{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:IVBAEHAJ3QQH5NPM5DJTENGJWL","short_pith_number":"pith:IVBAEHAJ","schema_version":"1.0","canonical_sha256":"4542021c09dc207eb5ece8d33234c9b2c2351df4d6e43abb9eee3326270eedae","source":{"kind":"arxiv","id":"2107.03402","version":1},"attestation_state":"computed","paper":{"title":"Self-organized criticality in neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.LG"],"primary_cat":"cond-mat.stat-mech","authors_text":"Mikhail I. Katsnelson, Tom Westerhout, Vitaly Vanchurin","submitted_at":"2021-07-07T18:00:03Z","abstract_excerpt":"We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable variables (e.g. states of neurons) and trainable variables (e.g. weight matrix). Non-trainable variables are rapidly driven towards stochastic equilibrium and trainable variables are slowly driven towards learning equilibrium described by a scale-invariant distribution on a wide range of scales. Our results suggest that the scale invariance observed in many physica"},"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":"2107.03402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2021-07-07T18:00:03Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG"],"title_canon_sha256":"654cb68133dbdf4ac769ebb37317624dee6872c627b144710d0d4940d878c3bc","abstract_canon_sha256":"be728dcf2a82036f994e7cf6994b765c47707900155b2e5bfc6de0f715234baf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:56:05.613593Z","signature_b64":"Wlhx/LQRsInlO7ZmNfD/OG2YOxjSz0LrsrBvOfWT/D50TSfbGVayuS2XOnUyQ49C2dbw3BdOO/sVNWi/V4a/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4542021c09dc207eb5ece8d33234c9b2c2351df4d6e43abb9eee3326270eedae","last_reissued_at":"2026-07-05T02:56:05.612852Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:56:05.612852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-organized criticality in neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.LG"],"primary_cat":"cond-mat.stat-mech","authors_text":"Mikhail I. Katsnelson, Tom Westerhout, Vitaly Vanchurin","submitted_at":"2021-07-07T18:00:03Z","abstract_excerpt":"We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable variables (e.g. states of neurons) and trainable variables (e.g. weight matrix). Non-trainable variables are rapidly driven towards stochastic equilibrium and trainable variables are slowly driven towards learning equilibrium described by a scale-invariant distribution on a wide range of scales. Our results suggest that the scale invariance observed in many physica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.03402","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/2107.03402/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":"2107.03402","created_at":"2026-07-05T02:56:05.612937+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.03402v1","created_at":"2026-07-05T02:56:05.612937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.03402","created_at":"2026-07-05T02:56:05.612937+00:00"},{"alias_kind":"pith_short_12","alias_value":"IVBAEHAJ3QQH","created_at":"2026-07-05T02:56:05.612937+00:00"},{"alias_kind":"pith_short_16","alias_value":"IVBAEHAJ3QQH5NPM","created_at":"2026-07-05T02:56:05.612937+00:00"},{"alias_kind":"pith_short_8","alias_value":"IVBAEHAJ","created_at":"2026-07-05T02:56:05.612937+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2601.19070","citing_title":"Critical Organization of Deep Neural Networks, and p-Adic Statistical Field Theories","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL","json":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL.json","graph_json":"https://pith.science/api/pith-number/IVBAEHAJ3QQH5NPM5DJTENGJWL/graph.json","events_json":"https://pith.science/api/pith-number/IVBAEHAJ3QQH5NPM5DJTENGJWL/events.json","paper":"https://pith.science/paper/IVBAEHAJ"},"agent_actions":{"view_html":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL","download_json":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL.json","view_paper":"https://pith.science/paper/IVBAEHAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.03402&json=true","fetch_graph":"https://pith.science/api/pith-number/IVBAEHAJ3QQH5NPM5DJTENGJWL/graph.json","fetch_events":"https://pith.science/api/pith-number/IVBAEHAJ3QQH5NPM5DJTENGJWL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/action/storage_attestation","attest_author":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/action/author_attestation","sign_citation":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/action/citation_signature","submit_replication":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/action/replication_record"}},"created_at":"2026-07-05T02:56:05.612937+00:00","updated_at":"2026-07-05T02:56:05.612937+00:00"}