches retain larger object fragments and more local cross-channel relationships. B mostly sees small fragments whose unordered collection offers weak evidence for left/right/above/below, especially when the objects are separated. Attention cannot recover patch ordering that was never supplied.\n\nThe shared optimizer and 300-update budget do not remove these representational limitations. There is material uncertainty about how efficiently C learns its implicit spatial cues and how much A exploits overlap geometry, but the expected ordering favors larger patches here.\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "The key difference is patch size: C uses 12×12 patches, A uses 6×6, and B uses 3×3. All three omit positional embeddings and average token outputs, so their predictions are invariant to patch-token permutations. This limits recovery of the global spatial relation, but each patch projection still preserves information about positions *within* a patch.\n\n**C over A:** C’s larger patches capture more of each object and more joint circle–square geometry. With only four patches, and object centers constrained away from image edges, within-patch locations and boundary truncations also provide useful implicit spatial cues. A fragments these cues across more tokens without supplying their global positions.\n\n**A over B:** A’s patches retain larger object fragments and more local cross-channel relationships. B mostly sees small fragments whose unordered collection offers weak evidence for left/right/above/below, especially when the objects are separated. Attention cannot recover patch ordering that was never supplied.\n\nThe shared optimizer and 300-update budget do not remove these representational limitations. There is material uncertainty about how efficiently C learns its implicit spatial cues and how much A exploits overlap geometry, but the expected ordering favors larger patches here.", "model_identity_matches": true, "question_sha256": "1ed74fdb24c4279febc8cc25695345ccb4178c002376e9f1e11c40ce1a5ae945", "prompt_sha256": "1b542c782593bec4e9a3b63caea8a34c2f95b491fcda8e2027d39985b3b21047" }, { "model": "claude-opus-5-5", "question_id": "q_a9889bdd9a39a4c2caad00b528356fbd", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842901", "status": "complete", "gold_order": [ "A", "C", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": false, "public_content": "\n**Task.** In `relative_position`, the circle is in channel 0 and the square in channel 1. The label is the dominant-axis sign of their center displacement. Mass normalization makes each channel's total mass roughly constant, up to the 0.8–1.2 intensity factor. So the needed signals are roughly the per-channel x and y centroids, which are nearly linear functionals of the pixels, plus a |dx|-vs-|dy| comparison. Training is short: 75 AdamW steps at lr 1e-3, about 2.3 epochs over 1024 images.\n\n**C (CNN) is best.** A 1×1 stem and two residual 3×3 conv blocks produce per-pixel object features. The 3×3 spatial pooling grid then hands the linear head an explicit coarse map of where each channel's mass lies. Objects of radius 2.5–4.5 straddle the 8-pixel cells, so partial-volume effects add sub-cell position information. This location-preserving readout gives a strong prior and few parameters, so it should fit fast and generalize from 1024 samples.\n\n**C before A.** The residual MLP (A) can learn ramp-like centroid templates directly; the CE gradient on the stem is essentially class-averaged images. That makes it a reasonable learner. However, it must estimate about 110k stem weights from 1024 noisy images in 75 steps, so its templates will be noisier and its calibration worse than C's. That should give somewhat higher test cross-entropy.\n\n**A before B.** The patch transformer (B) mean-pools its tokens, so the only route to location is the learned position embeddings. These start at std 0.02 and can move only about 0.075 per coordinate in 75 Adam steps. Attention also has to learn to bind each channel's content to position before cross-token comparison helps. Within this budget it should stay near chance-level loss (about ln 4) or only modestly below it.\n\n**Uncertainty.** The C-vs-A order is the least certain. The MLP's near-linear access to centroids could match or beat the CNN, whose 3×3 pooling quantizes position, especially on close-separation cases. B being last is fairly confident.\n\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "**Task.** In `relative_position`, the circle is in channel 0 and the square in channel 1. The label is the dominant-axis sign of their center displacement. Mass normalization makes each channel's total mass roughly constant, up to the 0.8–1.2 intensity factor. So the needed signals are roughly the per-channel x and y centroids, which are nearly linear functionals of the pixels, plus a |dx|-vs-|dy| comparison. Training is short: 75 AdamW steps at lr 1e-3, about 2.3 epochs over 1024 images.\n\n**C (CNN) is best.** A 1×1 stem and two residual 3×3 conv blocks produce per-pixel object features. The 3×3 spatial pooling grid then hands the linear head an explicit coarse map of where each channel's mass lies. Objects of radius 2.5–4.5 straddle the 8-pixel cells, so partial-volume effects add sub-cell position information. This location-preserving readout gives a strong prior and few parameters, so it should fit fast and generalize from 1024 samples.\n\n**C before A.** The residual MLP (A) can learn ramp-like centroid templates directly; the CE gradient on the stem is essentially class-averaged images. That makes it a reasonable learner. However, it must estimate about 110k stem weights from 1024 noisy images in 75 steps, so its templates will be noisier and its calibration worse than C's. That should give somewhat higher test cross-entropy.\n\n**A before B.** The patch transformer (B) mean-pools its tokens, so the only route to location is the learned position embeddings. These start at std 0.02 and can move only about 0.075 per coordinate in 75 Adam steps. Attention also has to learn to bind each channel's content to position before cross-token comparison helps. Within this budget it should stay near chance-level loss (about ln 4) or only modestly below it.\n\n**Uncertainty.** The C-vs-A order is the least certain. The MLP's near-linear access to centroids could match or beat the CNN, whose 3×3 pooling quantizes position, especially on close-separation cases. B being last is fairly confident.", "model_identity_matches": true, "question_sha256": "d0c2b11985e3d2889f05611562f6d47b14afafeef088af0b5083eb72dfeb2bb1", "prompt_sha256": "fb3ce4370e766515d4851692e138003fc2a48d385264afe509bde9f56bfb1505" }, { "model": "claude-opus-5-5", "question_id": "q_018f733cbf575236fbf126db4322c484", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_a9889bdd9a39a4c2caad00b528356fbd" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842901", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "B", "A", "C" ], "exact_order_correct": true, "public_content": "\n**Task structure.** This is the `relative_position` task. Channel 0 holds a circle and channel 1 a square, and the label is the dominant axis and sign of the centroid displacement. Because `normalize_mass=True` fixes each channel's total mass, up to an intensity factor of 0.8–1.2, each object's centroid coordinate is close to a linear function of the raw pixels. The class is then a piecewise-linear comparison of dx and dy. The training budget is short: 75 AdamW steps at lr 1e-3, about 2.3 epochs.\n\n**B (MLP) is best.** The flattened 1152-dimensional input gives the stem direct, exact access to pixel coordinates. A single linear layer can already approximate x and y centroid differences, and two residual GELU blocks can form the |dx| vs |dy| comparison. With about 120k parameters and Adam, it should fit quickly and calibrate reasonably within 75 steps.\n\n**A (CNN) is second.** Its stem is a 1×1 conv, followed by two 3×3 residual conv blocks, giving a receptive field of about 5 pixels. It then average-pools to a 3×3 grid of roughly 8×8-pixel cells. Positional information survives only as which coarse cell each channel's mass lands in, plus weak within-cell cues. Close or near-diagonal pairs therefore become ambiguous, which raises cross-entropy. The model is also small (width 24), so it learns more slowly per step. Even so, the spatial grid preserves explicit coarse layout, which is better than having to learn positions from scratch.\n\n**C (patch transformer) is worst.** It uses 4×4 patches (36 tokens), width 32, and mean-pools tokens before the head. Pooling destroys location unless the learned position embeddings, initialised at std 0.02 and therefore very weak, are trained to carry it. Attention must then compare the circle and square tokens' positions. Learning that relational, position-dependent computation in 75 steps from 1024 samples is hard, so loss likely stays near chance-level calibration longer.\n\n**Uncertainty.** The A vs B order is the least certain. The CNN's grid prior could let it beat an MLP that overfits or is miscalibrated, and intensity variation adds noise to the MLP's linear centroid readout. C being last is fairly confident.\n\n\n{\"best_to_worst\": [\"B\", \"A\", \"C\"]}", "public_explanation": "**Task structure.** This is the `relative_position` task. Channel 0 holds a circle and channel 1 a square, and the label is the dominant axis and sign of the centroid displacement. Because `normalize_mass=True` fixes each channel's total mass, up to an intensity factor of 0.8–1.2, each object's centroid coordinate is close to a linear function of the raw pixels. The class is then a piecewise-linear comparison of dx and dy. The training budget is short: 75 AdamW steps at lr 1e-3, about 2.3 epochs.\n\n**B (MLP) is best.** The flattened 1152-dimensional input gives the stem direct, exact access to pixel coordinates. A single linear layer can already approximate x and y centroid differences, and two residual GELU blocks can form the |dx| vs |dy| comparison. With about 120k parameters and Adam, it should fit quickly and calibrate reasonably within 75 steps.\n\n**A (CNN) is second.** Its stem is a 1×1 conv, followed by two 3×3 residual conv blocks, giving a receptive field of about 5 pixels. It then average-pools to a 3×3 grid of roughly 8×8-pixel cells. Positional information survives only as which coarse cell each channel's mass lands in, plus weak within-cell cues. Close or near-diagonal pairs therefore become ambiguous, which raises cross-entropy. The model is also small (width 24), so it learns more slowly per step. Even so, the spatial grid preserves explicit coarse layout, which is better than having to learn positions from scratch.\n\n**C (patch transformer) is worst.** It uses 4×4 patches (36 tokens), width 32, and mean-pools tokens before the head. Pooling destroys location unless the learned position embeddings, initialised at std 0.02 and therefore very weak, are trained to carry it. Attention must then compare the circle and square tokens' positions. Learning that relational, position-dependent computation in 75 steps from 1024 samples is hard, so loss likely stays near chance-level calibration longer.\n\n**Uncertainty.** The A vs B order is the least certain. The CNN's grid prior could let it beat an MLP that overfits or is miscalibrated, and intensity variation adds noise to the MLP's linear centroid readout. C being last is fairly confident.", "model_identity_matches": true, "question_sha256": "f1514b66e6151b6fceb6c4ae7168a41c6db186b9f7b42705569e764895c29113", "prompt_sha256": "7a0b3cc83d8eadcb682c289dc3eec30a046941fa0bb276ff0956c7875beefb09" }, { "model": "claude-opus-5-5", "question_id": "q_f41ad89255f54a110a6b78ac32e08910", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842902", "status": "complete", "gold_order": [ "A", "B", "C" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": true, "public_content": "\n**Task demands.** The task is `relative_position`. The label depends on the displacement between the channel‑0 circle and the channel‑1 square: first which axis dominates (|dx| > |dy|), then the sign along that axis. `normalize_mass` fixes each channel's total mass, apart from a 0.8–1.2 intensity factor. That makes per‑channel centroids almost linear functions of the pixels, so the ranking turns on how easily each model can reach a centroid‑like signal and compare the two objects in only 75 Adam steps.\n\n**A (MLP, best).** The flattened 1152→96 linear stem can directly learn coordinate‑weighted projections of each channel, which approximate dx and dy. Two residual GELU blocks then supply the nonlinearity needed for the dominant‑axis comparison. Dense gradients reach every stem weight from step 1, so a fit within 75 steps is plausible.\n\n**B (CNN), between A and C.**\n- The 3×3 convolutions with two blocks give only a small receptive field. The two objects are separated by at least about 3 px along the dominant axis, and often far more, so they are processed almost independently.\n- Spatial pooling to a 3×3 grid (8×8‑pixel cells), followed by a *linear* head, makes the logits roughly additive: g(circle location) + h(square location), quantized to cell resolution.\n- That structure can express the sign of the difference along an axis, but it cannot properly express the |dx| vs |dy| interaction. Near‑diagonal and same‑cell cases stay ambiguous.\n- LayerNorm keeps optimization stable, so it should still learn a meaningful partial solution. I expect it to beat C but trail A.\n\n**A vs B.** Both models must handle the dominant‑axis comparison. A's linear stem preserves fine positional information and its nonlinear blocks can combine the two objects. B loses within‑cell resolution and combines the objects only additively, so A should reach lower cross‑entropy.\n\n**C (patch transformer, worst).** The 4×4 patches give 36 tokens. The learned position embeddings start very small (std 0.02), and mean pooling discards token order unless positions have been absorbed into the content. Positional reasoning therefore has to emerge through attention and position embeddings that are still near their initial values. Small ViTs are known to learn slowly in short budgets, and 75 steps is likely too few, leaving cross‑entropy close to chance.\n\n**B vs C.** The CNN gets position information explicitly from the fixed pooling grid. The transformer has to learn it through near‑zero embeddings within 75 steps, so B should end with lower loss.\n\n**Uncertainty.** A vs B is the least certain pair. The CNN's normalized blocks might optimize faster than expected, and the MLP's 1152‑dimensional stem could fit noisily at lr 1e‑3. The C‑last placement is more confident.\n\n\n{\"best_to_worst\": [\"A\", \"B\", \"C\"]}", "public_explanation": "**Task demands.** The task is `relative_position`. The label depends on the displacement between the channel‑0 circle and the channel‑1 square: first which axis dominates (|dx| > |dy|), then the sign along that axis. `normalize_mass` fixes each channel's total mass, apart from a 0.8–1.2 intensity factor. That makes per‑channel centroids almost linear functions of the pixels, so the ranking turns on how easily each model can reach a centroid‑like signal and compare the two objects in only 75 Adam steps.\n\n**A (MLP, best).** The flattened 1152→96 linear stem can directly learn coordinate‑weighted projections of each channel, which approximate dx and dy. Two residual GELU blocks then supply the nonlinearity needed for the dominant‑axis comparison. Dense gradients reach every stem weight from step 1, so a fit within 75 steps is plausible.\n\n**B (CNN), between A and C.**\n- The 3×3 convolutions with two blocks give only a small receptive field. The two objects are separated by at least about 3 px along the dominant axis, and often far more, so they are processed almost independently.\n- Spatial pooling to a 3×3 grid (8×8‑pixel cells), followed by a *linear* head, makes the logits roughly additive: g(circle location) + h(square location), quantized to cell resolution.\n- That structure can express the sign of the difference along an axis, but it cannot properly express the |dx| vs |dy| interaction. Near‑diagonal and same‑cell cases stay ambiguous.\n- LayerNorm keeps optimization stable, so it should still learn a meaningful partial solution. I expect it to beat C but trail A.\n\n**A vs B.** Both models must handle the dominant‑axis comparison. A's linear stem preserves fine positional information and its nonlinear blocks can combine the two objects. B loses within‑cell resolution and combines the objects only additively, so A should reach lower cross‑entropy.\n\n**C (patch transformer, worst).** The 4×4 patches give 36 tokens. The learned position embeddings start very small (std 0.02), and mean pooling discards token order unless positions have been absorbed into the content. Positional reasoning therefore has to emerge through attention and position embeddings that are still near their initial values. Small ViTs are known to learn slowly in short budgets, and 75 steps is likely too few, leaving cross‑entropy close to chance.\n\n**B vs C.** The CNN gets position information explicitly from the fixed pooling grid. The transformer has to learn it through near‑zero embeddings within 75 steps, so B should end with lower loss.\n\n**Uncertainty.** A vs B is the least certain pair. The CNN's normalized blocks might optimize faster than expected, and the MLP's 1152‑dimensional stem could fit noisily at lr 1e‑3. The C‑last placement is more confident.", "model_identity_matches": true, "question_sha256": "265fcd17cb23554b617a57bfea7cb952934d1a4204aa69ba0b68f92abe28b48d", "prompt_sha256": "27654c0d84bd94e35c93f05379ff7f90c78d826947c7456eb743d2f2d16ebd40" }, { "model": "claude-opus-5-5", "question_id": "q_f2e0f5463396043d48d5c5ae87bedb87", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_f41ad89255f54a110a6b78ac32e08910" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842902", "status": "complete", "gold_order": [ "B", "C", "A" ], "predicted_order": [ "B", "C", "A" ], "exact_order_correct": true, "public_content": "\n**Task.** The label is the dominant-axis sign of the displacement between the circle's centre (channel 0) and the square's centre (channel 1). Mass normalisation keeps each channel's total mass roughly fixed, up to the 0.8–1.2 intensity multiplier. As a result, each object's centroid is close to a linear function of its pixels. Precise absolute-position information is the key feature, and the budget is short: 75 AdamW updates at lr 1e-3.\n\n**B (MLP) — predicted best.** The flat 1152→96 stem can directly express centroid-like linear projections for both channels. The residual GELU blocks then supply the nonlinearity needed for the |dx| vs |dy| comparison. This gives the most direct inductive match to the target and fast learning under Adam.\n\n**C (CNN) — predicted middle, below B.**\n- The stem is a 1×1 convolution and the two 3×3 blocks give only a 5×5 receptive field.\n- There are no coordinate channels.\n- Position reaches the head only through a 3×3 grid of 8×8 average-pooled cells. Sub-cell position is mostly lost in the averaging.\n- Some test pairs are separated by only about 3 px or have near-tied axes, so coarse cell information leaves residual confusion and higher cross-entropy than B.\n\n**A (patch transformer) — predicted worst, below C.**\n- Mean-pooling over tokens is permutation-invariant, so all position information must come from the learned position embeddings.\n- Those embeddings start at a 0.02 scale, and 75 steps are little time to grow them and learn the relational attention.\n- 4×4 patches also lose fine location within each patch.\n\n**Uncertainty.** Moderate. The B vs C gap is the least certain: the CNN's locality prior might learn faster than the MLP's 1152-dimensional dense stem with only 1024 training images. A finishing last is fairly confident.\n\n\n{\"best_to_worst\": [\"B\", \"C\", \"A\"]}", "public_explanation": "**Task.** The label is the dominant-axis sign of the displacement between the circle's centre (channel 0) and the square's centre (channel 1). Mass normalisation keeps each channel's total mass roughly fixed, up to the 0.8–1.2 intensity multiplier. As a result, each object's centroid is close to a linear function of its pixels. Precise absolute-position information is the key feature, and the budget is short: 75 AdamW updates at lr 1e-3.\n\n**B (MLP) — predicted best.** The flat 1152→96 stem can directly express centroid-like linear projections for both channels. The residual GELU blocks then supply the nonlinearity needed for the |dx| vs |dy| comparison. This gives the most direct inductive match to the target and fast learning under Adam.\n\n**C (CNN) — predicted middle, below B.**\n- The stem is a 1×1 convolution and the two 3×3 blocks give only a 5×5 receptive field.\n- There are no coordinate channels.\n- Position reaches the head only through a 3×3 grid of 8×8 average-pooled cells. Sub-cell position is mostly lost in the averaging.\n- Some test pairs are separated by only about 3 px or have near-tied axes, so coarse cell information leaves residual confusion and higher cross-entropy than B.\n\n**A (patch transformer) — predicted worst, below C.**\n- Mean-pooling over tokens is permutation-invariant, so all position information must come from the learned position embeddings.\n- Those embeddings start at a 0.02 scale, and 75 steps are little time to grow them and learn the relational attention.\n- 4×4 patches also lose fine location within each patch.\n\n**Uncertainty.** Moderate. The B vs C gap is the least certain: the CNN's locality prior might learn faster than the MLP's 1152-dimensional dense stem with only 1024 training images. A finishing last is fairly confident.", "model_identity_matches": true, "question_sha256": "e8c9cf5b5d874f791085a890e2df4b314527ca6f54efdedd47e4e42e9793bdb2", "prompt_sha256": "e5c9cd2df44039e83c370a64520fe53e9a14641a19cfcba002fbe51ef82e7bc4" }, { "model": "claude-opus-5-5", "question_id": "q_2e828a18000b8cfc54065a359bf0ab04", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842903", "status": "complete", "gold_order": [ "A", "C", "B" ], "predicted_order": [ "A", "C", "B" ], "exact_order_correct": true, "public_content": "\n**Task structure.** This is `relative_position`. Channel 0 holds a circle and channel 1 a square. Both are mass-normalized, so each channel's pixel sum is about 23 times an intensity factor in [0.8, 1.2]. The label is the argmax of (−dx, dx, −dy, dy), where dx and dy are the center displacement between the two objects. That rule is exactly an argmax over linear functions of the two objects' centroid differences. Centroids are close to linear in the pixels, scaled mildly by intensity. So a model with precise, direct access to absolute pixel positions can nearly solve the task with an almost-linear readout. The constraints are small: 75 updates on 1024 training images, AdamW at lr 1e-3.\n\n**A (MLP, best).** The flattened 1152→96 linear stem has direct access to every pixel's absolute position. It can learn x- and y-weighted sums per channel, and the residual GELU blocks plus the head can form the argmax comparison. Optimization is simple: no normalization interplay, and Adam moves each weight directly. A shortcut this close to linear should be learned within 75 steps, giving well-calibrated logits and the lowest cross entropy. The risk is overfitting on 1024 images, but at 2400 samples seen that is limited.\n\n**C (CNN, middle).