{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TKDOH5VEMQIPF6XGFLPWEXLJ74","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":"e66e15c823b68b148041597258040fa3919fdb0a9ea5346abafe7e7b69bcc977","cross_cats_sorted":["cs.LG","physics.data-an"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-31T10:49:55Z","title_canon_sha256":"0d1d5a90ac5df761c473141633247bc7d76883399cd2b6ae10a5ec541dee9ec7"},"schema_version":"1.0","source":{"id":"2112.15383","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.15383","created_at":"2026-07-05T05:00:14Z"},{"alias_kind":"arxiv_version","alias_value":"2112.15383v3","created_at":"2026-07-05T05:00:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.15383","created_at":"2026-07-05T05:00:14Z"},{"alias_kind":"pith_short_12","alias_value":"TKDOH5VEMQIP","created_at":"2026-07-05T05:00:14Z"},{"alias_kind":"pith_short_16","alias_value":"TKDOH5VEMQIPF6XG","created_at":"2026-07-05T05:00:14Z"},{"alias_kind":"pith_short_8","alias_value":"TKDOH5VE","created_at":"2026-07-05T05:00:14Z"}],"graph_snapshots":[{"event_id":"sha256:ae40605ec21721826afa9fcbd5be1ee783fddfd081aed182f18990f102d92ee4","target":"graph","created_at":"2026-07-05T05:00:14Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.15383/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deep neural networks (DNNs) are powerful tools for compressing and distilling information. Their scale and complexity, often involving billions of inter-dependent parameters, render direct microscopic analysis difficult. Under such circumstances, a common strategy is to identify slow variables that average the erratic behavior of the fast microscopic variables. Here, we identify a similar separation of scales occurring in fully trained finitely over-parameterized deep convolutional neural networks (CNNs) and fully connected networks (FCNs). Specifically, we show that DNN layers couple only thr","authors_text":"Gadi Naveh, Inbar Seroussi, Zohar Ringel","cross_cats":["cs.LG","physics.data-an"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-31T10:49:55Z","title":"Separation of Scales and a Thermodynamic Description of Feature Learning in Some CNNs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.15383","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5df108a7614478be9b0c2cea90c3ee245f0e08d2aa031d0b9d902a1f5a99e0e5","target":"record","created_at":"2026-07-05T05:00:14Z","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":"e66e15c823b68b148041597258040fa3919fdb0a9ea5346abafe7e7b69bcc977","cross_cats_sorted":["cs.LG","physics.data-an"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-31T10:49:55Z","title_canon_sha256":"0d1d5a90ac5df761c473141633247bc7d76883399cd2b6ae10a5ec541dee9ec7"},"schema_version":"1.0","source":{"id":"2112.15383","kind":"arxiv","version":3}},"canonical_sha256":"9a86e3f6a46410f2fae62adf625d69ff233a892d6b42082f341a080dfaefc53b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a86e3f6a46410f2fae62adf625d69ff233a892d6b42082f341a080dfaefc53b","first_computed_at":"2026-07-05T05:00:14.783194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:00:14.783194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZE2UPBya4TdBb5rZfcSl3QcVuC1mNPP5SC3N+0mSrKYFmkVR3VOfgh4kXUMLMOTEAFdPKgL/5fo7QSjBKad2Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:00:14.783632Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.15383","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5df108a7614478be9b0c2cea90c3ee245f0e08d2aa031d0b9d902a1f5a99e0e5","sha256:ae40605ec21721826afa9fcbd5be1ee783fddfd081aed182f18990f102d92ee4"],"state_sha256":"7eaa0666f31b9d6cf2c6019bd45b868bf10c6dfd3689b9c833d0b20e23c4d56e"}