{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:2SAIDR7M2WPV7CH7FZDBIZHXK4","short_pith_number":"pith:2SAIDR7M","canonical_record":{"source":{"id":"2201.02177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-06T18:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"aae4d6517ec56064910e587d7f48ff6067f4834ca66c4d0cf2947700346a86e2","abstract_canon_sha256":"9511d9be986d9d2a086afb5f53cb431ab6087348ade0e71e49051b0cff454e96"},"schema_version":"1.0"},"canonical_sha256":"d48081c7ecd59f5f88ff2e461464f757251ab620ace18acefaa0fcc821db0179","source":{"kind":"arxiv","id":"2201.02177","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.02177","created_at":"2026-07-05T03:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"2201.02177v1","created_at":"2026-07-05T03:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.02177","created_at":"2026-07-05T03:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"2SAIDR7M2WPV","created_at":"2026-07-05T03:46:30Z"},{"alias_kind":"pith_short_16","alias_value":"2SAIDR7M2WPV7CH7","created_at":"2026-07-05T03:46:30Z"},{"alias_kind":"pith_short_8","alias_value":"2SAIDR7M","created_at":"2026-07-05T03:46:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:2SAIDR7M2WPV7CH7FZDBIZHXK4","target":"record","payload":{"canonical_record":{"source":{"id":"2201.02177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-06T18:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"aae4d6517ec56064910e587d7f48ff6067f4834ca66c4d0cf2947700346a86e2","abstract_canon_sha256":"9511d9be986d9d2a086afb5f53cb431ab6087348ade0e71e49051b0cff454e96"},"schema_version":"1.0"},"canonical_sha256":"d48081c7ecd59f5f88ff2e461464f757251ab620ace18acefaa0fcc821db0179","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:46:30.869032Z","signature_b64":"0uUZRL+L8CN7/dB6L1uC/EHiB2Yz4X68je6WYVun+WvrpGidRWpjUVmSEdYkC9z1KNUswyooVj+vemkHFUkIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d48081c7ecd59f5f88ff2e461464f757251ab620ace18acefaa0fcc821db0179","last_reissued_at":"2026-07-05T03:46:30.868533Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:46:30.868533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.02177","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OQzH9GIysXnjzwgggfUEGiUGzhrfetz1K9SJCFGcqUeMif4wRk+BqpiPJU5KXh/63UNTS+FRJb8p1TrY/z97Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:33:46.798896Z"},"content_sha256":"78dca19ebd598d03946e83657149fef521bca123419f83699b36ae165e3b22dc","schema_version":"1.0","event_id":"sha256:78dca19ebd598d03946e83657149fef521bca123419f83699b36ae165e3b22dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:2SAIDR7M2WPV7CH7FZDBIZHXK4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Neural networks can suddenly achieve perfect generalization on small algorithmic tasks long after they have overfitted the training data.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Alethea Power, Harri Edwards, Igor Babuschkin, Vedant Misra, Yuri Burda","submitted_at":"2022-01-06T18:43:37Z","abstract_excerpt":"In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great detail. In some situations we show that neural networks learn through a process of \"grokking\" a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting. We also study generalization as a function of dataset size and f"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In some situations we show that neural networks learn through a process of 'grokking' a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the grokking behavior observed on these specific small algorithmic datasets reveals a general mechanism of neural network generalization rather than an artifact limited to the chosen tasks, architectures, and optimization regimes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Neural networks exhibit grokking on small algorithmic datasets, achieving perfect generalization well after overfitting.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Neural networks can suddenly achieve perfect generalization on small algorithmic tasks long after they have overfitted the training data.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"722347474a71b625707310696fdf048a17f2606f7da93d0152416b1e8593c9be"},"source":{"id":"2201.02177","kind":"arxiv","version":1},"verdict":{"id":"722bb388-3eae-4008-9e68-1e1a9619c700","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-11T19:22:31.706868Z","strongest_claim":"In some situations we show that neural networks learn through a process of 'grokking' a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting.","one_line_summary":"Neural networks exhibit grokking on small algorithmic datasets, achieving perfect generalization well after overfitting.