** The stem is a 1×1 conv, followed by two 3×3 residual blocks, so the receptive field is about 5 pixels. A 3×3 spatial mean-pool grid (8×8 cells) feeds the linear head. Absolute position reaches the head only through which cell holds an object's mass, plus partial sub-cell information when an object straddles cells. That resolution is coarse compared with the required margins: at least 2.9 px on the dominant axis and an axis gap of at least 1.5 px. Borderline cases will therefore stay uncertain, keeping cross entropy above A's. The CNN is still learnable quickly and gets the coarse layout right.\n\n**B (patch transformer, worst).** It uses 4×4 patches (36 tokens) at width 32 with mean pooling. Position comes only from learned embeddings initialized at scale 0.02, and mean pooling throws away token identity. To solve the task, attention has to learn to relate each object's token position to the other's. That is a slow-to-emerge mechanism, and 75 steps is unlikely to be enough, so the model probably stays near chance-level cross entropy for longer.\n\n**Uncertainty.** The A vs C order is the least certain. The CNN's locality bias plus the grid pooling might fit faster than the MLP's 1152-dimensional stem on only 1024 images. B being last is fairly confident.\n\n\n{\"best_to_worst\": [\"A\", \"C\", \"B\"]}", "public_explanation": "**Task structure.** This is `relative_position`. Channel 0 holds a circle and channel 1 a square. Both are mass-normalized, so each channel's pixel sum is about 23 times an intensity factor in [0.8, 1.2]. The label is the argmax of (−dx, dx, −dy, dy), where dx and dy are the center displacement between the two objects. That rule is exactly an argmax over linear functions of the two objects' centroid differences. Centroids are close to linear in the pixels, scaled mildly by intensity. So a model with precise, direct access to absolute pixel positions can nearly solve the task with an almost-linear readout. The constraints are small: 75 updates on 1024 training images, AdamW at lr 1e-3.\n\n**A (MLP, best).** The flattened 1152→96 linear stem has direct access to every pixel's absolute position. It can learn x- and y-weighted sums per channel, and the residual GELU blocks plus the head can form the argmax comparison. Optimization is simple: no normalization interplay, and Adam moves each weight directly. A shortcut this close to linear should be learned within 75 steps, giving well-calibrated logits and the lowest cross entropy. The risk is overfitting on 1024 images, but at 2400 samples seen that is limited.\n\n**C (CNN, middle).** The stem is a 1×1 conv, followed by two 3×3 residual blocks, so the receptive field is about 5 pixels. A 3×3 spatial mean-pool grid (8×8 cells) feeds the linear head. Absolute position reaches the head only through which cell holds an object's mass, plus partial sub-cell information when an object straddles cells. That resolution is coarse compared with the required margins: at least 2.9 px on the dominant axis and an axis gap of at least 1.5 px. Borderline cases will therefore stay uncertain, keeping cross entropy above A's. The CNN is still learnable quickly and gets the coarse layout right.\n\n**B (patch transformer, worst).** It uses 4×4 patches (36 tokens) at width 32 with mean pooling. Position comes only from learned embeddings initialized at scale 0.02, and mean pooling throws away token identity. To solve the task, attention has to learn to relate each object's token position to the other's. That is a slow-to-emerge mechanism, and 75 steps is unlikely to be enough, so the model probably stays near chance-level cross entropy for longer.\n\n**Uncertainty.** The A vs C order is the least certain. The CNN's locality bias plus the grid pooling might fit faster than the MLP's 1152-dimensional stem on only 1024 images. B being last is fairly confident.", "model_identity_matches": true, "question_sha256": "a85d544f1c1d558a23b44ad1d97799e53d5321cee414365edda17ec6a862c69b", "prompt_sha256": "d9deece1f02ae57e194f40a57e3c91838fb98334d728674af4ebce39b043ea0f" }, { "model": "claude-opus-5-5", "question_id": "q_89d77cd38238c082c9114a0773e6b261", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_2e828a18000b8cfc54065a359bf0ab04" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842903", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "B", "A", "C" ], "exact_order_correct": true, "public_content": "\n**Task structure.** In `relative_position`, channel 0 holds the circle and channel 1 holds the square. Each channel is mass-normalized, so its total is about 23 × intensity. That makes each object's centroid roughly a linear function of the raw pixels. Logits proportional to (−dx, dx, −dy, dy), where dx and dy are the circle-minus-square centroid differences, reproduce the \"dominant axis\" label rule exactly through argmax. A model that keeps full-resolution absolute position information and can compute near-linear pixel functionals therefore has an easy path to low cross entropy. With only 75 Adam steps, how quickly that path is found dominates the ranking.\n\n**B (MLP, best).** The 1152→96 linear stem with residual GELU blocks can directly represent the centroid-difference solution at pixel resolution. Adam at lr 1e-3 will align the stem with these smooth position gradients within tens of steps. Overfitting is a mild risk (1152 inputs, 1024 training images), but it is limited at this budget.\n\n**A (CNN, middle).** The CNN uses a 1×1 stem, two 3×3 residual conv blocks and 3×3 grid average pooling into a linear head. It keeps absolute position only through the coarse 8×8-pixel pooling cells. It can recover centroids from cell masses only crudely, unless the convs learn intra-cell position cues, which is hard because they are translation-equivariant. Class boundaries near diagonals (margin only 1.5 px) and short separations (≥2.88 px) will often fall within one cell. So it should be less confident and less accurate than the MLP, though better than the transformer.\n\n**C (patch transformer, worst).** The patch transformer mean-pools tokens. Position enters only through learned embeddings initialized at scale 0.02, so the model must first learn useful positional codes and then attention patterns that relate the two channels' locations. That is unlikely to converge in 75 steps at width 32, which leaves its loss closest to chance (about ln 4).\n\n**Uncertainty.** The B-vs-A gap carries the most uncertainty. The CNN's inductive bias could still learn reasonably fast, and the MLP could become overconfident on a few test images. C being last is fairly confident.\n\n\n{\"best_to_worst\": [\"B\", \"A\", \"C\"]}", "public_explanation": "**Task structure.** In `relative_position`, channel 0 holds the circle and channel 1 holds the square. Each channel is mass-normalized, so its total is about 23 × intensity. That makes each object's centroid roughly a linear function of the raw pixels. Logits proportional to (−dx, dx, −dy, dy), where dx and dy are the circle-minus-square centroid differences, reproduce the \"dominant axis\" label rule exactly through argmax. A model that keeps full-resolution absolute position information and can compute near-linear pixel functionals therefore has an easy path to low cross entropy. With only 75 Adam steps, how quickly that path is found dominates the ranking.\n\n**B (MLP, best).** The 1152→96 linear stem with residual GELU blocks can directly represent the centroid-difference solution at pixel resolution. Adam at lr 1e-3 will align the stem with these smooth position gradients within tens of steps. Overfitting is a mild risk (1152 inputs, 1024 training images), but it is limited at this budget.\n\n**A (CNN, middle).** The CNN uses a 1×1 stem, two 3×3 residual conv blocks and 3×3 grid average pooling into a linear head. It keeps absolute position only through the coarse 8×8-pixel pooling cells. It can recover centroids from cell masses only crudely, unless the convs learn intra-cell position cues, which is hard because they are translation-equivariant. Class boundaries near diagonals (margin only 1.5 px) and short separations (≥2.88 px) will often fall within one cell. So it should be less confident and less accurate than the MLP, though better than the transformer.\n\n**C (patch transformer, worst).** The patch transformer mean-pools tokens. Position enters only through learned embeddings initialized at scale 0.02, so the model must first learn useful positional codes and then attention patterns that relate the two channels' locations. That is unlikely to converge in 75 steps at width 32, which leaves its loss closest to chance (about ln 4).\n\n**Uncertainty.** The B-vs-A gap carries the most uncertainty. The CNN's inductive bias could still learn reasonably fast, and the MLP could become overconfident on a few test images. C being last is fairly confident.", "model_identity_matches": true, "question_sha256": "d7dca61949875a1cc3a4ea263e4e25148cb28e78133670ad99f56c761fa03571", "prompt_sha256": "893c63de1a94330af3befe0d4eb57e55c62e5a02cb08401764eb53805ea532ed" }, { "model": "claude-opus-5-5", "question_id": "q_04b93ce5a8d08dcf6f6328205dd254ad", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842901", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": true, "public_content": "\n**Task.** The dataset is `local_shape`. The label is the shape of the small channel-0 object (circle, square, diamond or cross). The object has radius 2.5–4.5 px and is placed at a random position in a 24×24 image. Mass normalization ties pixel intensity to area, but radius varies by 1.8×, so intensity alone is ambiguous. With only 1024 training images and about 37 epochs, the deciding factor is inductive bias, chiefly translation equivariance and locality. Overfitting is the main risk for test cross-entropy.\n\n**C (CNN) is best.**\n- It uses a 1×1 stem and two residual 3×3 conv blocks. That gives a 5×5 receptive field at full 24×24 resolution, enough to detect local edge and corner signatures: straight axis-aligned edges, diagonal edges, arcs, and the cross's concave corners.\n- The weight-shared detectors are pooled over a 3×3 grid, so the model is close to translation-invariant and uses parameters efficiently. That suits randomly placed shapes and a small dataset.\n- Its lr of 3e-3 with AdamW and gradient clipping is reasonable for a small convnet with LayerNorm. It should reach low training loss and generalize well.\n\n**A (patch transformer) is second.**\n- The 4×4 patch embedding is shared across positions, which gives some translation structure.\n- However, shapes 5–9 px wide fall across patch boundaries at arbitrary offsets. The model must learn shape from cross-patch attention with learned position embeddings, using only 1024 samples.\n- ViTs are data-hungry and tend to become overconfident on errors over many epochs, which inflates cross-entropy. It should still clearly beat a flat MLP.\n\n**B (MLP) is worst.**\n- It has a dense 1152→96 stem with no weight sharing, so it must learn each shape separately at every position.\n- With 1024 samples it will memorize the training set and generalize poorly. Its overconfident wrong predictions will drive test cross-entropy highest.\n\n**Uncertainty.** The A vs C gap is fairly confident. A vs B is less certain: a small ViT can overfit badly, but its shared patch embedding should still give it the edge over the MLP.\n\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "**Task.** The dataset is `local_shape`. The label is the shape of the small channel-0 object (circle, square, diamond or cross). The object has radius 2.5–4.5 px and is placed at a random position in a 24×24 image. Mass normalization ties pixel intensity to area, but radius varies by 1.8×, so intensity alone is ambiguous. With only 1024 training images and about 37 epochs, the deciding factor is inductive bias, chiefly translation equivariance and locality. Overfitting is the main risk for test cross-entropy.\n\n**C (CNN) is best.**\n- It uses a 1×1 stem and two residual 3×3 conv blocks. That gives a 5×5 receptive field at full 24×24 resolution, enough to detect local edge and corner signatures: straight axis-aligned edges, diagonal edges, arcs, and the cross's concave corners.\n- The weight-shared detectors are pooled over a 3×3 grid, so the model is close to translation-invariant and uses parameters efficiently. That suits randomly placed shapes and a small dataset.\n- Its lr of 3e-3 with AdamW and gradient clipping is reasonable for a small convnet with LayerNorm. It should reach low training loss and generalize well.\n\n**A (patch transformer) is second.**\n- The 4×4 patch embedding is shared across positions, which gives some translation structure.\n- However, shapes 5–9 px wide fall across patch boundaries at arbitrary offsets. The model must learn shape from cross-patch attention with learned position embeddings, using only 1024 samples.\n- ViTs are data-hungry and tend to become overconfident on errors over many epochs, which inflates cross-entropy. It should still clearly beat a flat MLP.\n\n**B (MLP) is worst.**\n- It has a dense 1152→96 stem with no weight sharing, so it must learn each shape separately at every position.\n- With 1024 samples it will memorize the training set and generalize poorly. Its overconfident wrong predictions will drive test cross-entropy highest.\n\n**Uncertainty.** The A vs C gap is fairly confident. A vs B is less certain: a small ViT can overfit badly, but its shared patch embedding should still give it the edge over the MLP.", "model_identity_matches": true, "question_sha256": "92a98eeec0d06b019e8e528487e1be9abc7074c7351968ae6fddb148646f2742", "prompt_sha256": "4a697beb14e725ce09fc114c5c0d23c756edb26da299573d36cdd87224e4a29c" }, { "model": "claude-opus-5-5", "question_id": "q_7945972839e5ef8403e9a2edfb6ae39f", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_04b93ce5a8d08dcf6f6328205dd254ad" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842901", "status": "complete", "gold_order": [ "A", "B", "C" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": true, "public_content": "\n**Task and main factors.** With `task='local_shape'`, the label is the shape in channel 0: circle, square, diamond or cross. The shape has radius 2.5–4.5 and a random position within roughly the central 44% of a 24×24 image. Channel 1 is an independent distractor. Mass normalization ties per-pixel intensity to shape area, but radius varies, so that cue is confounded. The model has to read local boundary geometry (straight vs. diagonal vs. curved edges, concave corners) wherever the object lands. There are only 1024 training images, seen for about 37 epochs (1200 steps × 32). So translation-equivariant inductive bias and resistance to overfitting dominate the outcome. Overfitting also inflates held-out cross entropy through overconfident errors.\n\n**A (CNN), best.** It uses a 1×1 stem and two residual blocks with dense 3×3 convolutions at full 24×24 resolution, giving a 5×5 receptive field. That is enough to detect edge orientation, corners and curvature, which are the discriminative features. The 3×3 spatial pooling grid then aggregates them with only mild position dependence. Weight sharing makes it sample-efficient on 1024 images. The higher learning rate (3e-3) with AdamW, gradient clipping and LayerNorm should be stable for such a small network.\n\n**B (patch transformer), middle.** It uses 4×4 patches, giving 36 tokens with learned positions, at width 32 and depth 2. The patch embedding is shared across positions, so it has some translation structure. However, shapes straddle patch boundaries at arbitrary offsets, and attention has to learn spatial composition from little data. ViTs are known to be data-hungry, so I expect worse generalization and calibration than the CNN, but a clear edge over the MLP.\n\n**C (MLP), worst.** It flattens the 1152 input pixels into width 96, about 110k stem parameters, with no spatial prior. It must learn each shape at each position separately from about 256 examples per class. It will memorize the training set, and its held-out cross entropy will likely grow with overconfident wrong predictions.\n\n**Uncertainty.** The B vs. C gap is fairly confident. A vs. B carries some uncertainty: the CNN at lr 3e-3 could end overconfident with a final checkpoint after constant-LR training. Still, its inductive bias advantage on this local-shape task should dominate.\n\n\n{\"best_to_worst\": [\"A\", \"B\", \"C\"]}", "public_explanation": "**Task and main factors.** With `task='local_shape'`, the label is the shape in channel 0: circle, square, diamond or cross. The shape has radius 2.5–4.5 and a random position within roughly the central 44% of a 24×24 image. Channel 1 is an independent distractor. Mass normalization ties per-pixel intensity to shape area, but radius varies, so that cue is confounded. The model has to read local boundary geometry (straight vs. diagonal vs. curved edges, concave corners) wherever the object lands. There are only 1024 training images, seen for about 37 epochs (1200 steps × 32). So translation-equivariant inductive bias and resistance to overfitting dominate the outcome. Overfitting also inflates held-out cross entropy through overconfident errors.\n\n**A (CNN), best.** It uses a 1×1 stem and two residual blocks with dense 3×3 convolutions at full 24×24 resolution, giving a 5×5 receptive field. That is enough to detect edge orientation, corners and curvature, which are the discriminative features. The 3×3 spatial pooling grid then aggregates them with only mild position dependence. Weight sharing makes it sample-efficient on 1024 images. The higher learning rate (3e-3) with AdamW, gradient clipping and LayerNorm should be stable for such a small network.\n\n**B (patch transformer), middle.** It uses 4×4 patches, giving 36 tokens with learned positions, at width 32 and depth 2. The patch embedding is shared across positions, so it has some translation structure. However, shapes straddle patch boundaries at arbitrary offsets, and attention has to learn spatial composition from little data. ViTs are known to be data-hungry, so I expect worse generalization and calibration than the CNN, but a clear edge over the MLP.\n\n**C (MLP), worst.** It flattens the 1152 input pixels into width 96, about 110k stem parameters, with no spatial prior. It must learn each shape at each position separately from about 256 examples per class. It will memorize the training set, and its held-out cross entropy will likely grow with overconfident wrong predictions.\n\n**Uncertainty.** The B vs. C gap is fairly confident. A vs. B carries some uncertainty: the CNN at lr 3e-3 could end overconfident with a final checkpoint after constant-LR training. Still, its inductive bias advantage on this local-shape task should dominate.", "model_identity_matches": true, "question_sha256": "d469dca0be63dbd5af5b14a5cb27765ad59e93f694ca465bc9fdff7e6d3ba2cd", "prompt_sha256": "77c0870d6e36da370eeda582e896d1f06b35aec1588122ebcef3937c2052cb83" }, { "model": "claude-opus-5-5", "question_id": "q_dc6a1198c1d2e494edd7b3618c36bf0b", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842902", "status": "complete", "gold_order": [ "B", "C", "A" ], "predicted_order": [ "B", "C", "A" ], "exact_order_correct": true, "public_content": "\n**Task.** With `task='local_shape'`, the label is the shape in channel 0: circle, square, diamond or cross. The radius is 2.5–4.5 px and the shape sits at a random position in a 24×24 image. Channel 1 is a distractor. There are only 1024 training images, and 1200 steps × 32 gives about 37 epochs. So translation invariance and local edge and corner features are what matter most. Overfitting will inflate the final-checkpoint cross entropy.\n\n**B (CNN) is best.** It has a 1×1 stem followed by two pre-norm residual blocks with dense 3×3 convolutions. These detect edge orientation and corner type (axis-aligned vs diagonal edges, curvature, concave cross corners), which is exactly what separates the classes. The detectors are shared across positions, so they work wherever the shape lands. The 3×3 spatial pool and linear head aggregate these features. The model is small, and lr 3e-3 with clipping is a reasonable setting for it. It should reach low test CE.\n\n**B beats C.** C is a patch transformer with 4×4 patches. The patch grid aligns with each shape differently from image to image, and the shapes are only about 5–9 px across, so each one spans a few patches. The model must learn shape from linear patch embeddings plus attention, using just 1024 samples. ViT-style models have weaker inductive bias in this low-data regime and usually train less cleanly than a convolutional network. That means higher cross entropy, often with overconfident errors.\n\n**C beats A.** C still shares the patch embedding across locations and mean-pools its tokens, which gives partial translation invariance. A is a flat MLP on 1152 raw pixels and has no translation invariance. It has to memorize shape-at-position templates from 1024 examples. It will fit the training set and generalize poorly. Its overconfident mistakes should give the highest test cross entropy.\n\n**Uncertainty.** The C vs A gap is the less certain one. A small ViT can also overfit badly, and the MLP benefits from mass normalization. Still, the MLP's lack of any spatial sharing should hurt more. B being first is fairly confident.\n\n\n{\"best_to_worst\": [\"B\", \"C\", \"A\"]}", "public_explanation": "**Task.** With `task='local_shape'`, the label is the shape in channel 0: circle, square, diamond or cross. The radius is 2.5–4.5 px and the shape sits at a random position in a 24×24 image. Channel 1 is a distractor. There are only 1024 training images, and 1200 steps × 32 gives about 37 epochs. So translation invariance and local edge and corner features are what matter most. Overfitting will inflate the final-checkpoint cross entropy.\n\n**B (CNN) is best.** It has a 1×1 stem followed by two pre-norm residual blocks with dense 3×3 convolutions. These detect edge orientation and corner type (axis-aligned vs diagonal edges, curvature, concave cross corners), which is exactly what separates the classes. The detectors are shared across positions, so they work wherever the shape lands. The 3×3 spatial pool and linear head aggregate these features. The model is small, and lr 3e-3 with clipping is a reasonable setting for it. It should reach low test CE.\n\n**B beats C.** C is a patch transformer with 4×4 patches. The patch grid aligns with each shape differently from image to image, and the shapes are only about 5–9 px across, so each one spans a few patches. The model must learn shape from linear patch embeddings plus attention, using just 1024 samples. ViT-style models have weaker inductive bias in this low-data regime and usually train less cleanly than a convolutional network. That means higher cross entropy, often with overconfident errors.\n\n**C beats A.** C still shares the patch embedding across locations and mean-pools its tokens, which gives partial translation invariance. A is a flat MLP on 1152 raw pixels and has no translation invariance. It has to memorize shape-at-position templates from 1024 examples. It will fit the training set and generalize poorly. Its overconfident mistakes should give the highest test cross entropy.\n\n**Uncertainty.