{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:HIMDRPSVDM6SWNKPEGXMZUXMTD","short_pith_number":"pith:HIMDRPSV","schema_version":"1.0","canonical_sha256":"3a1838be551b3d2b354f21aeccd2ec98f39f89a6060c073fe9f8dca5b21649bb","source":{"kind":"arxiv","id":"2210.15435","version":1},"attestation_state":"computed","paper":{"title":"Grokking phase transitions in learning local rules with gradient descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cond-mat.stat-mech","authors_text":"Bojan \\v{Z}unkovi\\v{c}, Enej Ilievski","submitted_at":"2022-10-26T11:07:04Z","abstract_excerpt":"We discuss two solvable grokking (generalisation beyond overfitting) models in a rule learning scenario. We show that grokking is a phase transition and find exact analytic expressions for the critical exponents, grokking probability, and grokking time distribution. Further, we introduce a tensor-network map that connects the proposed grokking setup with the standard (perceptron) statistical learning theory and show that grokking is a consequence of the locality of the teacher model. As an example, we analyse the cellular automata learning task, numerically determine the critical exponent and "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2210.15435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2022-10-26T11:07:04Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"d5be81131b242d5b512dfbdab527ce03a5dbee06edd5aca2ef78a18419dc1b15","abstract_canon_sha256":"710c1fc39114b0acd8efaf1e16d6a68cd3def7a8fccede1f16e063c7fa9fdaaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:11:06.196563Z","signature_b64":"HZMlo23oa+CikL2xe41iuvo9/PrX0RzRbaX8QgcM/zSTaTJO6p+dk9tKImINe90eDPn8bG1LEgBGcIaGLcCLAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a1838be551b3d2b354f21aeccd2ec98f39f89a6060c073fe9f8dca5b21649bb","last_reissued_at":"2026-07-05T05:11:06.196080Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:11:06.196080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Grokking phase transitions in learning local rules with gradient descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cond-mat.stat-mech","authors_text":"Bojan \\v{Z}unkovi\\v{c}, Enej Ilievski","submitted_at":"2022-10-26T11:07:04Z","abstract_excerpt":"We discuss two solvable grokking (generalisation beyond overfitting) models in a rule learning scenario. We show that grokking is a phase transition and find exact analytic expressions for the critical exponents, grokking probability, and grokking time distribution. Further, we introduce a tensor-network map that connects the proposed grokking setup with the standard (perceptron) statistical learning theory and show that grokking is a consequence of the locality of the teacher model. As an example, we analyse the cellular automata learning task, numerically determine the critical exponent and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.15435","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.15435/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2210.15435","created_at":"2026-07-05T05:11:06.196138+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.15435v1","created_at":"2026-07-05T05:11:06.196138+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.15435","created_at":"2026-07-05T05:11:06.196138+00:00"},{"alias_kind":"pith_short_12","alias_value":"HIMDRPSVDM6S","created_at":"2026-07-05T05:11:06.196138+00:00"},{"alias_kind":"pith_short_16","alias_value":"HIMDRPSVDM6SWNKP","created_at":"2026-07-05T05:11:06.196138+00:00"},{"alias_kind":"pith_short_8","alias_value":"HIMDRPSV","created_at":"2026-07-05T05:11:06.196138+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.22873","citing_title":"SingGuard: A Policy-Adaptive Multimodal LLM Guardrail with Dynamic Reasoning","ref_index":82,"is_internal_anchor":false},{"citing_arxiv_id":"2606.22873","citing_title":"SingGuard: A Policy-Adaptive Multimodal LLM Guardrail with Dynamic Reasoning","ref_index":82,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HIMDRPSVDM6SWNKPEGXMZUXMTD","json":"https://pith.science/pith/HIMDRPSVDM6SWNKPEGXMZUXMTD.json","graph_json":"https://pith.science/api/pith-number/HIMDRPSVDM6SWNKPEGXMZUXMTD/graph.json","events_json":"https://pith.science/api/pith-number/HIMDRPSVDM6SWNKPEGXMZUXMTD/events.json","paper":"https://pith.science/paper/HIMDRPSV"},"agent_actions":{"view_html":"https://pith.science/pith/HIMDRPSVDM6SWNKPEGXMZUXMTD","download_json":"https://pith.science/pith/HIMDRPSVDM6SWNKPEGXMZUXMTD.json","view_paper":"https://pith.science/paper/HIMDRPSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.15435&json=true","fetch_graph":"https://pith.science/api/pith-number/HIMDRPSVDM6SWNKPEGXMZUXMTD/graph.json","fetch_events":"https://pith.science/api/pith-number/HIMDRPSVDM6SWNKPEGXMZUXMTD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HIMDRPSVDM6SWNKPEGXMZUXMTD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HIMDRPSVDM6SWNKPEGXMZUXMTD/action/storage_attestation","attest_author":"https://pith.science/pith/HIMDRPSVDM6SWNKPEGXMZUXMTD/action/author_attestation","sign_citation":"https://pith.science/pith/HIMDRPSVDM6SWNKPEGXMZUXMTD/action/citation_signature","submit_replication":"https://pith.science/pith/HIMDRPSVDM6SWNKPEGXMZUXMTD/action/replication_record"}},"created_at":"2026-07-05T05:11:06.196138+00:00","updated_at":"2026-07-05T05:11:06.196138+00:00"}