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the grokking behavior observed on these specific small algorithmic datasets reveals a general mechanism of neural network generalization rather than an artifact limited to the chosen tasks, architectures, and optimization regimes.","pith_extraction_headline":"Neural networks can suddenly achieve perfect generalization on small algorithmic tasks long after they have overfitted the training data."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.02177/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":21,"sample":[{"doi":"","year":null,"title":"Proceedings of the National Academy of Sciences , volume =","work_id":"ec4e299e-f6bc-4097-a042-a9ff15850254","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"Triple descent and the two kinds of overfitting: Where & why do they appear? arXiv preprint arXiv:2006.03509","work_id":"a976b8b9-3127-44ae-8c63-5bb1981f52b9","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Universal Transformers","work_id":"8e5baefe-d209-411c-aefc-5acaa9275c8a","ref_index":3,"cited_arxiv_id":"1807.03819","is_internal_anchor":true},{"doi":"","year":null,"title":"Adaptive Computation Time for Recurrent Neural Networks","work_id":"75565443-173e-479c-b0e7-d2464e7630be","ref_index":4,"cited_arxiv_id":"1603.08983","is_internal_anchor":true},{"doi":"","year":null,"title":"Neural Turing Machines","work_id":"0a5ce53c-9670-42b9-8be5-386de7eed50c","ref_index":5,"cited_arxiv_id":"1410.5401","is_internal_anchor":true}],"resolved_work":21,"snapshot_sha256":"aca0d12721867ceeb06e20b696af507876ecb2a27f2b8eceb01e51b33c548201","internal_anchors":7},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"722bb388-3eae-4008-9e68-1e1a9619c700"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7tn57OdrhAV1zLD0iocvnstUUK/uDjfxk4cqQKzcznHKFbp8VO3B9fcQjbG1G2jlLY2/tSEJJi08oseTnjsBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:33:46.799508Z"},"content_sha256":"42777f7af9c14625172f6c66b6fed6980698175db7f7d226c1efde938c338c82","schema_version":"1.0","event_id":"sha256:42777f7af9c14625172f6c66b6fed6980698175db7f7d226c1efde938c338c82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2SAIDR7M2WPV7CH7FZDBIZHXK4/bundle.json","state_url":"https://pith.science/pith/2SAIDR7M2WPV7CH7FZDBIZHXK4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2SAIDR7M2WPV7CH7FZDBIZHXK4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T11:33:46Z","links":{"resolver":"https://pith.science/pith/2SAIDR7M2WPV7CH7FZDBIZHXK4","bundle":"https://pith.science/pith/2SAIDR7M2WPV7CH7FZDBIZHXK4/bundle.json","state":"https://pith.science/pith/2SAIDR7M2WPV7CH7FZDBIZHXK4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2SAIDR7M2WPV7CH7FZDBIZHXK4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2SAIDR7M2WPV7CH7FZDBIZHXK4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9511d9be986d9d2a086afb5f53cb431ab6087348ade0e71e49051b0cff454e96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-06T18:43:37Z","title_canon_sha256":"aae4d6517ec56064910e587d7f48ff6067f4834ca66c4d0cf2947700346a86e2"},"schema_version":"1.0","source":{"id":"2201.02177","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.02177","created_at":"2026-07-05T03:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"2201.02177v1","created_at":"2026-07-05T03:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.02177","created_at":"2026-07-05T03:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"2SAIDR7M2WPV","created_at":"2026-07-05T03:46:30Z"},{"alias_kind":"pith_short_16","alias_value":"2SAIDR7M2WPV7CH7","created_at":"2026-07-05T03:46:30Z"},{"alias_kind":"pith_short_8","alias_value":"2SAIDR7M","created_at":"2026-07-05T03:46:30Z"}],"graph_snapshots":[{"event_id":"sha256:42777f7af9c14625172f6c66b6fed6980698175db7f7d226c1efde938c338c82","target":"graph","created_at":"2026-07-05T03:46:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"In some situations we show that neural networks learn through a process of 'grokking' a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the grokking behavior observed on these specific small algorithmic datasets reveals a general mechanism of neural network generalization rather than an artifact limited to the chosen tasks, architectures, and optimization regimes."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Neural networks exhibit grokking on small algorithmic datasets, achieving perfect generalization well after overfitting."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Neural networks can suddenly achieve perfect generalization on small algorithmic tasks long after they have overfitted the training data."