** The C vs A gap is the less certain one. A small ViT can also overfit badly, and the MLP benefits from mass normalization. Still, the MLP's lack of any spatial sharing should hurt more. B being first is fairly confident.", "model_identity_matches": true, "question_sha256": "d3b698eb2cbd3c0339d6fafe28333df4794a1062bfa8887fa1a3e7ba8ab27849", "prompt_sha256": "a7df13a151777eba77efe2a89ce0ae8420134f2cb76f07f44143945ea5a0322e" }, { "model": "claude-opus-5-5", "question_id": "q_f2d7051e84a8d64012dfaf4f428f50e8", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_dc6a1198c1d2e494edd7b3618c36bf0b" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842902", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": true, "public_content": "\n**Task.** This is `local_shape`. The class is the shape in channel 0: circle, square, diamond or cross. The radius is 2.5–4.5 px, the shape sits at a random position within roughly [6.7, 16.9] px, and mass is normalized, so total intensity carries little class information. Classification depends on local boundary geometry: corners, straight versus curved edges, and the cross's arms. Those cues must be recognized regardless of position. There are only 1024 training images, seen about 37 times each over 1200 steps × 32. The metric is test cross entropy, so overconfident overfitting is penalized.\n\n**C (CNN) – best.** The stride-1 1×1 stem plus two 3×3 conv blocks give a translation-equivariant, LayerNorm'd, residual feature extractor. Its 5×5 receptive field detects edges, corners and curvature, which is what separates these shapes. The 3×3 spatial average pool keeps some layout while being largely shift-tolerant. The parameter count is small, so it generalizes well from 1024 samples. lr 3e-3 with AdamW is reasonable for a normalized small CNN, and gradient clipping guards stability.\n\n**C < A.** The patch transformer (4×4 patches, width 32, 2 layers, learned positions) shares its patch embedding across locations, which gives partial translation equivariance. Attention can combine patches into a whole-shape representation. However, the 4×4 patch grid is not aligned to the object, so the same shape splits differently across patches depending on position. Transformers are also less sample-efficient on 1024 images than a conv net with locality priors. I expect higher error and somewhat less calibrated CE than the CNN.\n\n**A < B.** The MLP flattens 1152 pixels into a width-96 residual MLP. It has no translation equivariance, so it must learn each shape at every position from about 256 examples per class. It will fit the training set and become overconfident on shifted test shapes, inflating test CE. It is the weakest inductive bias for this task.\n\n**Uncertainty.** The transformer could also overfit and become miscalibrated over about 37 epochs, which narrows the A–B gap. The CNN's lr of 3e-3 adds slight risk of late-training noise. Even so, C first and B last seem fairly robust.\n\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "**Task.** This is `local_shape`. The class is the shape in channel 0: circle, square, diamond or cross. The radius is 2.5–4.5 px, the shape sits at a random position within roughly [6.7, 16.9] px, and mass is normalized, so total intensity carries little class information. Classification depends on local boundary geometry: corners, straight versus curved edges, and the cross's arms. Those cues must be recognized regardless of position. There are only 1024 training images, seen about 37 times each over 1200 steps × 32. The metric is test cross entropy, so overconfident overfitting is penalized.\n\n**C (CNN) – best.** The stride-1 1×1 stem plus two 3×3 conv blocks give a translation-equivariant, LayerNorm'd, residual feature extractor. Its 5×5 receptive field detects edges, corners and curvature, which is what separates these shapes. The 3×3 spatial average pool keeps some layout while being largely shift-tolerant. The parameter count is small, so it generalizes well from 1024 samples. lr 3e-3 with AdamW is reasonable for a normalized small CNN, and gradient clipping guards stability.\n\n**C < A.** The patch transformer (4×4 patches, width 32, 2 layers, learned positions) shares its patch embedding across locations, which gives partial translation equivariance. Attention can combine patches into a whole-shape representation. However, the 4×4 patch grid is not aligned to the object, so the same shape splits differently across patches depending on position. Transformers are also less sample-efficient on 1024 images than a conv net with locality priors. I expect higher error and somewhat less calibrated CE than the CNN.\n\n**A < B.** The MLP flattens 1152 pixels into a width-96 residual MLP. It has no translation equivariance, so it must learn each shape at every position from about 256 examples per class. It will fit the training set and become overconfident on shifted test shapes, inflating test CE. It is the weakest inductive bias for this task.\n\n**Uncertainty.** The transformer could also overfit and become miscalibrated over about 37 epochs, which narrows the A–B gap. The CNN's lr of 3e-3 adds slight risk of late-training noise. Even so, C first and B last seem fairly robust.", "model_identity_matches": true, "question_sha256": "c1dcd274e5bfe3fa29efdf9b1068dbba8f848a78ccec8ff6b76e3453f5ff750b", "prompt_sha256": "fe70cee8f13b0d073487d6679c19a1f3e01a0315d8718a0064aba562d7b10cb2" }, { "model": "claude-opus-5-5", "question_id": "q_a03647bbfbcd65d2146723676eb79259", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842903", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "B", "A", "C" ], "exact_order_correct": true, "public_content": "\n**Task.** The frozen parameters select `local_shape`. The label is whether the channel-0 object is a circle, square, diamond or cross. Each object has radius 2.5–4.5 px and sits at a random position in a 24×24 image. Channel 1 is an independent distractor. Mass normalization makes per-pixel intensity depend on both shape area and radius, so intensity alone is a confounded cue. The model has to recognize the local boundary geometry at an arbitrary location. There are only 1024 training images, seen for about 37 epochs (1200 × 32).\n\n**B (CNN) is best.**\n- The 1×1 stem and two dense 3×3 conv blocks give it translation-equivariant local filters. Edge-orientation and corner detectors directly separate the four shapes: curved, axis-aligned, 45° and thin-arm edges.\n- The 3×3 spatial average pool keeps most of the translation tolerance.\n- The receptive field is about 5×5, which covers the corners and edges that distinguish the shapes even though it does not cover whole objects.\n- Weight sharing is a strong inductive bias on 1024 samples, and AdamW at lr 3e-3 is reasonable for a model this small.\n- I expect it to reach low test cross-entropy.\n\n**A (patch transformer) is behind B.**\n- The 4×4 non-overlapping patches fragment a 5–9 px object across 1–9 patches, with alignment that changes from image to image.\n- The patch embedding is shared across positions, so it still gets some translation bias. But it must learn to combine fragments through attention and learned positional embeddings, which is harder with limited data.\n- It has only 2 layers at width 32 and lr 1e-3, so it likely generalizes worse and is less calibrated than the CNN.\n\n**C (MLP) is last.**\n- It flattens 1152 inputs into a 96-wide residual MLP and has no translation structure at all. It must learn shape templates separately for every position, and 1024 samples cannot cover that.\n- With roughly 110k stem parameters and 37 epochs, it will fit the training set while generalizing poorly. Overconfident errors inflate test cross-entropy.\n\n**Uncertainty.**\n- B vs A: the CNN's small receptive field might limit it on larger objects. Still, local corner and edge cues should suffice, so I'm moderately confident in B over A.\n- A vs C: the transformer could also overfit, but its shared patch embedding gives it a clear advantage over the MLP.\n\n\n{\"best_to_worst\": [\"B\", \"A\", \"C\"]}", "public_explanation": "**Task.** The frozen parameters select `local_shape`. The label is whether the channel-0 object is a circle, square, diamond or cross. Each object has radius 2.5–4.5 px and sits at a random position in a 24×24 image. Channel 1 is an independent distractor. Mass normalization makes per-pixel intensity depend on both shape area and radius, so intensity alone is a confounded cue. The model has to recognize the local boundary geometry at an arbitrary location. There are only 1024 training images, seen for about 37 epochs (1200 × 32).\n\n**B (CNN) is best.**\n- The 1×1 stem and two dense 3×3 conv blocks give it translation-equivariant local filters. Edge-orientation and corner detectors directly separate the four shapes: curved, axis-aligned, 45° and thin-arm edges.\n- The 3×3 spatial average pool keeps most of the translation tolerance.\n- The receptive field is about 5×5, which covers the corners and edges that distinguish the shapes even though it does not cover whole objects.\n- Weight sharing is a strong inductive bias on 1024 samples, and AdamW at lr 3e-3 is reasonable for a model this small.\n- I expect it to reach low test cross-entropy.\n\n**A (patch transformer) is behind B.**\n- The 4×4 non-overlapping patches fragment a 5–9 px object across 1–9 patches, with alignment that changes from image to image.\n- The patch embedding is shared across positions, so it still gets some translation bias. But it must learn to combine fragments through attention and learned positional embeddings, which is harder with limited data.\n- It has only 2 layers at width 32 and lr 1e-3, so it likely generalizes worse and is less calibrated than the CNN.\n\n**C (MLP) is last.**\n- It flattens 1152 inputs into a 96-wide residual MLP and has no translation structure at all. It must learn shape templates separately for every position, and 1024 samples cannot cover that.\n- With roughly 110k stem parameters and 37 epochs, it will fit the training set while generalizing poorly. Overconfident errors inflate test cross-entropy.\n\n**Uncertainty.**\n- B vs A: the CNN's small receptive field might limit it on larger objects. Still, local corner and edge cues should suffice, so I'm moderately confident in B over A.\n- A vs C: the transformer could also overfit, but its shared patch embedding gives it a clear advantage over the MLP.", "model_identity_matches": true, "question_sha256": "0dfb1c35252b1b32dd15e13d43053aee3c0821628464debf9c87fcdff5796c97", "prompt_sha256": "3a6f9497c20315f937936b5fd8b513050e2a0b99110e1c68fedf05e13ae98741" }, { "model": "claude-opus-5-5", "question_id": "q_9d6e46a52044926788daa1beae022057", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_a03647bbfbcd65d2146723676eb79259" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842903", "status": "complete", "gold_order": [ "C", "B", "A" ], "predicted_order": [ "C", "B", "A" ], "exact_order_correct": true, "public_content": "\n**Task.** The task is `local_shape`. The label is the shape in channel 0 (circle, square, diamond or cross). Each shape has radius 2.5–4.5 px and sits at a uniformly random position inside a 24×24 image. Mass normalization means total intensity does not identify the shape, so the model must use boundary geometry: straight versus curved edges, axis-aligned versus diagonal edges, and convex versus concave corners. Channel 1 holds a random distractor shape. With only 1024 training images, translation invariance and a local inductive bias are the main factors.\n\n**Choice C (CNN, ranked best).**\n- The stem is a 1×1 convolution, followed by two residual blocks with dense 3×3 convolutions. This gives a 5×5 receptive field.\n- That is enough to detect local edge orientation, curvature and corner type, which are the cues separating the four shapes.\n- Weight sharing makes these detectors translation-equivariant, so the random positions cost little.\n- The 3×3 spatial-average pool and linear head aggregate the evidence.\n- lr = 3e-3 with AdamW and gradient clipping should converge well within 1200 steps.\n- I expect the lowest test cross-entropy.\n\n**C < B.**\n- The patch transformer (B) also shares its 4×4 patch embedding across positions.\n- However, shape boundaries straddle patch borders at arbitrary offsets, and the learned position embeddings plus attention must be learned from only 1024 samples.\n- ViTs on small data are typically less sample-efficient than CNNs and tend to be more overconfident on errors, which raises cross-entropy.\n- B uses a lower lr (1e-3), which may leave it less converged after 1200 steps.\n\n**B < A.**\n- The MLP (A) flattens 1152 inputs into a 96-wide residual network.\n- It has no translation structure, so it must memorize shape templates at every location from 1024 examples. This overfits badly.\n- The result should be the highest test cross-entropy: near-zero training loss but confident mistakes on held-out positions.\n\n**Uncertainty.**\n- The C vs B gap is the less certain call. The CNN's small receptive field could limit global shape cues, for example distinguishing a large circle from a diamond. Even so, local curvature and edge-orientation cues should suffice.\n- The MLP being last is high-confidence.\n\n\n{\"best_to_worst\": [\"C\", \"B\", \"A\"]}", "public_explanation": "**Task.** The task is `local_shape`. The label is the shape in channel 0 (circle, square, diamond or cross). Each shape has radius 2.5–4.5 px and sits at a uniformly random position inside a 24×24 image. Mass normalization means total intensity does not identify the shape, so the model must use boundary geometry: straight versus curved edges, axis-aligned versus diagonal edges, and convex versus concave corners. Channel 1 holds a random distractor shape. With only 1024 training images, translation invariance and a local inductive bias are the main factors.\n\n**Choice C (CNN, ranked best).**\n- The stem is a 1×1 convolution, followed by two residual blocks with dense 3×3 convolutions. This gives a 5×5 receptive field.\n- That is enough to detect local edge orientation, curvature and corner type, which are the cues separating the four shapes.\n- Weight sharing makes these detectors translation-equivariant, so the random positions cost little.\n- The 3×3 spatial-average pool and linear head aggregate the evidence.\n- lr = 3e-3 with AdamW and gradient clipping should converge well within 1200 steps.\n- I expect the lowest test cross-entropy.\n\n**C < B.**\n- The patch transformer (B) also shares its 4×4 patch embedding across positions.\n- However, shape boundaries straddle patch borders at arbitrary offsets, and the learned position embeddings plus attention must be learned from only 1024 samples.\n- ViTs on small data are typically less sample-efficient than CNNs and tend to be more overconfident on errors, which raises cross-entropy.\n- B uses a lower lr (1e-3), which may leave it less converged after 1200 steps.\n\n**B < A.**\n- The MLP (A) flattens 1152 inputs into a 96-wide residual network.\n- It has no translation structure, so it must memorize shape templates at every location from 1024 examples. This overfits badly.\n- The result should be the highest test cross-entropy: near-zero training loss but confident mistakes on held-out positions.\n\n**Uncertainty.**\n- The C vs B gap is the less certain call. The CNN's small receptive field could limit global shape cues, for example distinguishing a large circle from a diamond. Even so, local curvature and edge-orientation cues should suffice.\n- The MLP being last is high-confidence.", "model_identity_matches": true, "question_sha256": "2bd9e2c73e99389ca37a213247435dfde05fcb94ad0d6da4ec71191b0f090cca", "prompt_sha256": "b233197f4130204277de0e1c8031551f9056e87969c65100ea9f3ad5065e90c1" }, { "model": "claude-opus-5-5", "question_id": "q_5aa7514c54a69ed6cf080475ebf4304e", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842901", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "B", "A", "C" ], "exact_order_correct": true, "public_content": "\n**Main factor: there is no positional embedding.** `position` is `\"none\"` and the tokens are mean-pooled, so the transformer treats its tokens as an unordered set. The `relative_position` label depends on where the circle (channel 0) sits relative to the square (channel 1). The only spatial information left is what each patch-embedding convolution sees inside its own patch: the object's position within that patch, plus any co-occurrence of both objects in one patch.\n\n**B (patch 12) is best.** It has 4 tokens in a 2×2 grid. The synthesis code restricts object centers to about [5, 18] (margin = 4.5 + 0.5), and the patch boundary is at 12. An object in the left or top patch therefore has a local coordinate of roughly 5–11. One in the right or bottom patch has a local coordinate of roughly 0–6. That makes the within-patch position largely reveal which patch the object is in, so absolute position, and hence the relation, is mostly recoverable. The two objects also often share a 12×12 patch, where the convolution sees their relation directly. Attention can then compare the circle token with the square token.\n\n**A (patch 6) is in the middle.** It has 16 tokens. Centers in [5, 18] span all four patch rows and columns, so a local coordinate in 0–5 no longer identifies the patch. Some cues remain: objects with radius 2.5–4.5 straddle patch boundaries, and nearby objects can partly share a patch. It should therefore beat chance, but generalize clearly worse than B.\n\n**C (patch 3) is worst.** It has 64 tiny tokens. Each object covers many 3×3 patches, and a permutation-invariant set of such fragments carries almost no information about global displacement. The only remaining signal is near-shape statistics, which are uninformative because the label is purely positional. Its test cross-entropy should stay near ln 4 ≈ 1.386, possibly worse if it overfits noise.\n\n**Uncertainty:**\n- A might extract more partial-overlap cues than expected, narrowing the A–B gap.\n- B's very few tokens could limit capacity, but its positional leakage should dominate.\n- Ordering A ahead of C is fairly confident.\n\n\n{\"best_to_worst\": [\"B\", \"A\", \"C\"]}", "public_explanation": "**Main factor: there is no positional embedding.** `position` is `\"none\"` and the tokens are mean-pooled, so the transformer treats its tokens as an unordered set. The `relative_position` label depends on where the circle (channel 0) sits relative to the square (channel 1). The only spatial information left is what each patch-embedding convolution sees inside its own patch: the object's position within that patch, plus any co-occurrence of both objects in one patch.\n\n**B (patch 12) is best.** It has 4 tokens in a 2×2 grid. The synthesis code restricts object centers to about [5, 18] (margin = 4.5 + 0.5), and the patch boundary is at 12. An object in the left or top patch therefore has a local coordinate of roughly 5–11. One in the right or bottom patch has a local coordinate of roughly 0–6. That makes the within-patch position largely reveal which patch the object is in, so absolute position, and hence the relation, is mostly recoverable. The two objects also often share a 12×12 patch, where the convolution sees their relation directly. Attention can then compare the circle token with the square token.\n\n**A (patch 6) is in the middle.** It has 16 tokens. Centers in [5, 18] span all four patch rows and columns, so a local coordinate in 0–5 no longer identifies the patch. Some cues remain: objects with radius 2.5–4.5 straddle patch boundaries, and nearby objects can partly share a patch. It should therefore beat chance, but generalize clearly worse than B.\n\n**C (patch 3) is worst.** It has 64 tiny tokens. Each object covers many 3×3 patches, and a permutation-invariant set of such fragments carries almost no information about global displacement. The only remaining signal is near-shape statistics, which are uninformative because the label is purely positional. Its test cross-entropy should stay near ln 4 ≈ 1.386, possibly worse if it overfits noise.\n\n**Uncertainty:**\n- A might extract more partial-overlap cues than expected, narrowing the A–B gap.\n- B's very few tokens could limit capacity, but its positional leakage should dominate.\n- Ordering A ahead of C is fairly confident.", "model_identity_matches": true, "question_sha256": "7ed0219aec4b9051563488fa2c2790f13b55f7b44a251b85606dcfd34c3a502f", "prompt_sha256": "8b50362835072e3e6ec6df8405146d0f06e4026755e6cd55e1d5eeee9758fe64" }, { "model": "claude-opus-5-5", "question_id": "q_8da922eda3a7c018f59492bcb3c32238", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_5aa7514c54a69ed6cf080475ebf4304e" }, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842901", "status": "complete", "gold_order": [ "C", "B", "A" ], "predicted_order": [ "C", "B", "A" ], "exact_order_correct": true, "public_content": "\n**Main factor: no positional embeddings.** The model sets `position: \"none\"` and mean-pools tokens. Attention plus mean pooling is permutation-invariant over tokens, so the model cannot tell which patch a token came from. The only spatial information left is inside each patch, where the patch-embedding conv weights encode pixel location. The task, `relative_position`, depends entirely on where the channel‑0 circle sits relative to the channel‑1 square. So the usable signal depends on how much geometry fits inside one patch.\n\n**C (patch 12) is best.** It produces four 12×12 tokens. Object centers lie roughly in [5, 18.5], and the objects are at most about 9 px across. Often both objects fall in the same patch, and then their relative offset is directly readable by the embedding conv. When they fall in different patches, objects straddling the boundary and the larger local coordinate frame still give partial cues. This is the most positional information available among the choices, though local coordinates still alias modulo 12.\n\n**B (patch 6) is next.** It produces 16 tokens, each with local coordinates modulo 6. The two objects rarely share a 6×6 patch, and cross-token relations carry no position. Attention can only use content plus within-patch offsets, such as which edge of a patch an object touches. That gives weak, aliased cues, so B should land well above C but somewhat below chance loss.\n\n**A (patch 3) is worst.** It produces 64 tokens of 3×3 pixels. Each token sees only a fragment of an object's boundary with a 3‑px aliased position, so almost no relational information survives. Expect near-chance cross entropy (about ln 4 ≈ 1.386). Overconfident fitting of the 1024 training images could push it slightly higher.\n\n**Uncertainty.** B and A could both sit near chance, which would make that gap small and noisy across seeds. C's advantage over B is the most confident part of the ranking.\n\n\n{\"best_to_worst\": [\"C\", \"B\", \"A\"]}", "public_explanation": "**Main factor: no positional embeddings.** The model sets `position: \"none\"` and mean-pools tokens. Attention plus mean pooling is permutation-invariant over tokens, so the model cannot tell which patch a token came from. The only spatial information left is inside each patch, where the patch-embedding conv weights encode pixel location. The task, `relative_position`, depends entirely on where the channel‑0 circle sits relative to the channel‑1 square. So the usable signal depends on how much geometry fits inside one patch.\n\n**C (patch 12) is best.** It produces four 12×12 tokens. Object centers lie roughly in [5, 18.5], and the objects are at most about 9 px across. Often both objects fall in the same patch, and then their relative offset is directly readable by the embedding conv. When they fall in different patches, objects straddling the boundary and the larger local coordinate frame still give partial cues. This is the most positional information available among the choices, though local coordinates still alias modulo 12.\n\n**B (patch 6) is next.** It produces 16 tokens, each with local coordinates modulo 6. The two objects rarely share a 6×6 patch, and cross-token relations carry no position. Attention can only use content plus within-patch offsets, such as which edge of a patch an object touches. That gives weak, aliased cues, so B should land well above C but somewhat below chance loss.\n\n**A (patch 3) is worst.** It produces 64 tokens of 3×3 pixels. Each token sees only a fragment of an object's boundary with a 3‑px aliased position, so almost no relational information survives. Expect near-chance cross entropy (about ln 4 ≈ 1.386). Overconfident fitting of the 1024 training images could push it slightly higher.\n\n**Uncertainty.** B and A could both sit near chance, which would make that gap small and noisy across seeds. C's advantage over B is the most confident part of the ranking.", "model_identity_matches": true, "question_sha256": "0a08c68af53658c387e61079f81eb5be48c7c13909e4eb29ece0078e92e70391", "prompt_sha256": "bc802d4b5fa52f58451c3101a14cef4d8ee97309ddcf03e147976e005a8cba0d" }, { "model": "claude-opus-5-5", "question_id": "q_7c4d6ba0c545202de44c8f79483454a8", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842902", "status": "complete", "gold_order": [ "C", "B", "A" ], "predicted_order": [ "C", "B", "A" ], "exact_order_correct": true, "public_content": "\n**Main factor: where position information comes from.** The task is `relative_position`, so the label depends on where the circle (channel 0) sits relative to the square (channel 1). The model has `position: \"none\"`, and its token blocks are attention plus a per-token feedforward, followed by mean pooling. That makes the network invariant to permuting tokens: it cannot tell which patch a token came from. The only spatial information it gets is from the patch-embedding conv, which encodes where content sits *inside* a patch, i.e. coordinates modulo the patch size. Larger patches therefore keep more of the geometry the label depends on.\n\n**C (patch 12) vs B (patch 6).** Patch 12 gives 4 tokens, one per image quadrant. Each token encodes positions within a 12×12 window, so coordinates are known modulo 12. Object centers lie roughly in [5, 18], so both objects often share a quadrant or straddle a single boundary. In those cases the relative displacement is largely recoverable. Patch 6 only gives coordinates modulo 6, which is much more ambiguous. With objects of radius 2.5–4.5 split across several 6×6 tokens, global placement is mostly lost. So C should reach clearly lower cross entropy than B.\n\n**B (patch 6) vs A (patch 3).** Patch 3 gives coordinates modulo 3, smaller than the objects themselves. Each token sees only an edge or interior fragment, and absolute and relative placement is essentially unrecoverable. A should therefore sit near chance cross entropy (about ln 4 ≈ 1.386). It may do slightly worse if it overfits the 1024 training images over 300 steps. B keeps somewhat more usable layout than A.\n\n**Uncertainty.** B and A might both be close to chance, which would make their order noisy across the 16 seeds. The ordering C < B is the most confident part of the ranking.\n\n\n{\"best_to_worst\": [\"C\", \"B\", \"A\"]}", "public_explanation": "**Main factor: where position information comes from.** The task is `relative_position`, so the label depends on where the circle (channel 0) sits relative to the square (channel 1). The model has `position: \"none\"`, and its token blocks are attention plus a per-token feedforward, followed by mean pooling. That makes the network invariant to permuting tokens: it cannot tell which patch a token came from. The only spatial information it gets is from the patch-embedding conv, which encodes where content sits *inside* a patch, i.e. coordinates modulo the patch size. Larger patches therefore keep more of the geometry the label depends on.\n\n**C (patch 12) vs B (patch 6).** Patch 12 gives 4 tokens, one per image quadrant. Each token encodes positions within a 12×12 window, so coordinates are known modulo 12. Object centers lie roughly in [5, 18], so both objects often share a quadrant or straddle a single boundary. In those cases the relative displacement is largely recoverable. Patch 6 only gives coordinates modulo 6, which is much more ambiguous. With objects of radius 2.5–4.5 split across several 6×6 tokens, global placement is mostly lost. So C should reach clearly lower cross entropy than B.\n\n**B (patch 6) vs A (patch 3).** Patch 3 gives coordinates modulo 3, smaller than the objects themselves. Each token sees only an edge or interior fragment, and absolute and relative placement is essentially unrecoverable. A should therefore sit near chance cross entropy (about ln 4 ≈ 1.386). It may do slightly worse if it overfits the 1024 training images over 300 steps. B keeps somewhat more usable layout than A.\n\n**Uncertainty.** B and A might both be close to chance, which would make their order noisy across the 16 seeds. The ordering C < B is the most confident part of the ranking.", "model_identity_matches": true, "question_sha256": "c51f4fc9654aeccf18b9c0291212baf9c84872536be74d391e2f2fa11e711243", "prompt_sha256": "36003f34cf6c558f3bc65b4380aa27b0216aaad6c950d5ee4f4c399fc38c9dbc" }, { "model": "claude-opus-5-5", "question_id": "q_c179b9eb52ffd8f3f234de5863020a7a", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_7c4d6ba0c545202de44c8f79483454a8" }, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842902", "status": "complete", "gold_order": [ "A", "C", "B" ], "predicted_order": [ "A", "C", "B" ], "exact_order_correct": true, "public_content": "\n**Main factor: no positional encoding.** The base model sets `position: \"none\"` and mean-pools the tokens. That makes the transformer permutation-invariant over patch tokens. The only spatial information the model sees is position inside each patch, which the patch-embedding convolution captures. The task (`relative_position`) depends entirely on where the circle (channel 0) sits relative to the square (channel 1), so the patch size controls how much of that geometry survives.\n\n**A (patch 12) is best.** There are 4 tokens, one per 12×12 quadrant. Object centers are sampled within [5, 18] (margin 5), so they cluster near the image middle.\n- An object in a left or top quadrant has its center near that patch's right or bottom inner edge.\n- An object in a right or bottom quadrant has its center near the patch's left or top edge.\n\nSo the in-patch coordinate largely reveals which quadrant a token is, recovering near-absolute positions even without position embeddings. Objects that share a quadrant are also seen together by one token, which also helps. With mass normalization and no label noise, cross entropy can get fairly low.\n\n**A beats C (patch 6).** Patch 6 gives 16 tokens on a 4×4 grid. Inner patches (6–12, 12–18) hold centers anywhere within them, so local coordinates no longer identify which patch a token is. C still gets partial signal: objects with diameter 5–9 px often straddle patches, and tokens holding pieces of both objects encode their relative displacement. That leaves a noticeably weaker signal than A.\n\n**C beats B (patch 3).** Patch 3 gives 64 tiny tokens with almost no global geometry; each 3×3 token sees only a sliver of an edge. The pooled set of tokens is close to invariant to where the objects are, so B should stay near chance (cross entropy ≈ ln 4 ≈ 1.386), perhaps slightly lower or higher.\n\n**Uncertainty.** C and B may both sit near chance, so their gap is the least certain. Over-confident overfitting on 1024 samples could also inflate cross entropy for the weak models. A being best is the most confident call.\n\n\n{\"best_to_worst\": [\"A\", \"C\", \"B\"]}", "public_explanation": "**Main factor: no positional encoding.** The base model sets `position: \"none\"` and mean-pools the tokens. That makes the transformer permutation-invariant over patch tokens. The only spatial information the model sees is position inside each patch, which the patch-embedding convolution captures. The task (`relative_position`) depends entirely on where the circle (channel 0) sits relative to the square (channel 1), so the patch size controls how much of that geometry survives.\n\n**A (patch 12) is best.** There are 4 tokens, one per 12×12 quadrant. Object centers are sampled within [5, 18] (margin 5), so they cluster near the image middle.\n- An object in a left or top quadrant has its center near that patch's right or bottom inner edge.\n- An object in a right or bottom quadrant has its center near the patch's left or top edge.\n\nSo the in-patch coordinate largely reveals which quadrant a token is, recovering near-absolute positions even without position embeddings. Objects that share a quadrant are also seen together by one token, which also helps. With mass normalization and no label noise, cross entropy can get fairly low.\n\n**A beats C (patch 6).** Patch 6 gives 16 tokens on a 4×4 grid. Inner patches (6–12, 12–18) hold centers anywhere within them, so local coordinates no longer identify which patch a token is. C still gets partial signal: objects with diameter 5–9 px often straddle patches, and tokens holding pieces of both objects encode their relative displacement. That leaves a noticeably weaker signal than A.\n\n**C beats B (patch 3).** Patch 3 gives 64 tiny tokens with almost no global geometry; each 3×3 token sees only a sliver of an edge. The pooled set of tokens is close to invariant to where the objects are, so B should stay near chance (cross entropy ≈ ln 4 ≈ 1.386), perhaps slightly lower or higher.\n\n**Uncertainty.** C and B may both sit near chance, so their gap is the least certain. Over-confident overfitting on 1024 samples could also inflate cross entropy for the weak models. A being best is the most confident call.", "model_identity_matches": true, "question_sha256": "4327fab3306887d72c21d9fbe2f5c301db6ab223eac36525743fd056e18528f9", "prompt_sha256": "c24266d7c88d813d3534d88aaed5c8b684604ff9d5ee731d7863c25fba7a9432" }, { "model": "claude-opus-5-5", "question_id": "q_76cac3671eecb9ff4306d1b86e28b45c", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842903", "status": "complete", "gold_order": [ "B", "C", "A" ], "predicted_order": [ "B", "C", "A" ], "exact_order_correct": true, "public_content": "The ranking is B, then C, then A. The deciding factor is how much absolute position information each patch size keeps, because the model has no positional encoding.\n\n\n**Main factor: the model cannot see where tokens are.** The model uses `position: \"none\"` and mean-pools over tokens. The transformer is therefore permutation-invariant over patch tokens. The only spatial information it gets is the pixel layout inside each patch, which the patch-embedding conv encodes.\n\nThe task is `relative_position`, which needs to know whether the circle is left of, right of, above or below the square. So performance depends on how much absolute layout survives inside a single patch.\n\n- **B (patch 12, a 2×2 grid of tokens):** Each token covers half the image on each axis, so it encodes position across a 12-pixel span. Object centres fall roughly between 5 and 18. Within-patch offsets, plus how an object splits across the boundary at 12, carry a lot of usable left/right and up/down evidence. Ambiguity remains only when the two objects sit in different patches at similar local offsets. With 32-wide tokens and 300 steps, B should reach the lowest cross-entropy.\n- **C (patch 6, a 4×4 grid of tokens):** Position is known only modulo 6 pixels. Objects with radius 2.5–4.5 split across several patches. Global layout must be inferred from boundary fragments, and permutation invariance discards most of it. The loss should be clearly above B but some weak cues remain.\n- **A (patch 3, an 8×8 grid of tokens):** Each token sees only a 3×3 piece of an object, and position is known only modulo 3. Almost no relative-position information survives the orderless pooling. A should stay near chance, around ln 4 ≈ 1.386, and may overfit somewhat beyond that.\n\n**Pairwise justification:**\n- B before C: larger patches keep more absolute layout.\n- C before A: C keeps some coarse within-patch geometry; A is essentially blind to layout.\n\n**Uncertainty:** B's 4 tokens may still confuse the model when the two objects fall in different quadrants. It is also possible that C exploits boundary fragments better than expected. Even so, the ordering by patch size seems the most robust prediction.\n\n\n{\"best_to_worst\": [\"B\", \"C\", \"A\"]}", "public_explanation": "**Main factor: the model cannot see where tokens are.** The model uses `position: \"none\"` and mean-pools over tokens. The transformer is therefore permutation-invariant over patch tokens. The only spatial information it gets is the pixel layout inside each patch, which the patch-embedding conv encodes.\n\nThe task is `relative_position`, which needs to know whether the circle is left of, right of, above or below the square. So performance depends on how much absolute layout survives inside a single patch.\n\n- **B (patch 12, a 2×2 grid of tokens):** Each token covers half the image on each axis, so it encodes position across a 12-pixel span. Object centres fall roughly between 5 and 18. Within-patch offsets, plus how an object splits across the boundary at 12, carry a lot of usable left/right and up/down evidence. Ambiguity remains only when the two objects sit in different patches at similar local offsets. With 32-wide tokens and 300 steps, B should reach the lowest cross-entropy.\n- **C (patch 6, a 4×4 grid of tokens):** Position is known only modulo 6 pixels. Objects with radius 2.5–4.5 split across several patches. Global layout must be inferred from boundary fragments, and permutation invariance discards most of it. The loss should be clearly above B but some weak cues remain.\n- **A (patch 3, an 8×8 grid of tokens):** Each token sees only a 3×3 piece of an object, and position is known only modulo 3. Almost no relative-position information survives the orderless pooling. A should stay near chance, around ln 4 ≈ 1.386, and may overfit somewhat beyond that.\n\n**Pairwise justification:**\n- B before C: larger patches keep more absolute layout.\n- C before A: C keeps some coarse within-patch geometry; A is essentially blind to layout.\n\n**Uncertainty:** B's 4 tokens may still confuse the model when the two objects fall in different quadrants. It is also possible that C exploits boundary fragments better than expected. Even so, the ordering by patch size seems the most robust prediction.", "model_identity_matches": true, "question_sha256": "6b4fa08d1969fd32b3dd6aa13fe9c2ee0d4666d4e7cbcf203da570a32971d052", "prompt_sha256": "13573df98c8675006a14f0c15c929b41bdcdcb74b326cf53f235898480a567dc" }, { "model": "claude-opus-5-5", "question_id": "q_21ca0ff91a02c38e27e1bebe5867c24d", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_76cac3671eecb9ff4306d1b86e28b45c" }, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842903", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": true, "public_content": "\n**Main factor: how much absolute position the tokens can carry.** All three models use `position: \"none\"` and mean-pool their tokens. That makes the transformer permutation-invariant over patch tokens, so it sees only a \"bag of patches.\" The task is `relative_position`, so it needs to know where the circle (channel 0) sits relative to the square (channel 1). The only spatial information left is what the patch-embedding conv encodes about where content lies inside each patch. Larger patches therefore keep more usable geometry.\n\n**C (patch 12) is best.** The image splits into 4 tokens of 12×12 pixels. Object centers are drawn from about [5, 18] on each axis (margin 5.0).\n- In the left/top patch, centers fall at local coordinates of roughly 5–11.\n- In the right/bottom patch, they fall at roughly 0–6.\n- So the position of an object within its patch almost identifies its absolute coordinate. The two ranges only overlap around local 5–6.\n- When both objects land in the same patch, one token sees the relation directly.\n\nThis gives a near-complete positional code, so the loss should be clearly lowest.\n\n**A (patch 6) is second.** A 4×4 grid of 6×6 patches gives less absolute information. Only the outermost rows and columns are partly informative, because centers rarely fall in them. Objects sometimes share a patch, but separation is at least 2.88 px and usually larger, so this is uncommon. A should be weak but better than chance.\n\n**B (patch 3) is worst.** With 64 tokens of 3×3 pixels, each token sees only a fragment of an edge or interior. The circle and square almost never share a token. Pooling across tokens throws away nearly all relative geometry. Cross-entropy should stay near ln 4.\n\n**Uncertainty:** A and B may both sit close to chance. If so, their order depends on seed noise and on overconfident overfitting with 1024 training samples. C beating both is the most confident part of the ranking.\n\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "**Main factor: how much absolute position the tokens can carry.** All three models use `position: \"none\"` and mean-pool their tokens. That makes the transformer permutation-invariant over patch tokens, so it sees only a \"bag of patches.\" The task is `relative_position`, so it needs to know where the circle (channel 0) sits relative to the square (channel 1). The only spatial information left is what the patch-embedding conv encodes about where content lies inside each patch. Larger patches therefore keep more usable geometry.\n\n**C (patch 12) is best.** The image splits into 4 tokens of 12×12 pixels. Object centers are drawn from about [5, 18] on each axis (margin 5.0).\n- In the left/top patch, centers fall at local coordinates of roughly 5–11.\n- In the right/bottom patch, they fall at roughly 0–6.\n- So the position of an object within its patch almost identifies its absolute coordinate. The two ranges only overlap around local 5–6.\n- When both objects land in the same patch, one token sees the relation directly.\n\nThis gives a near-complete positional code, so the loss should be clearly lowest.\n\n**A (patch 6) is second.** A 4×4 grid of 6×6 patches gives less absolute information. Only the outermost rows and columns are partly informative, because centers rarely fall in them. Objects sometimes share a patch, but separation is at least 2.88 px and usually larger, so this is uncommon. A should be weak but better than chance.\n\n**B (patch 3) is worst.** With 64 tokens of 3×3 pixels, each token sees only a fragment of an edge or interior. The circle and square almost never share a token. Pooling across tokens throws away nearly all relative geometry. Cross-entropy should stay near ln 4.\n\n**Uncertainty:** A and B may both sit close to chance. If so, their order depends on seed noise and on overconfident overfitting with 1024 training samples. C beating both is the most confident part of the ranking.", "model_identity_matches": true, "question_sha256": "1ed74fdb24c4279febc8cc25695345ccb4178c002376e9f1e11c40ce1a5ae945", "prompt_sha256": "1b542c782593bec4e9a3b63caea8a34c2f95b491fcda8e2027d39985b3b21047" }, { "model": "claude-haiku-5-5", "question_id": "q_a9889bdd9a39a4c2caad00b528356fbd", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842901", "status": "complete", "gold_order": [ "A", "C", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": false, "public_content": "\n**Setup.** All three choices train for 75 AdamW steps at batch size 32 (2400 samples, about 2.3 epochs over the 1024-image training set), lr 1e-3, with identical data order and initial weights per seed. The only difference is the architecture, so ranking depends on how quickly each model fits the relative-position task within this short budget and how well-calibrated its outputs are on held-out data (cross-entropy penalizes overconfident errors).\n\n**Task demands.** The `relative_position` task requires comparing the spatial location of two objects in different channels. Flattened MLPs can learn this but must rediscover translation structure from scratch, which is data-hungry. Convolutions give translation equivariance and local feature sharing, which suits object shapes and their relative placement. Attention over patches can model global relations, but with 1024 examples and very few steps it has little inductive bias for precise position comparisons.\n\n**Choice A (MLP, width 96, depth 2, residual).** Roughly 2×24×24 = 1152 inputs into a 96-wide stem, about 0.12M parameters. It is fast to optimize, but it treats every pixel position as a separate feature. With 75 updates it is likely to learn a coarse signal, leaving higher residual loss than the convolutional model.\n\n**Choice B (patch transformer, width 32, 4×4 patches, 36 tokens, 2 layers, 4 heads, learned positions, mean pooling).** Patch embedding gives a 6×6 token grid with learned positional embeddings and global self-attention. Mean pooling over tokens discards explicit position information except through the learned position embeddings, which start small (std 0.02) and need many updates to become useful. At width 32 and only 75 steps, the transformer is likely undertrained and noisy. Its loss is probably the highest of the three, or near Choice A's.\n\n**Choice C (CNN, width 24, 3×3 dense convs, 1×1 bottleneck MLP, layer norm, 3×3 spatial pooling, linear head).** Stride-1 convolutions preserve the 24×24 resolution, and the 3×3 spatial pooling grid retains coarse location information before the linear head. Since the head sees location-tagged features, it can express \"left/right/above/below\" directly. Convolutional inductive bias should give the fastest and most stable fit within 75 steps.\n\n**Ranking.** I predict C < A < B (best to worst). The main uncertainty is between A and B. The MLP has a crude but direct path to the position signal, while the transformer may catch up if the learned positional embeddings and attention adapt quickly under AdamW at lr 1e-3. Seed variance over 16 runs could also reorder A and B if their means are close. The confidence in C being best is higher, because its architecture most closely matches the spatial-relation structure of the task.\n\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "**Setup.** All three choices train for 75 AdamW steps at batch size 32 (2400 samples, about 2.3 epochs over the 1024-image training set), lr 1e-3, with identical data order and initial weights per seed. The only difference is the architecture, so ranking depends on how quickly each model fits the relative-position task within this short budget and how well-calibrated its outputs are on held-out data (cross-entropy penalizes overconfident errors).\n\n**Task demands.** The `relative_position` task requires comparing the spatial location of two objects in different channels. Flattened MLPs can learn this but must rediscover translation structure from scratch, which is data-hungry. Convolutions give translation equivariance and local feature sharing, which suits object shapes and their relative placement. Attention over patches can model global relations, but with 1024 examples and very few steps it has little inductive bias for precise position comparisons.\n\n**Choice A (MLP, width 96, depth 2, residual).** Roughly 2×24×24 = 1152 inputs into a 96-wide stem, about 0.12M parameters. It is fast to optimize, but it treats every pixel position as a separate feature. With 75 updates it is likely to learn a coarse signal, leaving higher residual loss than the convolutional model.