}],"snapshot_sha256":"722347474a71b625707310696fdf048a17f2606f7da93d0152416b1e8593c9be"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2201.02177/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great detail. In some situations we show that neural networks learn through a process of \"grokking\" a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting. We also study generalization as a function of dataset size and f","authors_text":"Alethea Power, Harri Edwards, Igor Babuschkin, Vedant Misra, Yuri Burda","cross_cats":[],"headline":"Neural networks can suddenly achieve perfect generalization on small algorithmic tasks long after they have overfitted the training data.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-06T18:43:37Z","title":"Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets"},"references":{"count":21,"internal_anchors":7,"resolved_work":21,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Proceedings of the National Academy of Sciences , volume =","work_id":"ec4e299e-f6bc-4097-a042-a9ff15850254","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Triple descent and the two kinds of overfitting: Where & why do they appear? arXiv preprint arXiv:2006.03509","work_id":"a976b8b9-3127-44ae-8c63-5bb1981f52b9","year":2006},{"cited_arxiv_id":"1807.03819","doi":"","is_internal_anchor":true,"ref_index":3,"title":"Universal Transformers","work_id":"8e5baefe-d209-411c-aefc-5acaa9275c8a","year":null},{"cited_arxiv_id":"1603.08983","doi":"","is_internal_anchor":true,"ref_index":4,"title":"Adaptive Computation Time for Recurrent Neural Networks","work_id":"75565443-173e-479c-b0e7-d2464e7630be","year":null},{"cited_arxiv_id":"1410.5401","doi":"","is_internal_anchor":true,"ref_index":5,"title":"Neural Turing Machines","work_id":"0a5ce53c-9670-42b9-8be5-386de7eed50c","year":null}],"snapshot_sha256":"aca0d12721867ceeb06e20b696af507876ecb2a27f2b8eceb01e51b33c548201"},"source":{"id":"2201.02177","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-11T19:22:31.706868Z","id":"722bb388-3eae-4008-9e68-1e1a9619c700","model_set":{"reader":"grok-4.3"},"one_line_summary":"Neural networks exhibit grokking on small algorithmic datasets, achieving perfect generalization well after overfitting.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Neural networks can suddenly achieve perfect generalization on small algorithmic tasks long after they have overfitted the training data.","strongest_claim":"In some situations we show that neural networks learn through a process of 'grokking' a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting.","weakest_assumption":"That the grokking behavior observed on these specific small algorithmic datasets reveals a general mechanism of neural network generalization rather than an artifact limited to the chosen tasks, architectures, and optimization regimes."}},"verdict_id":"722bb388-3eae-4008-9e68-1e1a9619c700"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:78dca19ebd598d03946e83657149fef521bca123419f83699b36ae165e3b22dc","target":"record","created_at":"2026-07-05T03:46:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9511d9be986d9d2a086afb5f53cb431ab6087348ade0e71e49051b0cff454e96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-06T18:43:37Z","title_canon_sha256":"aae4d6517ec56064910e587d7f48ff6067f4834ca66c4d0cf2947700346a86e2"},"schema_version":"1.0","source":{"id":"2201.02177","kind":"arxiv","version":1}},"canonical_sha256":"d48081c7ecd59f5f88ff2e461464f757251ab620ace18acefaa0fcc821db0179","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d48081c7ecd59f5f88ff2e461464f757251ab620ace18acefaa0fcc821db0179","first_computed_at":"2026-07-05T03:46:30.868533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:46:30.868533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0uUZRL+L8CN7/dB6L1uC/EHiB2Yz4X68je6WYVun+WvrpGidRWpjUVmSEdYkC9z1KNUswyooVj+vemkHFUkIAA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:46:30.869032Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.02177","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78dca19ebd598d03946e83657149fef521bca123419f83699b36ae165e3b22dc","sha256:42777f7af9c14625172f6c66b6fed6980698175db7f7d226c1efde938c338c82"],"state_sha256":"be634dd31936484bca4e8690e29c7011311664caebdd00b19ef0d3cf781b9a31"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJUn7Rw2VoMh2cNYHwr1sbeh5eABA1EnG1aFIOW1HdEaN4fQnpqtpXi3tcTHr0rIkWi3t29uvDVp2jjPPcPNBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:33:46.802007Z","bundle_sha256":"bd5d7480e2bd3bd79f49efe863737512c6d78f60259634e3c01e93bcbc97436e"}}