\n\n**Choice B (patch transformer, width 32, 4×4 patches, 36 tokens, 2 layers, 4 heads, learned positions, mean pooling).** Patch embedding gives a 6×6 token grid with learned positional embeddings and global self-attention. Mean pooling over tokens discards explicit position information except through the learned position embeddings, which start small (std 0.02) and need many updates to become useful. At width 32 and only 75 steps, the transformer is likely undertrained and noisy. Its loss is probably the highest of the three, or near Choice A's.\n\n**Choice C (CNN, width 24, 3×3 dense convs, 1×1 bottleneck MLP, layer norm, 3×3 spatial pooling, linear head).** Stride-1 convolutions preserve the 24×24 resolution, and the 3×3 spatial pooling grid retains coarse location information before the linear head. Since the head sees location-tagged features, it can express \"left/right/above/below\" directly. Convolutional inductive bias should give the fastest and most stable fit within 75 steps.\n\n**Ranking.** I predict C < A < B (best to worst). The main uncertainty is between A and B. The MLP has a crude but direct path to the position signal, while the transformer may catch up if the learned positional embeddings and attention adapt quickly under AdamW at lr 1e-3. Seed variance over 16 runs could also reorder A and B if their means are close. The confidence in C being best is higher, because its architecture most closely matches the spatial-relation structure of the task.", "model_identity_matches": true, "question_sha256": "d0c2b11985e3d2889f05611562f6d47b14afafeef088af0b5083eb72dfeb2bb1", "prompt_sha256": "fb3ce4370e766515d4851692e138003fc2a48d385264afe509bde9f56bfb1505" }, { "model": "claude-haiku-5-5", "question_id": "q_018f733cbf575236fbf126db4322c484", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_a9889bdd9a39a4c2caad00b528356fbd" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842901", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": false, "public_content": "\n**Main factors.** All three candidates share the same data, optimizer (AdamW, lr 1e-3, weight decay 0.01), batch size (32), and budget (75 updates, about 2.3 passes over 1024 training images). The only axis that varies is the architecture. Under this short budget, the main factors are:\n- **Inductive bias for the task.** Relative position needs to locate two objects and compare their coordinates, so architectures that preserve spatial structure should learn faster.\n- **Trainability in 75 steps.** Models with fewer, better-conditioned parameters tend to reach lower cross entropy sooner.\n- **Parameter efficiency.** The flat MLP has roughly 110k parameters in its stem alone, and nothing in its structure is translation-aware.\n\n**Choice A (CNN, lowest loss expected).** Two 3×3 conv blocks with LayerNorm and residuals give a receptive field of about 7×7 at stride 1. The `spatial` 3×3 average pool keeps coarse position information, so the 216-dimensional linear head can read off which region each object occupies. Convolutions are translation-equivariant, so they do not have to relearn each location from scratch. The model is small and should fit quickly.\n\n**Choice B (flat MLP, middle expected).** The 1152-dimensional flat input goes through a 96-wide residual MLP. It has no spatial prior, so it must learn position from pixel patterns, which generalizes poorly from 1024 examples. It can still learn coarse intensity-weighted features quickly, which should keep it ahead of a struggling transformer.\n\n**Choice C (patch transformer, highest loss expected).** The model uses 4×4 patches (36 tokens), width 32, 4 heads, and learned positional embeddings initialized at 0.02. It is mean-pooled before the head. With width 32 and only 75 updates, attention layers usually stay near chance for a while. Mean pooling also discards the explicit per-token location, so the learned position signal must be strong enough to survive averaging.\n\n**Adjacent pairs.**\n- A over B: the convolutional prior should matter more than the MLP's raw capacity at this sample size.\n- B over C: the MLP trains more reliably in this regime than the tiny patch transformer, which has to learn both attention and positional structure.\n\n**Uncertainty.** The B-versus-C ordering is the least certain. Both may sit close to chance (about ln 4 ≈ 1.386), so seed variance could reorder them. A ranking from A's advantage over the others is more reliable, since the CNN's inductive bias should dominate here. I reasoned from the code and settings alone and did not run any training.\n\n\n{\"best_to_worst\": [\"A\", \"B\", \"C\"]}", "public_explanation": "**Main factors.** All three candidates share the same data, optimizer (AdamW, lr 1e-3, weight decay 0.01), batch size (32), and budget (75 updates, about 2.3 passes over 1024 training images). The only axis that varies is the architecture. Under this short budget, the main factors are:\n- **Inductive bias for the task.** Relative position needs to locate two objects and compare their coordinates, so architectures that preserve spatial structure should learn faster.\n- **Trainability in 75 steps.** Models with fewer, better-conditioned parameters tend to reach lower cross entropy sooner.\n- **Parameter efficiency.** The flat MLP has roughly 110k parameters in its stem alone, and nothing in its structure is translation-aware.\n\n**Choice A (CNN, lowest loss expected).** Two 3×3 conv blocks with LayerNorm and residuals give a receptive field of about 7×7 at stride 1. The `spatial` 3×3 average pool keeps coarse position information, so the 216-dimensional linear head can read off which region each object occupies. Convolutions are translation-equivariant, so they do not have to relearn each location from scratch. The model is small and should fit quickly.\n\n**Choice B (flat MLP, middle expected).** The 1152-dimensional flat input goes through a 96-wide residual MLP. It has no spatial prior, so it must learn position from pixel patterns, which generalizes poorly from 1024 examples. It can still learn coarse intensity-weighted features quickly, which should keep it ahead of a struggling transformer.\n\n**Choice C (patch transformer, highest loss expected).** The model uses 4×4 patches (36 tokens), width 32, 4 heads, and learned positional embeddings initialized at 0.02. It is mean-pooled before the head. With width 32 and only 75 updates, attention layers usually stay near chance for a while. Mean pooling also discards the explicit per-token location, so the learned position signal must be strong enough to survive averaging.\n\n**Adjacent pairs.**\n- A over B: the convolutional prior should matter more than the MLP's raw capacity at this sample size.\n- B over C: the MLP trains more reliably in this regime than the tiny patch transformer, which has to learn both attention and positional structure.\n\n**Uncertainty.** The B-versus-C ordering is the least certain. Both may sit close to chance (about ln 4 ≈ 1.386), so seed variance could reorder them. A ranking from A's advantage over the others is more reliable, since the CNN's inductive bias should dominate here. I reasoned from the code and settings alone and did not run any training.", "model_identity_matches": true, "question_sha256": "f1514b66e6151b6fceb6c4ae7168a41c6db186b9f7b42705569e764895c29113", "prompt_sha256": "7a0b3cc83d8eadcb682c289dc3eec30a046941fa0bb276ff0956c7875beefb09" }, { "model": "claude-haiku-5-5", "question_id": "q_f41ad89255f54a110a6b78ac32e08910", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842902", "status": "complete", "gold_order": [ "A", "B", "C" ], "predicted_order": [ "B", "A", "C" ], "exact_order_correct": false, "public_content": "\n**Main factors.** The task is `relative_position`: the model must compare where a circle (channel 0) sits relative to a square (channel 1). The label depends on the dominant center-displacement axis, so the model needs spatial layout information from both channels. Training is short and identical across choices: 75 AdamW steps at lr 1e-3, batch 32, about 2.3 passes over 1024 images, with no schedule. In this regime, inductive bias and how quickly each architecture can extract object positions matter more than raw capacity. Mass normalization means intensity alone carries no label information.\n\n**Choice B (small dense CNN, width 24).** Two pre-norm residual 3x3 conv blocks give a 5x5 receptive field with channel mixing. The 3x3 spatial pooling grid keeps coarse position information (216 features into the linear head), so the head can read \"which region holds which object.\" Local convolutions learn object-presence features quickly, and the position-preserving pooling suits this task. It has far fewer parameters than the MLP, so it should generalize better from 1024 samples. Its main limit is the coarse 8x8-cell pooling for fine position differences.\n\n**Choice A (MLP, width 96).** The 1152-to-96 linear stem can learn absolute position directly, which is adequate because object placement is confined to the central 28–72% of the frame. With no spatial inductive bias, though, it must learn position-specific weights for every pixel from few samples. It is likely to fit the training set faster than it generalizes, and its test cross-entropy after 75 steps should sit between B and C in my estimate.\n\n**Choice C (patch transformer, width 32).** Patch-4 tokenization gives 36 tokens with learned positional embeddings. Two attention blocks can in principle compare the two objects, but a tiny width with 75 updates is very undertrained. Mean pooling after attention also dilutes the relational signal, and attention models usually need more steps than this to escape near-chance loss (~1.386). I expect it to have the highest held-out loss.\n\n**Ranking and uncertainty.** I predict B < A < C. The B-versus-A gap is the least certain: a wider MLP could fit this layout quickly enough to beat the CNN. The A-versus-C ordering is more confident, since the transformer is the most undertrained. Seed variance over 16 runs could also reorder close pairs. This is a reasoning-based prediction, not a measured result.\n\n\n{\"best_to_worst\": [\"B\", \"A\", \"C\"]}", "public_explanation": "**Main factors.** The task is `relative_position`: the model must compare where a circle (channel 0) sits relative to a square (channel 1). The label depends on the dominant center-displacement axis, so the model needs spatial layout information from both channels. Training is short and identical across choices: 75 AdamW steps at lr 1e-3, batch 32, about 2.3 passes over 1024 images, with no schedule. In this regime, inductive bias and how quickly each architecture can extract object positions matter more than raw capacity. Mass normalization means intensity alone carries no label information.\n\n**Choice B (small dense CNN, width 24).** Two pre-norm residual 3x3 conv blocks give a 5x5 receptive field with channel mixing. The 3x3 spatial pooling grid keeps coarse position information (216 features into the linear head), so the head can read \"which region holds which object.\" Local convolutions learn object-presence features quickly, and the position-preserving pooling suits this task. It has far fewer parameters than the MLP, so it should generalize better from 1024 samples. Its main limit is the coarse 8x8-cell pooling for fine position differences.\n\n**Choice A (MLP, width 96).** The 1152-to-96 linear stem can learn absolute position directly, which is adequate because object placement is confined to the central 28–72% of the frame. With no spatial inductive bias, though, it must learn position-specific weights for every pixel from few samples. It is likely to fit the training set faster than it generalizes, and its test cross-entropy after 75 steps should sit between B and C in my estimate.\n\n**Choice C (patch transformer, width 32).** Patch-4 tokenization gives 36 tokens with learned positional embeddings. Two attention blocks can in principle compare the two objects, but a tiny width with 75 updates is very undertrained. Mean pooling after attention also dilutes the relational signal, and attention models usually need more steps than this to escape near-chance loss (~1.386). I expect it to have the highest held-out loss.\n\n**Ranking and uncertainty.** I predict B < A < C. The B-versus-A gap is the least certain: a wider MLP could fit this layout quickly enough to beat the CNN. The A-versus-C ordering is more confident, since the transformer is the most undertrained. Seed variance over 16 runs could also reorder close pairs. This is a reasoning-based prediction, not a measured result.", "model_identity_matches": true, "question_sha256": "265fcd17cb23554b617a57bfea7cb952934d1a4204aa69ba0b68f92abe28b48d", "prompt_sha256": "27654c0d84bd94e35c93f05379ff7f90c78d826947c7456eb743d2f2d16ebd40" }, { "model": "claude-haiku-5-5", "question_id": "q_f2e0f5463396043d48d5c5ae87bedb87", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_f41ad89255f54a110a6b78ac32e08910" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842902", "status": "complete", "gold_order": [ "B", "C", "A" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": false, "public_content": "\n**Task setting.** The dataset is the `relative_position` task: 24×24 two-channel images, four classes, with the label set by which side the circle sits on relative to the square. Training uses 75 AdamW updates at batch size 32 (2400 samples, roughly 2.3 passes over 1024 training images), learning rate 1e-3, and gradient clipping at norm 1.0. Every choice shares this budget and the same data, so the ranking depends on how well each architecture's inductive bias fits the task and how quickly it learns in this short budget.\n\n**Choice B (base MLP).** The stem is a dense `Linear` on the flattened 2×24×24 = 1152-pixel input, to width 96, followed by two residual GELU blocks. A dense layer has no translation equivariance, so it must learn position-dependent features separately for every location. The relative-position rule is a comparison of object centers, so a flat MLP has to discover that structure from 1024 examples in 75 steps. It is the weakest inductive bias of the three.\n\n**Choice C (CNN).** It uses 3×3 dense convolutions at full resolution, residual pre-LayerNorm blocks, width 24, and a 3×3 spatial average pool before a linear head. The pooling keeps coarse location information, which is what the task needs. Convolutions share weights across positions, so the network can detect the circle and square anywhere in the image and compare their coarse positions. This is a strong match to a local-object, relative-position problem and should learn quickly.\n\n**Choice A (patch transformer).** It uses 4×4 patches, giving 36 tokens, with width 32, learned position embeddings, two attention blocks, and mean pooling. Attention can relate the two objects globally. However, the model has only 2 blocks and width 32, and it has to learn from scratch with positional embeddings and no convolutional locality prior. Mean pooling over tokens also discards the explicit position information that the head would need, except what the positional embeddings encode. With 75 updates, this model is likely to remain undertrained compared with the CNN.\n\n**Predicted ordering.** CNN (C) should have the lowest test cross-entropy because its locality and translation-sharing biases fit the object-based relative-position rule and it trains quickly with few samples. The patch transformer (A) should come second, since attention can capture the pairwise relation but learns more slowly from scratch. The flat MLP (B) should be worst, because it lacks any spatial structure and must learn position-specific weights for every location.\n\n**Material uncertainty.** All three models are small and trained for only 75 steps, so the seed-to-seed variance may be large relative to the gaps. The A-versus-B gap is probably the more reliable of the two adjacent pairs, since the MLP has no spatial prior at all. The C-versus-A ordering is less certain, because a transformer with patch size 4 might learn the coarse relation faster than expected. Cross-entropy also depends on calibration after few updates, which could shift the order for the least-trained model.\n\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "**Task setting.** The dataset is the `relative_position` task: 24×24 two-channel images, four classes, with the label set by which side the circle sits on relative to the square. Training uses 75 AdamW updates at batch size 32 (2400 samples, roughly 2.3 passes over 1024 training images), learning rate 1e-3, and gradient clipping at norm 1.0. Every choice shares this budget and the same data, so the ranking depends on how well each architecture's inductive bias fits the task and how quickly it learns in this short budget.\n\n**Choice B (base MLP).** The stem is a dense `Linear` on the flattened 2×24×24 = 1152-pixel input, to width 96, followed by two residual GELU blocks. A dense layer has no translation equivariance, so it must learn position-dependent features separately for every location. The relative-position rule is a comparison of object centers, so a flat MLP has to discover that structure from 1024 examples in 75 steps. It is the weakest inductive bias of the three.\n\n**Choice C (CNN).** It uses 3×3 dense convolutions at full resolution, residual pre-LayerNorm blocks, width 24, and a 3×3 spatial average pool before a linear head. The pooling keeps coarse location information, which is what the task needs. Convolutions share weights across positions, so the network can detect the circle and square anywhere in the image and compare their coarse positions. This is a strong match to a local-object, relative-position problem and should learn quickly.\n\n**Choice A (patch transformer).** It uses 4×4 patches, giving 36 tokens, with width 32, learned position embeddings, two attention blocks, and mean pooling. Attention can relate the two objects globally. However, the model has only 2 blocks and width 32, and it has to learn from scratch with positional embeddings and no convolutional locality prior. Mean pooling over tokens also discards the explicit position information that the head would need, except what the positional embeddings encode. With 75 updates, this model is likely to remain undertrained compared with the CNN.\n\n**Predicted ordering.** CNN (C) should have the lowest test cross-entropy because its locality and translation-sharing biases fit the object-based relative-position rule and it trains quickly with few samples. The patch transformer (A) should come second, since attention can capture the pairwise relation but learns more slowly from scratch. The flat MLP (B) should be worst, because it lacks any spatial structure and must learn position-specific weights for every location.\n\n**Material uncertainty.** All three models are small and trained for only 75 steps, so the seed-to-seed variance may be large relative to the gaps. The A-versus-B gap is probably the more reliable of the two adjacent pairs, since the MLP has no spatial prior at all. The C-versus-A ordering is less certain, because a transformer with patch size 4 might learn the coarse relation faster than expected. Cross-entropy also depends on calibration after few updates, which could shift the order for the least-trained model.", "model_identity_matches": true, "question_sha256": "e8c9cf5b5d874f791085a890e2df4b314527ca6f54efdedd47e4e42e9793bdb2", "prompt_sha256": "e5c9cd2df44039e83c370a64520fe53e9a14641a19cfcba002fbe51ef82e7bc4" }, { "model": "claude-haiku-5-5", "question_id": "q_2e828a18000b8cfc54065a359bf0ab04", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842903", "status": "complete", "gold_order": [ "A", "C", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": false, "public_content": "\n**Main factors.** All three candidates share the same data, optimizer (AdamW, lr 1e-3, weight decay 0.01), batch size 32, and only 75 updates, so the comparison is mostly about how quickly each architecture can pick up the relative-position signal in that budget. The task needs spatial information: the label depends on where the channel-0 circle sits relative to the channel-1 square. Each architecture encodes location differently:\n\n- **A (MLP):** Flattens the 2×24×24 input into a 1152-dim vector, then uses a 96-wide residual MLP. It has no spatial inductive bias, but a linear map over raw pixels can already read off coarse positional mass, and the parameter count (about 110k) is small enough to fit quickly.\n- **B (patch transformer):** Uses 4×4 patches (36 tokens), width 32, 2 layers, 4 heads, learned positions, and mean pooling over tokens. Position enters only through the learned embeddings, and the final mean pool discards token identity, so the model must learn a fairly indirect route to the displacement. Width 32 and 75 steps leave little capacity or training time for that, so it is likely the least trained of the three.\n- **C (CNN):** Uses dense 3×3 convolutions (receptive field 5×5), 2 residual blocks, and a 3×3 spatial pooling grid before a linear head. This keeps coarse location in the features (each pooled cell covers about 8×8 pixels) and is translation-equivariant. That fits a task defined by relative geometry, so it should learn the rule fastest.\n\n**Pairwise justification.**\n- **C vs. A:** I expect C to be lower. Its convolutional locality and spatial pooling match the relative-position rule better than a flattened MLP, and its head is small (216→4). The margin is material but not certain, because the MLP can exploit the simple linear mass-location cues.\n- **A vs. B:** I expect A to be lower. With only 75 updates, a small transformer that has to infer displacement through attention and mean pooling is likely to stay near chance. The MLP has a more direct path to the positional signal.\n\n**Uncertainty.** Every model is trained for only 75 steps, so all three may remain near the uniform-prediction loss (about ln 4 ≈ 1.386), and seed variance could reorder close pairs, especially A vs. B. The C-vs-A ordering is the more likely of the two calls to hold. I did not run anything; this is reasoning from the code and budget.\n\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "**Main factors.** All three candidates share the same data, optimizer (AdamW, lr 1e-3, weight decay 0.01), batch size 32, and only 75 updates, so the comparison is mostly about how quickly each architecture can pick up the relative-position signal in that budget. The task needs spatial information: the label depends on where the channel-0 circle sits relative to the channel-1 square. Each architecture encodes location differently:\n\n- **A (MLP):** Flattens the 2×24×24 input into a 1152-dim vector, then uses a 96-wide residual MLP. It has no spatial inductive bias, but a linear map over raw pixels can already read off coarse positional mass, and the parameter count (about 110k) is small enough to fit quickly.\n- **B (patch transformer):** Uses 4×4 patches (36 tokens), width 32, 2 layers, 4 heads, learned positions, and mean pooling over tokens. Position enters only through the learned embeddings, and the final mean pool discards token identity, so the model must learn a fairly indirect route to the displacement. Width 32 and 75 steps leave little capacity or training time for that, so it is likely the least trained of the three.\n- **C (CNN):** Uses dense 3×3 convolutions (receptive field 5×5), 2 residual blocks, and a 3×3 spatial pooling grid before a linear head. This keeps coarse location in the features (each pooled cell covers about 8×8 pixels) and is translation-equivariant. That fits a task defined by relative geometry, so it should learn the rule fastest.\n\n**Pairwise justification.**\n- **C vs. A:** I expect C to be lower. Its convolutional locality and spatial pooling match the relative-position rule better than a flattened MLP, and its head is small (216→4). The margin is material but not certain, because the MLP can exploit the simple linear mass-location cues.\n- **A vs. B:** I expect A to be lower. With only 75 updates, a small transformer that has to infer displacement through attention and mean pooling is likely to stay near chance. The MLP has a more direct path to the positional signal.\n\n**Uncertainty.** Every model is trained for only 75 steps, so all three may remain near the uniform-prediction loss (about ln 4 ≈ 1.386), and seed variance could reorder close pairs, especially A vs. B. The C-vs-A ordering is the more likely of the two calls to hold. I did not run anything; this is reasoning from the code and budget.", "model_identity_matches": true, "question_sha256": "a85d544f1c1d558a23b44ad1d97799e53d5321cee414365edda17ec6a862c69b", "prompt_sha256": "d9deece1f02ae57e194f40a57e3c91838fb98334d728674af4ebce39b043ea0f" }, { "model": "claude-haiku-5-5", "question_id": "q_89d77cd38238c082c9114a0773e6b261", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_2e828a18000b8cfc54065a359bf0ab04" }, "template_id": "operator_learning_speed", "instance_id": "operator_learning_speed_s842903", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": false, "public_content": "\n**Main factors.** All three candidates share the same data, optimizer (AdamW, lr 1e-3, weight decay 0.01), batch size 32, and 75 updates. They differ only in architecture. With a short budget, the key questions are how quickly each architecture picks up the signal and how well its inductive bias matches the task. Test cross-entropy is the metric, so confident wrong predictions are penalized, and near-uniform predictions give about ln 4 ≈ 1.386.\n\n**Choice A (CNN, width 24).** This is a small, convolutional model with 3×3 convolutions, two residual pre-norm blocks, and a 3×3 spatial average pool into a linear head. Local weight sharing and translation equivariance suit the task. The circle and square positions in `relative_position`, and the local shapes in `local_shape`, are spatially local, and the 3×3 pooling keeps coarse location. This is the strongest inductive bias for the data, and its small parameter count should let it fit quickly at lr 1e-3. Its weakness is that the receptive field is small and the pooled grid is coarse, so it cannot represent fine relative offsets perfectly.\n\n**Choice B (residual MLP, width 96).** The model flattens the 2×24×24 input into a 1152-dimensional vector and applies a dense stem of about 110k parameters. It has no spatial prior, so it must learn shift-dependent features from 1024 training images. It can fit quickly, since a dense layer with 96 units responds strongly to the input. Its generalization is weaker than a convolution's on position-based labels, and the test loss may stay higher even if training loss drops.\n\n**Choice C (patch transformer, width 32).** This is a 2-layer transformer over 36 patch tokens, with learned positions and mean pooling. Attention can relate the two objects globally, which helps `relative_position`. But with width 32, 75 steps, no warmup, and mean pooling, transformers usually learn slowly from scratch on small data. The output is likely closest to uniform at this budget, so its loss is probably the least improved from initialization.\n\n**Ranking.**\n- A before B: the convolutional prior should give lower held-out CE in 75 steps on these localized synthetic labels. This is the pair I'm most confident in.\n- B before C: the width-96 MLP has more capacity and a simpler optimization path than the narrow, under-trained transformer, so I expect it to reach a lower loss within this budget.\n\n**Uncertainty.** Each pairwise gap may be small relative to seed variance, since all three models may stay near ln 4 after 75 steps. The B-vs-C ordering is the least certain. A transformer could overtake the MLP if the mean-pooled tokens learn quickly, and the MLP could overfit enough to lose on test. I did not run the training, so this ranking rests on architectural reasoning.\n\n\n{\"best_to_worst\": [\"A\", \"B\", \"C\"]}", "public_explanation": "**Main factors.** All three candidates share the same data, optimizer (AdamW, lr 1e-3, weight decay 0.01), batch size 32, and 75 updates. They differ only in architecture. With a short budget, the key questions are how quickly each architecture picks up the signal and how well its inductive bias matches the task. Test cross-entropy is the metric, so confident wrong predictions are penalized, and near-uniform predictions give about ln 4 ≈ 1.386.\n\n**Choice A (CNN, width 24).** This is a small, convolutional model with 3×3 convolutions, two residual pre-norm blocks, and a 3×3 spatial average pool into a linear head. Local weight sharing and translation equivariance suit the task. The circle and square positions in `relative_position`, and the local shapes in `local_shape`, are spatially local, and the 3×3 pooling keeps coarse location. This is the strongest inductive bias for the data, and its small parameter count should let it fit quickly at lr 1e-3. Its weakness is that the receptive field is small and the pooled grid is coarse, so it cannot represent fine relative offsets perfectly.\n\n**Choice B (residual MLP, width 96).** The model flattens the 2×24×24 input into a 1152-dimensional vector and applies a dense stem of about 110k parameters. It has no spatial prior, so it must learn shift-dependent features from 1024 training images. It can fit quickly, since a dense layer with 96 units responds strongly to the input. Its generalization is weaker than a convolution's on position-based labels, and the test loss may stay higher even if training loss drops.\n\n**Choice C (patch transformer, width 32).** This is a 2-layer transformer over 36 patch tokens, with learned positions and mean pooling. Attention can relate the two objects globally, which helps `relative_position`. But with width 32, 75 steps, no warmup, and mean pooling, transformers usually learn slowly from scratch on small data. The output is likely closest to uniform at this budget, so its loss is probably the least improved from initialization.\n\n**Ranking.**\n- A before B: the convolutional prior should give lower held-out CE in 75 steps on these localized synthetic labels. This is the pair I'm most confident in.\n- B before C: the width-96 MLP has more capacity and a simpler optimization path than the narrow, under-trained transformer, so I expect it to reach a lower loss within this budget.\n\n**Uncertainty.** Each pairwise gap may be small relative to seed variance, since all three models may stay near ln 4 after 75 steps. The B-vs-C ordering is the least certain. A transformer could overtake the MLP if the mean-pooled tokens learn quickly, and the MLP could overfit enough to lose on test. I did not run the training, so this ranking rests on architectural reasoning.", "model_identity_matches": true, "question_sha256": "d7dca61949875a1cc3a4ea263e4e25148cb28e78133670ad99f56c761fa03571", "prompt_sha256": "893c63de1a94330af3befe0d4eb57e55c62e5a02cb08401764eb53805ea532ed" }, { "model": "claude-haiku-5-5", "question_id": "q_04b93ce5a8d08dcf6f6328205dd254ad", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842901", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": true, "public_content": "\nThe task is `local_shape`: classify the shape of the channel-0 object (circle, square, diamond, cross) from a 24×24 image. All choices see the same data and the same 38,400-sample budget (1200 steps × batch 32 for A and B; C also uses 1200×32 per the shared settings).\n\nChoice A is the base: a 2-layer patch transformer (patch 4, width 32, learned positions). It has 36 tokens, so attention mixes local patch information globally, but there is no inductive bias toward translation equivariance beyond the patch embedding. Shape recognition from a small patch grid is learnable but needs more samples to generalize well with only 1024 training images; the learned position embeddings add capacity to memorize.\n\nChoice B replaces the model with a flat MLP on the 1152-dimensional input (width 96, two residual blocks). It has no spatial weight sharing, so it must learn shape position-by-position from 1024 examples. Shapes appear at random locations (centers sampled over roughly 28%–72% of the image), so a flat MLP is the least data-efficient for translation-varying shape recognition. I expect it to generalize worst and have the highest cross-entropy on test.\n\nChoice C uses a convolutional network: 3×3 dense convolutions with residual blocks, width 24, a spatial 3×3 pooled readout, and a learning rate of 0.003 (3× the base). Convolutions are translation-equivariant, which matches the task (the shape class is independent of its location), and the local 3×3 receptive field with two blocks suits edge-level shape cues such as corners distinguishing square/diamond/cross. The higher learning rate speeds convergence within the fixed budget, though it adds some optimization risk. Overall I expect C to achieve the lowest test cross-entropy.\n\nPredicted order: C (best), then A, then B (worst). The A-versus-B gap should be clearer than the C-versus-A gap, since C's conv inductive bias and higher LR are both favorable but the learning-rate change is a second source of variance.\n\nMaterial uncertainty: the C learning rate of 0.003 could destabilize AdamW training with a residual conv stack and no warmup, which could make C worse than A. Also, the 3×3 spatial pooling in C leaves some position information in the head, so the advantage over the transformer is less certain than the MLP-versus-conv gap.\n\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "The task is `local_shape`: classify the shape of the channel-0 object (circle, square, diamond, cross) from a 24×24 image. All choices see the same data and the same 38,400-sample budget (1200 steps × batch 32 for A and B; C also uses 1200×32 per the shared settings).\n\nChoice A is the base: a 2-layer patch transformer (patch 4, width 32, learned positions). It has 36 tokens, so attention mixes local patch information globally, but there is no inductive bias toward translation equivariance beyond the patch embedding. Shape recognition from a small patch grid is learnable but needs more samples to generalize well with only 1024 training images; the learned position embeddings add capacity to memorize.\n\nChoice B replaces the model with a flat MLP on the 1152-dimensional input (width 96, two residual blocks). It has no spatial weight sharing, so it must learn shape position-by-position from 1024 examples. Shapes appear at random locations (centers sampled over roughly 28%–72% of the image), so a flat MLP is the least data-efficient for translation-varying shape recognition. I expect it to generalize worst and have the highest cross-entropy on test.\n\nChoice C uses a convolutional network: 3×3 dense convolutions with residual blocks, width 24, a spatial 3×3 pooled readout, and a learning rate of 0.003 (3× the base). Convolutions are translation-equivariant, which matches the task (the shape class is independent of its location), and the local 3×3 receptive field with two blocks suits edge-level shape cues such as corners distinguishing square/diamond/cross. The higher learning rate speeds convergence within the fixed budget, though it adds some optimization risk. Overall I expect C to achieve the lowest test cross-entropy.\n\nPredicted order: C (best), then A, then B (worst). The A-versus-B gap should be clearer than the C-versus-A gap, since C's conv inductive bias and higher LR are both favorable but the learning-rate change is a second source of variance.\n\nMaterial uncertainty: the C learning rate of 0.003 could destabilize AdamW training with a residual conv stack and no warmup, which could make C worse than A. Also, the 3×3 spatial pooling in C leaves some position information in the head, so the advantage over the transformer is less certain than the MLP-versus-conv gap.", "model_identity_matches": true, "question_sha256": "92a98eeec0d06b019e8e528487e1be9abc7074c7351968ae6fddb148646f2742", "prompt_sha256": "4a697beb14e725ce09fc114c5c0d23c756edb26da299573d36cdd87224e4a29c" }, { "model": "claude-haiku-5-5", "question_id": "q_7945972839e5ef8403e9a2edfb6ae39f", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_04b93ce5a8d08dcf6f6328205dd254ad" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842901", "status": "complete", "gold_order": [ "A", "B", "C" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": true, "public_content": "\n**Task setting.** The dataset is the `local_shape` task: a 2-channel 24×24 image where the class is the channel-0 shape (circle, square, diamond, cross). The shape is a large, high-contrast, spatially localized object, so a model needs local shape discrimination plus some spatial aggregation. Channel 1 is a distractor only in the texture tasks; here it is a second object with random shape, which is mild clutter. Budget is fixed at 38,400 samples, so all candidates see the same number of examples.\n\n**Choice A (conv CNN, lr 3e-3).** A 2-layer residual conv stack with 3×3 kernels, width 24, followed by a 3×3 spatial pooling grid and a linear head. This preserves coarse spatial layout and gives local receptive fields (5×5 effective after two blocks) well matched to shape recognition. Convolutional weight sharing gives a strong inductive bias for translated shapes, and the spatial pooling keeps position information that a shape classifier does not really need but that does not hurt. The learning rate is raised to 3e-3, which for a small conv net with LayerNorm and 1200 AdamW updates is usually productive rather than unstable, so it should converge faster than the base. Parameter count is small, so overfitting over 1024 training images is a risk, but weight sharing limits it.\n\n**Choice B (base: patch transformer, lr 1e-3).** Patch size 4 gives 36 tokens with learned position embeddings, two attention blocks, width 32, and mean pooling over tokens. Attention over 4×4 patches can represent shape structure, but with only 1024 training images and no convolutional locality prior, it is data-hungry. The mean pooling discards explicit position, and learned embeddings must be learned from scratch. Expect higher test cross-entropy than a conv model here.\n\n**Choice C (MLP, width 96).** A flattened 1152-dimensional input through a dense stem and two residual MLP blocks. Dense layers have no translation equivariance, so a shape must be relearned at every location from 1024 examples. With large input dimensionality and a fixed sample budget, this is typically the weakest inductive bias for this kind of synthetic spatial task. It may still fit well, but generalization is likely worst.\n\n**Ordering.** The main factor is inductive bias for local spatial shape: conv (A) > patch transformer (B) > flat MLP (C). A's higher learning rate further helps it reach low loss within 1200 updates. Among A and B the gap is driven mostly by the conv prior and the learning-rate difference, so I am reasonably confident A is best.\n\n**Uncertainty.** The B vs. C ordering is less certain: with 16 seeds, a width-96 MLP could fit this simple task well enough to compete with a small patch transformer, and cross-entropy (rather than error) is sensitive to overconfidence, which could reorder close pairs. The lr 3e-3 in A could also cause instability for some seeds, though LayerNorm and gradient clipping make this unlikely.\n\n\n{\"best_to_worst\": [\"A\", \"B\", \"C\"]}", "public_explanation": "**Task setting.** The dataset is the `local_shape` task: a 2-channel 24×24 image where the class is the channel-0 shape (circle, square, diamond, cross). The shape is a large, high-contrast, spatially localized object, so a model needs local shape discrimination plus some spatial aggregation. Channel 1 is a distractor only in the texture tasks; here it is a second object with random shape, which is mild clutter. Budget is fixed at 38,400 samples, so all candidates see the same number of examples.\n\n**Choice A (conv CNN, lr 3e-3).** A 2-layer residual conv stack with 3×3 kernels, width 24, followed by a 3×3 spatial pooling grid and a linear head. This preserves coarse spatial layout and gives local receptive fields (5×5 effective after two blocks) well matched to shape recognition. Convolutional weight sharing gives a strong inductive bias for translated shapes, and the spatial pooling keeps position information that a shape classifier does not really need but that does not hurt. The learning rate is raised to 3e-3, which for a small conv net with LayerNorm and 1200 AdamW updates is usually productive rather than unstable, so it should converge faster than the base. Parameter count is small, so overfitting over 1024 training images is a risk, but weight sharing limits it.\n\n**Choice B (base: patch transformer, lr 1e-3).** Patch size 4 gives 36 tokens with learned position embeddings, two attention blocks, width 32, and mean pooling over tokens. Attention over 4×4 patches can represent shape structure, but with only 1024 training images and no convolutional locality prior, it is data-hungry. The mean pooling discards explicit position, and learned embeddings must be learned from scratch. Expect higher test cross-entropy than a conv model here.\n\n**Choice C (MLP, width 96).** A flattened 1152-dimensional input through a dense stem and two residual MLP blocks. Dense layers have no translation equivariance, so a shape must be relearned at every location from 1024 examples. With large input dimensionality and a fixed sample budget, this is typically the weakest inductive bias for this kind of synthetic spatial task. It may still fit well, but generalization is likely worst.\n\n**Ordering.** The main factor is inductive bias for local spatial shape: conv (A) > patch transformer (B) > flat MLP (C). A's higher learning rate further helps it reach low loss within 1200 updates. Among A and B the gap is driven mostly by the conv prior and the learning-rate difference, so I am reasonably confident A is best.\n\n**Uncertainty.** The B vs. C ordering is less certain: with 16 seeds, a width-96 MLP could fit this simple task well enough to compete with a small patch transformer, and cross-entropy (rather than error) is sensitive to overconfidence, which could reorder close pairs. The lr 3e-3 in A could also cause instability for some seeds, though LayerNorm and gradient clipping make this unlikely.", "model_identity_matches": true, "question_sha256": "d469dca0be63dbd5af5b14a5cb27765ad59e93f694ca465bc9fdff7e6d3ba2cd", "prompt_sha256": "77c0870d6e36da370eeda582e896d1f06b35aec1588122ebcef3937c2052cb83" }, { "model": "claude-haiku-5-5", "question_id": "q_dc6a1198c1d2e494edd7b3618c36bf0b", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842902", "status": "complete", "gold_order": [ "B", "C", "A" ], "predicted_order": [ "B", "C", "A" ], "exact_order_correct": true, "public_content": "\nThe task is `local_shape`: classify the channel-0 object as circle, square, diamond, or cross. Object positions, radii, and intensities vary, and channel 1 is an unrelated object that acts as a distractor. The training set is small (1024 images), and the budget is fixed at 38,400 samples, about 37 epochs at batch size 32.\n\n- **Choice B (CNN):** The 3×3 convolutions with residual connections and a 5×5 receptive field match local shape geometry. The 3×3 spatial pooling keeps coarse position information while the head stays small (about 216 features). LayerNorm with a learning rate of 3e-3 should train stably. Translation equivariance suits objects placed at random locations, so this is the strongest inductive bias. I expect it to reach the lowest test cross-entropy.\n- **Choice C (patch transformer):** Patch-4 tokens (36 of them), learned positions, and mean pooling give a reasonable model. Attention over only 36 tokens with 1024 training examples is data-hungry, and it has no built-in translation invariance beyond what the learned positions provide. It should land in the middle.\n- **Choice A (MLP):** The flattened 1152-dimensional input feeds a width-96 MLP with no spatial weight sharing. It must learn the shape-by-position mapping separately for each location, which is poorly matched to randomly placed objects and is prone to overfitting on 1024 samples. I expect it to be the worst.\n\nAdjacent pairs: B over C because the convolutional bias is much better matched to this data. C over A because attention with patch tokens retains some locality and a more structured representation than a flat MLP, though this gap is the least certain. Material uncertainty: the MLP and transformer could be closer than I expect, and the transformer could overfit or underfit depending on the seed. The B-first ordering is the most robust part of the ranking.\n\n\n{\"best_to_worst\": [\"B\", \"C\", \"A\"]}", "public_explanation": "The task is `local_shape`: classify the channel-0 object as circle, square, diamond, or cross. Object positions, radii, and intensities vary, and channel 1 is an unrelated object that acts as a distractor. The training set is small (1024 images), and the budget is fixed at 38,400 samples, about 37 epochs at batch size 32.\n\n- **Choice B (CNN):** The 3×3 convolutions with residual connections and a 5×5 receptive field match local shape geometry. The 3×3 spatial pooling keeps coarse position information while the head stays small (about 216 features). LayerNorm with a learning rate of 3e-3 should train stably. Translation equivariance suits objects placed at random locations, so this is the strongest inductive bias. I expect it to reach the lowest test cross-entropy.\n- **Choice C (patch transformer):** Patch-4 tokens (36 of them), learned positions, and mean pooling give a reasonable model. Attention over only 36 tokens with 1024 training examples is data-hungry, and it has no built-in translation invariance beyond what the learned positions provide. It should land in the middle.\n- **Choice A (MLP):** The flattened 1152-dimensional input feeds a width-96 MLP with no spatial weight sharing. It must learn the shape-by-position mapping separately for each location, which is poorly matched to randomly placed objects and is prone to overfitting on 1024 samples. I expect it to be the worst.\n\nAdjacent pairs: B over C because the convolutional bias is much better matched to this data. C over A because attention with patch tokens retains some locality and a more structured representation than a flat MLP, though this gap is the least certain. Material uncertainty: the MLP and transformer could be closer than I expect, and the transformer could overfit or underfit depending on the seed. The B-first ordering is the most robust part of the ranking.", "model_identity_matches": true, "question_sha256": "d3b698eb2cbd3c0339d6fafe28333df4794a1062bfa8887fa1a3e7ba8ab27849", "prompt_sha256": "a7df13a151777eba77efe2a89ce0ae8420134f2cb76f07f44143945ea5a0322e" }, { "model": "claude-haiku-5-5", "question_id": "q_f2d7051e84a8d64012dfaf4f428f50e8", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_dc6a1198c1d2e494edd7b3618c36bf0b" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842902", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "C", "A", "B" ], "exact_order_correct": true, "public_content": "\n**Task factors.** The label is the channel-0 shape (circle, square, diamond, cross). Objects are roughly 5–9 px across and placed at random positions across a 24×24 grid. Channel 1 is a distractor. Shape recognition therefore depends on local structure, and the model must generalize across positions with only 1024 training images and no augmentation.\n\n**Choice C (CNN, lr 3e-3)** has the strongest inductive bias for this task. Its 3×3 convolutions are weight-shared across positions, so it learns a shape detector once and applies it everywhere. The 3×3 spatial pooling then keeps a coarse position signal for the head. It is small (width 24), so overfitting is limited. The 3e-3 learning rate is higher than the others, but LayerNorm and gradient clipping make it stable. The receptive field is modest (about 5 px from two 3×3 convs), which limits how much of a shape it sees at once, but the pooled features should still separate the four shapes well.\n\n**Choice A (patch transformer, lr 1e-3)** uses 4×4 patches, so a shape spans only about 2–3 tokens. Each patch is embedded by a linear layer, and attention mixes tokens. Learned position embeddings are not shift-equivariant, and the model has no convolutional locality prior, so it must learn shape-and-position relationships from 1024 samples. Mean-pooling over tokens adds some invariance. Transformers are usually data-hungry, so I expect it to generalize worse than C, though it probably beats the MLP because its per-patch embedding and attention still exploit local structure.\n\n**Choice B (MLP, width 96)** flattens the 2×24×24 input into a 1152-dimensional vector. A dense first layer has no translation equivariance, so it must learn each shape at every position separately. With 1024 samples and about 110k parameters in the stem, it is most prone to overfitting. Its test cross-entropy should therefore be the highest. Its learning rate and budget match the base, so the gap comes from architecture rather than optimization.\n\n**Ordering.** C < A < B. The most uncertain pair is C versus A. Both use the same budget (1200 steps × 32), and a small transformer with patch tokens could do better than expected. The A-versus-B gap is less certain, since both are weaker than C and the MLP might not overfit as badly as I expect. The C-versus-B gap is the most confident.\n\n\n{\"best_to_worst\": [\"C\", \"A\", \"B\"]}", "public_explanation": "**Task factors.** The label is the channel-0 shape (circle, square, diamond, cross). Objects are roughly 5–9 px across and placed at random positions across a 24×24 grid. Channel 1 is a distractor. Shape recognition therefore depends on local structure, and the model must generalize across positions with only 1024 training images and no augmentation.\n\n**Choice C (CNN, lr 3e-3)** has the strongest inductive bias for this task. Its 3×3 convolutions are weight-shared across positions, so it learns a shape detector once and applies it everywhere. The 3×3 spatial pooling then keeps a coarse position signal for the head. It is small (width 24), so overfitting is limited. The 3e-3 learning rate is higher than the others, but LayerNorm and gradient clipping make it stable. The receptive field is modest (about 5 px from two 3×3 convs), which limits how much of a shape it sees at once, but the pooled features should still separate the four shapes well.\n\n**Choice A (patch transformer, lr 1e-3)** uses 4×4 patches, so a shape spans only about 2–3 tokens. Each patch is embedded by a linear layer, and attention mixes tokens. Learned position embeddings are not shift-equivariant, and the model has no convolutional locality prior, so it must learn shape-and-position relationships from 1024 samples. Mean-pooling over tokens adds some invariance. Transformers are usually data-hungry, so I expect it to generalize worse than C, though it probably beats the MLP because its per-patch embedding and attention still exploit local structure.\n\n**Choice B (MLP, width 96)** flattens the 2×24×24 input into a 1152-dimensional vector. A dense first layer has no translation equivariance, so it must learn each shape at every position separately. With 1024 samples and about 110k parameters in the stem, it is most prone to overfitting. Its test cross-entropy should therefore be the highest. Its learning rate and budget match the base, so the gap comes from architecture rather than optimization.\n\n**Ordering.** C < A < B. The most uncertain pair is C versus A. Both use the same budget (1200 steps × 32), and a small transformer with patch tokens could do better than expected. The A-versus-B gap is less certain, since both are weaker than C and the MLP might not overfit as badly as I expect. The C-versus-B gap is the most confident.", "model_identity_matches": true, "question_sha256": "c1dcd274e5bfe3fa29efdf9b1068dbba8f848a78ccec8ff6b76e3453f5ff750b", "prompt_sha256": "fe70cee8f13b0d073487d6679c19a1f3e01a0315d8718a0064aba562d7b10cb2" }, { "model": "claude-haiku-5-5", "question_id": "q_a03647bbfbcd65d2146723676eb79259", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842903", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "B", "A", "C" ], "exact_order_correct": true, "public_content": "\n**Main factors.** All three choices share the same data (the `local_shape` task, where only channel 0 determines the label and channel 1 is a distractor), the same 38,400-sample budget, AdamW, and the same seeds. The ranking therefore depends on how well each architecture's inductive bias fits a translation-varying shape-recognition task with only 1,024 training images, plus the learning rate.\n\n**Choice B (CNN) ranked first.** Its 3x3 convolutions are translation-equivariant, and the shape classes are defined by local geometry that can appear anywhere in the image. Two stride-1 conv blocks give a 5x5 receptive field, which covers most of a shape with radius 2.5–4.5 px. The 3x3 spatial pooling keeps coarse position information without relying on it. The learning rate is 3e-3, which is higher than the others but should be stable for a small conv net under gradient clipping. The 1,024-image training set is small, so this inductive bias should lower held-out cross-entropy.\n\n**Choice A (patch transformer) ranked second.** It uses 4x4 patches (36 tokens), learned position embeddings, and mean pooling, at width 32 with lr 1e-3. It can learn shape features, but attention over patches has weaker locality bias than a CNN. With so little data it probably overfits more, and its learned positional embeddings add a position-dependent component the task does not need. Over 1,200 steps it likely reaches a higher test cross-entropy than B.\n\n**Choice C (MLP) ranked last.** It flattens the 2x24x24 input and applies dense layers with no translation structure. A shape can appear anywhere, so the network must learn each position separately from 1,024 examples. This is the most data-hungry setup, and it has the weakest generalization, so it most likely has the highest held-out loss.\n\n**Uncertainty.** The B-vs-A gap is the most uncertain. The transformer could close much of it, and B's higher learning rate adds some risk. The C-last placement is the most confident, since it lacks any locality or translation bias and has the most parameters per useful signal. Across 16 seeds the means could still be close, so the ordering is a reasoned prediction, not a verified result.\n\n\n{\"best_to_worst\": [\"B\", \"A\", \"C\"]}", "public_explanation": "**Main factors.** All three choices share the same data (the `local_shape` task, where only channel 0 determines the label and channel 1 is a distractor), the same 38,400-sample budget, AdamW, and the same seeds. The ranking therefore depends on how well each architecture's inductive bias fits a translation-varying shape-recognition task with only 1,024 training images, plus the learning rate.\n\n**Choice B (CNN) ranked first.** Its 3x3 convolutions are translation-equivariant, and the shape classes are defined by local geometry that can appear anywhere in the image. Two stride-1 conv blocks give a 5x5 receptive field, which covers most of a shape with radius 2.5–4.5 px. The 3x3 spatial pooling keeps coarse position information without relying on it. The learning rate is 3e-3, which is higher than the others but should be stable for a small conv net under gradient clipping. The 1,024-image training set is small, so this inductive bias should lower held-out cross-entropy.\n\n**Choice A (patch transformer) ranked second.** It uses 4x4 patches (36 tokens), learned position embeddings, and mean pooling, at width 32 with lr 1e-3. It can learn shape features, but attention over patches has weaker locality bias than a CNN. With so little data it probably overfits more, and its learned positional embeddings add a position-dependent component the task does not need. Over 1,200 steps it likely reaches a higher test cross-entropy than B.\n\n**Choice C (MLP) ranked last.** It flattens the 2x24x24 input and applies dense layers with no translation structure. A shape can appear anywhere, so the network must learn each position separately from 1,024 examples. This is the most data-hungry setup, and it has the weakest generalization, so it most likely has the highest held-out loss.\n\n**Uncertainty.** The B-vs-A gap is the most uncertain. The transformer could close much of it, and B's higher learning rate adds some risk. The C-last placement is the most confident, since it lacks any locality or translation bias and has the most parameters per useful signal. Across 16 seeds the means could still be close, so the ordering is a reasoned prediction, not a verified result.", "model_identity_matches": true, "question_sha256": "0dfb1c35252b1b32dd15e13d43053aee3c0821628464debf9c87fcdff5796c97", "prompt_sha256": "3a6f9497c20315f937936b5fd8b513050e2a0b99110e1c68fedf05e13ae98741" }, { "model": "claude-haiku-5-5", "question_id": "q_9d6e46a52044926788daa1beae022057", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_a03647bbfbcd65d2146723676eb79259" }, "template_id": "operator_shape_generalization", "instance_id": "operator_shape_generalization_s842903", "status": "complete", "gold_order": [ "C", "B", "A" ], "predicted_order": [ "C", "B", "A" ], "exact_order_correct": true, "public_content": "\n**Task setting.** The dataset is the `local_shape` variant: 24×24 two-channel images, four classes (circle, square, diamond, cross) defined by the channel-0 shape. Channel 1 is a distractor. Training uses 38,400 samples total for every choice, with batch size 32 and 1200 updates, and the ranking is by mean test cross-entropy over 16 seeds.\n\n**Choice B (base).** A patch transformer: 4×4 patches give 36 tokens, width 32, depth 2, 4 heads, learned positions, mean pooling, AdamW at lr 1e-3. The patch embedding is a single linear projection per 4×4 patch, so local shape detail within a patch must be recovered by attention across tokens. With 1024 training images, this is a small-data regime, and attention models tend to be less sample-efficient than convolutions on localized shape recognition.\n\n**Choice C.** A convolutional network: stem conv (stride 1), two residual blocks with 3×3 depthwise-free dense convolutions and 1×1 MLP-style channel mixing, width 24, then a 3×3 spatial average pool into a linear head. Local shape is precisely the kind of translation-equivariant, local feature a 3×3 convolution stack captures well, and the 3×3 pooled head keeps some spatial layout. The learning rate is raised to 3e-3, which is a reasonable choice for a small CNN with AdamW and layer norm, and gradient clipping at 1.0 limits instability. Overall this is the inductive bias best matched to the task, so I expect the lowest test cross-entropy.\n\n**Choice A.** A flat MLP: the 1152-dimensional input is flattened and passed through a 96-wide linear stem, two residual linear blocks, and a head. It has no spatial inductive bias, so it must learn translation-invariant shape detectors from 1024 examples. The shape signal is spatially localized and the object position varies widely, so this is typically the hardest setting for generalization. It probably overfits or underfits more than the others, giving the highest cross-entropy.\n\n**Ranking rationale.**\n- C vs. B: both have comparable parameter counts, but C's convolutional bias suits local shape features and the higher learning rate is sound, so C should beat the patch transformer.\n- B vs. A: the patch transformer still retains some structure (patch tokens plus attention across positions), whereas the flat MLP has none. B should be ahead of A.\n\n**Uncertainty.** The gap between B and C could be small, since both are reasonably expressive and the sample budget is modest. The higher lr in C is a risk if it causes noisy training at 1200 steps, though with clipping it is unlikely to diverge. The MLP's position as worst is the most confident part of the ordering.\n\n\n{\"best_to_worst\": [\"C\", \"B\", \"A\"]}", "public_explanation": "**Task setting.** The dataset is the `local_shape` variant: 24×24 two-channel images, four classes (circle, square, diamond, cross) defined by the channel-0 shape. Channel 1 is a distractor. Training uses 38,400 samples total for every choice, with batch size 32 and 1200 updates, and the ranking is by mean test cross-entropy over 16 seeds.\n\n**Choice B (base).** A patch transformer: 4×4 patches give 36 tokens, width 32, depth 2, 4 heads, learned positions, mean pooling, AdamW at lr 1e-3. The patch embedding is a single linear projection per 4×4 patch, so local shape detail within a patch must be recovered by attention across tokens. With 1024 training images, this is a small-data regime, and attention models tend to be less sample-efficient than convolutions on localized shape recognition.\n\n**Choice C.** A convolutional network: stem conv (stride 1), two residual blocks with 3×3 depthwise-free dense convolutions and 1×1 MLP-style channel mixing, width 24, then a 3×3 spatial average pool into a linear head. Local shape is precisely the kind of translation-equivariant, local feature a 3×3 convolution stack captures well, and the 3×3 pooled head keeps some spatial layout. The learning rate is raised to 3e-3, which is a reasonable choice for a small CNN with AdamW and layer norm, and gradient clipping at 1.0 limits instability. Overall this is the inductive bias best matched to the task, so I expect the lowest test cross-entropy.\n\n**Choice A.** A flat MLP: the 1152-dimensional input is flattened and passed through a 96-wide linear stem, two residual linear blocks, and a head. It has no spatial inductive bias, so it must learn translation-invariant shape detectors from 1024 examples. The shape signal is spatially localized and the object position varies widely, so this is typically the hardest setting for generalization. It probably overfits or underfits more than the others, giving the highest cross-entropy.\n\n**Ranking rationale.**\n- C vs. B: both have comparable parameter counts, but C's convolutional bias suits local shape features and the higher learning rate is sound, so C should beat the patch transformer.\n- B vs. A: the patch transformer still retains some structure (patch tokens plus attention across positions), whereas the flat MLP has none. B should be ahead of A.\n\n**Uncertainty.** The gap between B and C could be small, since both are reasonably expressive and the sample budget is modest. The higher lr in C is a risk if it causes noisy training at 1200 steps, though with clipping it is unlikely to diverge. The MLP's position as worst is the most confident part of the ordering.", "model_identity_matches": true, "question_sha256": "2bd9e2c73e99389ca37a213247435dfde05fcb94ad0d6da4ec71191b0f090cca", "prompt_sha256": "b233197f4130204277de0e1c8031551f9056e87969c65100ea9f3ad5065e90c1" }, { "model": "claude-haiku-5-5", "question_id": "q_5aa7514c54a69ed6cf080475ebf4304e", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842901", "status": "complete", "gold_order": [ "B", "A", "C" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": false, "public_content": "\nThe three choices differ only in the patch size of the patch-embedding transformer: A uses 6 (tokens = 4×4 = 16), B uses 12 (tokens = 2×2 = 4), and C uses 3 (tokens = 8×8 = 64). Width (32), depth (2), heads (4), AdamW at lr 1e-3, batch size 32, 300 updates, and the seed-matched initial weights are shared, so the comparison isolates how the tokenization granularity affects learning.\n\nMain factors:\n- **Parameter count:** The patch conv has 2·p²·32 weights, so the patch embedding is small in all cases (about 1.2k, 4.6k, and 18k parameters for p = 3, 6, 12 respectively, versus roughly 17k for the rest of the model in the blocks). The models stay well under the 2M cap, so capacity is not the limiting factor.\n- **Receptive field and spatial resolution:** The task has distinct demands. `relative_position` needs coarse localization of two objects (radius 2.5–4.5 px, images 24 px), so very large patches (12) lose spatial detail inside each token, but 4 tokens with global attention and mean pooling still carry the centroid information in the embedding. Patch 6 gives a moderate grid. Patch 3 gives fine detail but a 64-token sequence that must be pooled by mean, which dilutes per-token signal and makes attention harder to train in only 300 steps.\n- **Optimization in 300 steps:** With no positional encoding (\"position\": \"none\") and mean pooling, the transformer is close to permutation-invariant over tokens. Mean pooling over many small tokens tends to wash out the spatial relations that the label depends on, so the 64-token model is likely the slowest to fit. The 4-token model is easiest to optimize but has the least spatial information per token; the 16-token model is the usual balance.\n- **Held-out cross entropy:** Since the metric is CE rather than error, overconfident wrong predictions are penalized, which favors the model that trains most stably in the short budget.\n\nPredicted ordering: A (patch 6) best, then B (patch 12), then C (patch 3) worst. The B vs. C ordering is the most uncertain part: the 4-token model could underfit spatial structure, and the 64-token model could fit reasonably well given the small images. The A-first placement is a moderate-confidence judgment; the true ranking could shift if patch 12 captures enough coarse position information for this dataset.\n\n\n{\"best_to_worst\": [\"A\", \"B\", \"C\"]}", "public_explanation": "The three choices differ only in the patch size of the patch-embedding transformer: A uses 6 (tokens = 4×4 = 16), B uses 12 (tokens = 2×2 = 4), and C uses 3 (tokens = 8×8 = 64). Width (32), depth (2), heads (4), AdamW at lr 1e-3, batch size 32, 300 updates, and the seed-matched initial weights are shared, so the comparison isolates how the tokenization granularity affects learning.\n\nMain factors:\n- **Parameter count:** The patch conv has 2·p²·32 weights, so the patch embedding is small in all cases (about 1.2k, 4.6k, and 18k parameters for p = 3, 6, 12 respectively, versus roughly 17k for the rest of the model in the blocks). The models stay well under the 2M cap, so capacity is not the limiting factor.\n- **Receptive field and spatial resolution:** The task has distinct demands. `relative_position` needs coarse localization of two objects (radius 2.5–4.5 px, images 24 px), so very large patches (12) lose spatial detail inside each token, but 4 tokens with global attention and mean pooling still carry the centroid information in the embedding. Patch 6 gives a moderate grid. Patch 3 gives fine detail but a 64-token sequence that must be pooled by mean, which dilutes per-token signal and makes attention harder to train in only 300 steps.\n- **Optimization in 300 steps:** With no positional encoding (\"position\": \"none\") and mean pooling, the transformer is close to permutation-invariant over tokens. Mean pooling over many small tokens tends to wash out the spatial relations that the label depends on, so the 64-token model is likely the slowest to fit. The 4-token model is easiest to optimize but has the least spatial information per token; the 16-token model is the usual balance.\n- **Held-out cross entropy:** Since the metric is CE rather than error, overconfident wrong predictions are penalized, which favors the model that trains most stably in the short budget.\n\nPredicted ordering: A (patch 6) best, then B (patch 12), then C (patch 3) worst. The B vs. C ordering is the most uncertain part: the 4-token model could underfit spatial structure, and the 64-token model could fit reasonably well given the small images. The A-first placement is a moderate-confidence judgment; the true ranking could shift if patch 12 captures enough coarse position information for this dataset.", "model_identity_matches": true, "question_sha256": "7ed0219aec4b9051563488fa2c2790f13b55f7b44a251b85606dcfd34c3a502f", "prompt_sha256": "8b50362835072e3e6ec6df8405146d0f06e4026755e6cd55e1d5eeee9758fe64" }, { "model": "claude-haiku-5-5", "question_id": "q_8da922eda3a7c018f59492bcb3c32238", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_5aa7514c54a69ed6cf080475ebf4304e" }, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842901", "status": "complete", "gold_order": [ "C", "B", "A" ], "predicted_order": [ "C", "B", "A" ], "exact_order_correct": true, "public_content": "\nThe three choices differ only in patch size: A uses 3 (64 tokens), B uses 6 (16 tokens, the base), and C uses 12 (4 tokens). Everything else is shared: width 32, depth 2, 4 heads, `position: \"none\"`, AdamW at lr 1e-3, 300 steps at batch 32, and identical data.\n\nThe key structural fact is that there is no positional encoding. The non-overlapping strided conv embeds each patch independently, attention is permutation-equivariant, and the head mean-pools over tokens. The output is therefore nearly invariant to token order. Relative position is a spatial-layout property, so the architecture has almost no direct path to it. Every choice is likely to sit near chance, with test cross-entropy close to ln 4 ≈ 1.386.\n\nWithin that near-chance regime, the differences come from optimization and calibration rather than from the ability to solve the task:\n\n- **C (patch 12):** Four tokens, each seeing a 12×12 region of both channels, give the shallowest attention computation and the fewest token interactions. Training is the most stable and least prone to overconfident logits, so I expect it to have the lowest held-out loss.\n- **B (patch 6):** The base configuration sits in the middle, with 16 tokens. It should be somewhat less stable than C but better calibrated than A.\n- **A (patch 3):** Sixty-four tokens with 18 input values each give a longer attention sequence and more capacity. With only ~9 epochs over 1024 samples, that extra capacity is more likely to yield noisy, overconfident predictions on held-out data than to learn position, since no positional signal exists to exploit. I expect the highest test loss.\n\nMaterial uncertainty: because the position signal is largely absent, all three may land within seed-to-seed noise of each other, so the B–C and A–B adjacencies are low-confidence. The C-best call is more plausible than the rest of the order. If the model does pick up some local-texture or mass-distribution cues, the finer tiling of A could help, which would reverse the expected order.\n\n\n{\"best_to_worst\": [\"C\", \"B\", \"A\"]}", "public_explanation": "The three choices differ only in patch size: A uses 3 (64 tokens), B uses 6 (16 tokens, the base), and C uses 12 (4 tokens). Everything else is shared: width 32, depth 2, 4 heads, `position: \"none\"`, AdamW at lr 1e-3, 300 steps at batch 32, and identical data.\n\nThe key structural fact is that there is no positional encoding. The non-overlapping strided conv embeds each patch independently, attention is permutation-equivariant, and the head mean-pools over tokens. The output is therefore nearly invariant to token order. Relative position is a spatial-layout property, so the architecture has almost no direct path to it. Every choice is likely to sit near chance, with test cross-entropy close to ln 4 ≈ 1.386.\n\nWithin that near-chance regime, the differences come from optimization and calibration rather than from the ability to solve the task:\n\n- **C (patch 12):** Four tokens, each seeing a 12×12 region of both channels, give the shallowest attention computation and the fewest token interactions. Training is the most stable and least prone to overconfident logits, so I expect it to have the lowest held-out loss.\n- **B (patch 6):** The base configuration sits in the middle, with 16 tokens. It should be somewhat less stable than C but better calibrated than A.\n- **A (patch 3):** Sixty-four tokens with 18 input values each give a longer attention sequence and more capacity. With only ~9 epochs over 1024 samples, that extra capacity is more likely to yield noisy, overconfident predictions on held-out data than to learn position, since no positional signal exists to exploit. I expect the highest test loss.\n\nMaterial uncertainty: because the position signal is largely absent, all three may land within seed-to-seed noise of each other, so the B–C and A–B adjacencies are low-confidence. The C-best call is more plausible than the rest of the order. If the model does pick up some local-texture or mass-distribution cues, the finer tiling of A could help, which would reverse the expected order.", "model_identity_matches": true, "question_sha256": "0a08c68af53658c387e61079f81eb5be48c7c13909e4eb29ece0078e92e70391", "prompt_sha256": "bc802d4b5fa52f58451c3101a14cef4d8ee97309ddcf03e147976e005a8cba0d" }, { "model": "claude-haiku-5-5", "question_id": "q_7c4d6ba0c545202de44c8f79483454a8", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842902", "status": "complete", "gold_order": [ "C", "B", "A" ], "predicted_order": [ "A", "B", "C" ], "exact_order_correct": false, "public_content": "\nThe task is relative_position on 24×24 two-channel images, where the label depends on the relative displacement of a circle and a square. All three choices share the same tiny patch transformer (width 32, depth 2, 4 heads, no positional embedding), AdamW at lr 1e-3, 300 updates at batch size 32, and the same initial weights per seed. The only difference is the patch size of the initial convolutional patch embedding: A uses 3 (tokens = 8×8 = 64), B uses 6 (tokens = 4×4 = 16), and C uses 12 (tokens = 2×2 = 4).\n\nMain factors:\n- Spatial resolution of tokens. The label requires locating two objects and comparing their centers. Smaller patches keep more spatial detail (64 tokens), so the model can localize objects more precisely before pooling. Larger patches compress each object into fewer, coarser tokens, which hurts localization.\n- No positional encoding. With `position: \"none\"`, the mean-pooled output of the attention blocks is permutation-invariant over tokens. Each patch embedding must therefore encode its own absolute location through content alone, which is impossible for a convolution with fixed weights unless the content itself encodes position. This makes the model rely on the patch conv's per-patch features and on attention mixing across tokens. Relative-position reasoning is therefore hard in all three choices. Finer tokens give more chances for the content to carry partial location information (e.g., which token contains the object), so A has the most usable signal.\n- Parameter count and optimization. The patch conv has 2·p²·32 weights, so it is small for all choices. Training dynamics are similar; the attention cost and the number of tokens are the largest differences, with A having the most attention computation.\n\nRanking: A (patch 3) should reach the lowest cross entropy because it preserves the most spatial information. B (patch 6) is an intermediate compromise with 16 tokens. C (patch 12) reduces the image to 2×2 tokens, which leaves very little spatial structure to work with and should give the highest loss.\n\nUncertainty: With only 300 updates and no positional encoding, all models may remain close to chance-level cross entropy (around ln 4 ≈ 1.386), so the gaps between A and B could be small or within seed variance. The A-versus-B ordering is more confident than the B-versus-C ordering, which is the most uncertain pair given the limited training budget.\n\n\n{\"best_to_worst\": [\"A\", \"B\", \"C\"]}", "public_explanation": "The task is relative_position on 24×24 two-channel images, where the label depends on the relative displacement of a circle and a square. All three choices share the same tiny patch transformer (width 32, depth 2, 4 heads, no positional embedding), AdamW at lr 1e-3, 300 updates at batch size 32, and the same initial weights per seed. The only difference is the patch size of the initial convolutional patch embedding: A uses 3 (tokens = 8×8 = 64), B uses 6 (tokens = 4×4 = 16), and C uses 12 (tokens = 2×2 = 4).\n\nMain factors:\n- Spatial resolution of tokens. The label requires locating two objects and comparing their centers. Smaller patches keep more spatial detail (64 tokens), so the model can localize objects more precisely before pooling. Larger patches compress each object into fewer, coarser tokens, which hurts localization.\n- No positional encoding. With `position: \"none\"`, the mean-pooled output of the attention blocks is permutation-invariant over tokens. Each patch embedding must therefore encode its own absolute location through content alone, which is impossible for a convolution with fixed weights unless the content itself encodes position. This makes the model rely on the patch conv's per-patch features and on attention mixing across tokens. Relative-position reasoning is therefore hard in all three choices. Finer tokens give more chances for the content to carry partial location information (e.g., which token contains the object), so A has the most usable signal.\n- Parameter count and optimization. The patch conv has 2·p²·32 weights, so it is small for all choices. Training dynamics are similar; the attention cost and the number of tokens are the largest differences, with A having the most attention computation.\n\nRanking: A (patch 3) should reach the lowest cross entropy because it preserves the most spatial information. B (patch 6) is an intermediate compromise with 16 tokens. C (patch 12) reduces the image to 2×2 tokens, which leaves very little spatial structure to work with and should give the highest loss.\n\nUncertainty: With only 300 updates and no positional encoding, all models may remain close to chance-level cross entropy (around ln 4 ≈ 1.386), so the gaps between A and B could be small or within seed variance. The A-versus-B ordering is more confident than the B-versus-C ordering, which is the most uncertain pair given the limited training budget.", "model_identity_matches": true, "question_sha256": "c51f4fc9654aeccf18b9c0291212baf9c84872536be74d391e2f2fa11e711243", "prompt_sha256": "36003f34cf6c558f3bc65b4380aa27b0216aaad6c950d5ee4f4c399fc38c9dbc" }, { "model": "claude-haiku-5-5", "question_id": "q_c179b9eb52ffd8f3f234de5863020a7a", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_7c4d6ba0c545202de44c8f79483454a8" }, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842902", "status": "complete", "gold_order": [ "A", "C", "B" ], "predicted_order": [ "B", "C", "A" ], "exact_order_correct": false, "public_content": "\nThe three choices differ only in patch size of a two-layer, width-32 patch transformer on 24×24, 2-channel inputs. Everything else (AdamW at lr 1e-3, 300 updates at batch 32, clip 1.0, no positional encoding, mean-pooled tokens) is identical.\n\n- Choice B (patch 3): 8×8 = 64 tokens. Each token covers a 3×3 region. Attention can compare many local regions, and the mean-pooled readout keeps a fairly fine spatial summary.\n- Choice C (patch 6): 4×4 = 16 tokens. Each token covers a 6×6 region, so the model has coarser units and fewer tokens to attend over.\n- Choice A (patch 12): 2×2 = 4 tokens. Each token covers a 12×12 region, which is half the image. Only four tokens are available, so the model has very little spatial resolution for the task.\n\nThe task is `relative_position`: the model must determine the relative placement of a circle and a square, which requires spatial comparison across the image. Because there is no positional embedding, the model must recover location from patch content alone. Coarser patches hold more of each object's extent in a single token but make the precise center displacement harder to localize. Patch 3 retains the most spatial detail and the most attention structure, so it should reach the lowest cross entropy. Patch 6 is a middle ground. Patch 12 is the most restrictive, since with four tokens the relation between two objects is compressed heavily, and the mean pooling loses much of the positional signal.\n\nParameter counts are similar, since the patch embedding conv grows with patch area (2·p²·32 weights), but the difference is small relative to the transformer blocks. The main driver is token count and spatial granularity, not capacity.\n\nMaterial uncertainty: 300 steps of AdamW on 1024 examples is short training, so all models may still be underfit, and seed variance could blur the B-vs-C gap. The ordering C-vs-A is more clearly determined by token count, so I hold that pair with somewhat more confidence than B-vs-C.\n\n\n{\"best_to_worst\": [\"B\", \"C\", \"A\"]}", "public_explanation": "The three choices differ only in patch size of a two-layer, width-32 patch transformer on 24×24, 2-channel inputs. Everything else (AdamW at lr 1e-3, 300 updates at batch 32, clip 1.0, no positional encoding, mean-pooled tokens) is identical.\n\n- Choice B (patch 3): 8×8 = 64 tokens. Each token covers a 3×3 region. Attention can compare many local regions, and the mean-pooled readout keeps a fairly fine spatial summary.\n- Choice C (patch 6): 4×4 = 16 tokens. Each token covers a 6×6 region, so the model has coarser units and fewer tokens to attend over.\n- Choice A (patch 12): 2×2 = 4 tokens. Each token covers a 12×12 region, which is half the image. Only four tokens are available, so the model has very little spatial resolution for the task.\n\nThe task is `relative_position`: the model must determine the relative placement of a circle and a square, which requires spatial comparison across the image. Because there is no positional embedding, the model must recover location from patch content alone. Coarser patches hold more of each object's extent in a single token but make the precise center displacement harder to localize. Patch 3 retains the most spatial detail and the most attention structure, so it should reach the lowest cross entropy. Patch 6 is a middle ground. Patch 12 is the most restrictive, since with four tokens the relation between two objects is compressed heavily, and the mean pooling loses much of the positional signal.\n\nParameter counts are similar, since the patch embedding conv grows with patch area (2·p²·32 weights), but the difference is small relative to the transformer blocks. The main driver is token count and spatial granularity, not capacity.\n\nMaterial uncertainty: 300 steps of AdamW on 1024 examples is short training, so all models may still be underfit, and seed variance could blur the B-vs-C gap. The ordering C-vs-A is more clearly determined by token count, so I hold that pair with somewhat more confidence than B-vs-C.", "model_identity_matches": true, "question_sha256": "4327fab3306887d72c21d9fbe2f5c301db6ab223eac36525743fd056e18528f9", "prompt_sha256": "c24266d7c88d813d3534d88aaed5c8b684604ff9d5ee731d7863c25fba7a9432" }, { "model": "claude-haiku-5-5", "question_id": "q_76cac3671eecb9ff4306d1b86e28b45c", "family": "image_classification", "task": "ranking3", "probe": null, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842903", "status": "complete", "gold_order": [ "B", "C", "A" ], "predicted_order": [ "A", "C", "B" ], "exact_order_correct": false, "public_content": "\nThe three choices differ only in the patch size of the patch-embedding convolution: A uses 3 (a 8×8 = 64-token grid), B uses 12 (a 2×2 = 4-token grid), and C uses 6 (a 4×4 = 16-token grid). Width (32), depth (2), heads (4), optimizer, loss, data, budget (300 steps, batch 32), and seeds are all shared.\n\nMain factors:\n- **Tokenization granularity.** The task is a relative-position or shape/texture decision over a 24×24 two-channel image. With patch 3, each token covers a 3×3 region, so the model retains fine spatial structure and can attend across 64 tokens. Mean pooling over tokens then feeds the head. This gives the most spatial resolution for localizing the relative displacement between two objects.\n- **Capacity to localize.** Patch 12 yields only 4 tokens, each embedding 12×12 pixels linearly, so the first layer must summarize large regions with a single linear projection. Relative position of the circle versus the square is hard to encode in such coarse tokens, and the attention layers have little to work with. Patch 6 sits in between (16 tokens).\n- **Learning dynamics.** With no positional encoding, the model is permutation-invariant over tokens. The mean pooling therefore discards where each token sits. Position information must come entirely from the content of each patch embedding. Larger patches make this harder because the patch content must encode absolute position within a larger region, which favors finer patches in this setup. Fewer tokens also mean less attention capacity to route information.\n- **Training budget.** All runs use 300 AdamW steps at lr 1e-3, so optimization is short and roughly comparable. Choices with larger token counts may fit more slowly per step but have more usable signal.\n\nRanking rationale: A (patch 3) is predicted best because its fine tokenization preserves the most localization signal under the shared budget. C (patch 6) is predicted second, retaining a useful grid while being coarser. B (patch 12) is predicted worst because 4 tokens cannot represent the relative geometry well without positional information.\n\nMaterial uncertainty: the gap between A and C may be small, since both have enough tokens to see both objects, and the absolute losses may be close with overlapping seed variance over 16 seeds. The ordering of B relative to the others is the more confident part of the prediction. Short training could also cause some surprises if a coarser model converges faster on the dominant axis-of-displacement cue.\n\n\n{\"best_to_worst\": [\"A\", \"C\", \"B\"]}", "public_explanation": "The three choices differ only in the patch size of the patch-embedding convolution: A uses 3 (a 8×8 = 64-token grid), B uses 12 (a 2×2 = 4-token grid), and C uses 6 (a 4×4 = 16-token grid). Width (32), depth (2), heads (4), optimizer, loss, data, budget (300 steps, batch 32), and seeds are all shared.\n\nMain factors:\n- **Tokenization granularity.** The task is a relative-position or shape/texture decision over a 24×24 two-channel image. With patch 3, each token covers a 3×3 region, so the model retains fine spatial structure and can attend across 64 tokens. Mean pooling over tokens then feeds the head. This gives the most spatial resolution for localizing the relative displacement between two objects.\n- **Capacity to localize.** Patch 12 yields only 4 tokens, each embedding 12×12 pixels linearly, so the first layer must summarize large regions with a single linear projection. Relative position of the circle versus the square is hard to encode in such coarse tokens, and the attention layers have little to work with. Patch 6 sits in between (16 tokens).\n- **Learning dynamics.** With no positional encoding, the model is permutation-invariant over tokens. The mean pooling therefore discards where each token sits. Position information must come entirely from the content of each patch embedding. Larger patches make this harder because the patch content must encode absolute position within a larger region, which favors finer patches in this setup. Fewer tokens also mean less attention capacity to route information.\n- **Training budget.** All runs use 300 AdamW steps at lr 1e-3, so optimization is short and roughly comparable. Choices with larger token counts may fit more slowly per step but have more usable signal.\n\nRanking rationale: A (patch 3) is predicted best because its fine tokenization preserves the most localization signal under the shared budget. C (patch 6) is predicted second, retaining a useful grid while being coarser. B (patch 12) is predicted worst because 4 tokens cannot represent the relative geometry well without positional information.\n\nMaterial uncertainty: the gap between A and C may be small, since both have enough tokens to see both objects, and the absolute losses may be close with overlapping seed variance over 16 seeds. The ordering of B relative to the others is the more confident part of the prediction. Short training could also cause some surprises if a coarser model converges faster on the dominant axis-of-displacement cue.", "model_identity_matches": true, "question_sha256": "6b4fa08d1969fd32b3dd6aa13fe9c2ee0d4666d4e7cbcf203da570a32971d052", "prompt_sha256": "13573df98c8675006a14f0c15c929b41bdcdcb74b326cf53f235898480a567dc" }, { "model": "claude-haiku-5-5", "question_id": "q_21ca0ff91a02c38e27e1bebe5867c24d", "family": "image_classification", "task": "ranking3", "probe": { "type": "letter_permutation", "source_question_id": "q_76cac3671eecb9ff4306d1b86e28b45c" }, "template_id": "patch_coordinate_retention", "instance_id": "patch_coordinate_retention_s842903", "status": "complete", "gold_order": [ "C", "A", "B" ], "predicted_order": [ "B", "A", "C" ], "exact_order_correct": false, "public_content": "\nThe three choices differ only in the patch size of the patch-transformer's first-layer convolution: Choice B uses patch 3 (a 8×8 = 64-token grid), Choice A uses patch 6 (4×4 = 16 tokens), and Choice C uses patch 12 (2×2 = 4 tokens). Width, depth, heads, optimizer, loss, budget (300 AdamW steps, batch 32), and seeds are identical.\n\nMain factors:\n- **Receptive field and spatial resolution.** The task is `relative_position` on 24×24 images, where circle and square centers are separated by at least about 2.9 pixels along the dominant axis. Patch 3 keeps fine spatial detail, so the transformer can localize both objects precisely. Patch 6 still resolves coarse positions. Patch 12 leaves only a 2×2 grid, so the pooled tokens can barely encode which object lies left/right/above/below the other.\n- **Information bottleneck before attention.** Attention with no positional embedding (`position: none`) is permutation-invariant over tokens, and the final mean-pool discards token order entirely. Position information therefore has to come from the patch content itself. Smaller patches carry more of it per token, so the mean-pooled representation retains more relative-location signal. Larger patches compress more of that signal into each token before pooling.\n- **Optimization.** With 300 steps and a fixed learning rate, a larger token count (patch 3) gives more attention structure to fit, but the model is small (width 32), so optimization is still fast. Patch 12 has very few tokens and the least capacity to express the target, so it is likely to plateau at higher cross-entropy.\n\nRanking: B (patch 3) < A (patch 6) < C (patch 12). The adjacent pair B vs. A is the more uncertain comparison, since both have enough resolution to make progress in 300 steps and seed variance could reorder them. A vs. C is more clearly separated by the token-count bottleneck. Material uncertainty remains because the model is trained for only 300 updates, so under-training could compress differences, and I have not verified these expectations empirically.\n\n\n{\"best_to_worst\": [\"B\", \"A\", \"C\"]}", "public_explanation": "The three choices differ only in the patch size of the patch-transformer's first-layer convolution: Choice B uses patch 3 (a 8×8 = 64-token grid), Choice A uses patch 6 (4×4 = 16 tokens), and Choice C uses patch 12 (2×2 = 4 tokens). Width, depth, heads, optimizer, loss, budget (300 AdamW steps, batch 32), and seeds are identical.\n\nMain factors:\n- **Receptive field and spatial resolution.** The task is `relative_position` on 24×24 images, where circle and square centers are separated by at least about 2.9 pixels along the dominant axis. Patch 3 keeps fine spatial detail, so the transformer can localize both objects precisely. Patch 6 still resolves coarse positions. Patch 12 leaves only a 2×2 grid, so the pooled tokens can barely encode which object lies left/right/above/below the other.\n- **Information bottleneck before attention.** Attention with no positional embedding (`position: none`) is permutation-invariant over tokens, and the final mean-pool discards token order entirely. Position information therefore has to come from the patch content itself. Smaller patches carry more of it per token, so the mean-pooled representation retains more relative-location signal. Larger patches compress more of that signal into each token before pooling.\n- **Optimization.** With 300 steps and a fixed learning rate, a larger token count (patch 3) gives more attention structure to fit, but the model is small (width 32), so optimization is still fast. Patch 12 has very few tokens and the least capacity to express the target, so it is likely to plateau at higher cross-entropy.\n\nRanking: B (patch 3) < A (patch 6) < C (patch 12). The adjacent pair B vs. A is the more uncertain comparison, since both have enough resolution to make progress in 300 steps and seed variance could reorder them. A vs. C is more clearly separated by the token-count bottleneck. Material uncertainty remains because the model is trained for only 300 updates, so under-training could compress differences, and I have not verified these expectations empirically.", "model_identity_matches": true, "question_sha256": "1ed74fdb24c4279febc8cc25695345ccb4178c002376e9f1e11c40ce1a5ae945", "prompt_sha256": "1b542c782593bec4e9a3b63caea8a34c2f95b491fcda8e2027d39985b3b21047" } ], "missing": [ { "requested_model": "gpt-6-luna", "question_id": "q_f41ad89255f54a110a6b78ac32e08910", "probe": null }, { "requested_model": "gpt-6-luna", "question_id": "q_dc6a1198c1d2e494edd7b3618c36bf0b", "probe": null }, { "requested_model": "gpt-6-luna", "question_id": "q_a03647bbfbcd65d2146723676eb79259", "probe": null }, { "requested_model": "gpt-6-luna", "question_id": "q_8da922eda3a7c018f59492bcb3c32238", "probe": { "type": "letter_permutation", "source_question_id": "q_5aa7514c54a69ed6cf080475ebf4304e" } }, { "requested_model": "gpt-6.1-sol", "question_id": "q_f2e0f5463396043d48d5c5ae87bedb87", "probe": { "type": "letter_permutation", "source_question_id": "q_f41ad89255f54a110a6b78ac32e08910" } }, { "requested_model": "gpt-6.1-sol", "question_id": "q_2e828a18000b8cfc54065a359bf0ab04", "probe": null }, { "requested_model": "gpt-6.1-sol", "question_id": "q_7c4d6ba0c545202de44c8f79483454a8", "probe": null }, { "requested_model": "gpt-6.1-sol", "question_id": "q_c179b9eb52ffd8f3f234de5863020a7a", "probe": { "type": "letter_permutation", "source_question_id": "q_7c4d6ba0c545202de44c8f79483454a8" } } ], "contains_raw_transport_attempts": false }