{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PNZBMFYBUAS5O56A7WBYSYFI34","short_pith_number":"pith:PNZBMFYB","schema_version":"1.0","canonical_sha256":"7b72161701a025d777c0fd838960a8df0f04ff2a9c974d31f6c921718bfcc0c6","source":{"kind":"arxiv","id":"2407.19353","version":4},"attestation_state":"computed","paper":{"title":"Spring-block theory of feature learning in deep neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.LG","stat.ML"],"primary_cat":"cond-mat.dis-nn","authors_text":"Cheng Shi, Ivan Dokmani\\'c, Liming Pan","submitted_at":"2024-07-28T00:07:20Z","abstract_excerpt":"Feature-learning deep nets progressively collapse data to a regular low-dimensional geometry. How this emerges from the collective action of nonlinearity, noise, learning rate, and other factors, has eluded first-principles theories built from microscopic neuronal dynamics. We exhibit a noise-nonlinearity phase diagram that identifies regimes where shallow or deep layers learn more effectively and propose a macroscopic mechanical theory that reproduces the diagram and links feature learning across layers to generalization."},"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":"2407.19353","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2024-07-28T00:07:20Z","cross_cats_sorted":["cond-mat.stat-mech","cs.LG","stat.ML"],"title_canon_sha256":"616cdeb288362cdd0cd665caf2add29c6ef008bf88ef7e1e613af4539d745e68","abstract_canon_sha256":"783e803b75ff9da1bc3c6c165cfa6627c5a2ac3b79b046101ff40f707bad8145"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:10.643558Z","signature_b64":"D8enbrUmkuKyejaqO4Nxbd0yp0WFcYji1p04CdDBqWaqg1XRfAQXqbIzpLgQYl+5R/UTKHlWSi0UCVsobGWiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b72161701a025d777c0fd838960a8df0f04ff2a9c974d31f6c921718bfcc0c6","last_reissued_at":"2026-07-05T11:28:10.643073Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:10.643073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spring-block theory of feature learning in deep neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.LG","stat.ML"],"primary_cat":"cond-mat.dis-nn","authors_text":"Cheng Shi, Ivan Dokmani\\'c, Liming Pan","submitted_at":"2024-07-28T00:07:20Z","abstract_excerpt":"Feature-learning deep nets progressively collapse data to a regular low-dimensional geometry. How this emerges from the collective action of nonlinearity, noise, learning rate, and other factors, has eluded first-principles theories built from microscopic neuronal dynamics. We exhibit a noise-nonlinearity phase diagram that identifies regimes where shallow or deep layers learn more effectively and propose a macroscopic mechanical theory that reproduces the diagram and links feature learning across layers to generalization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.19353","kind":"arxiv","version":4},"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/2407.19353/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":"2407.19353","created_at":"2026-07-05T11:28:10.643138+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.19353v4","created_at":"2026-07-05T11:28:10.643138+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.19353","created_at":"2026-07-05T11:28:10.643138+00:00"},{"alias_kind":"pith_short_12","alias_value":"PNZBMFYBUAS5","created_at":"2026-07-05T11:28:10.643138+00:00"},{"alias_kind":"pith_short_16","alias_value":"PNZBMFYBUAS5O56A","created_at":"2026-07-05T11:28:10.643138+00:00"},{"alias_kind":"pith_short_8","alias_value":"PNZBMFYB","created_at":"2026-07-05T11:28:10.643138+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.15911","citing_title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PNZBMFYBUAS5O56A7WBYSYFI34","json":"https://pith.science/pith/PNZBMFYBUAS5O56A7WBYSYFI34.json","graph_json":"https://pith.science/api/pith-number/PNZBMFYBUAS5O56A7WBYSYFI34/graph.json","events_json":"https://pith.science/api/pith-number/PNZBMFYBUAS5O56A7WBYSYFI34/events.json","paper":"https://pith.science/paper/PNZBMFYB"},"agent_actions":{"view_html":"https://pith.science/pith/PNZBMFYBUAS5O56A7WBYSYFI34","download_json":"https://pith.science/pith/PNZBMFYBUAS5O56A7WBYSYFI34.json","view_paper":"https://pith.science/paper/PNZBMFYB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.19353&json=true","fetch_graph":"https://pith.science/api/pith-number/PNZBMFYBUAS5O56A7WBYSYFI34/graph.json","fetch_events":"https://pith.science/api/pith-number/PNZBMFYBUAS5O56A7WBYSYFI34/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PNZBMFYBUAS5O56A7WBYSYFI34/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PNZBMFYBUAS5O56A7WBYSYFI34/action/storage_attestation","attest_author":"https://pith.science/pith/PNZBMFYBUAS5O56A7WBYSYFI34/action/author_attestation","sign_citation":"https://pith.science/pith/PNZBMFYBUAS5O56A7WBYSYFI34/action/citation_signature","submit_replication":"https://pith.science/pith/PNZBMFYBUAS5O56A7WBYSYFI34/action/replication_record"}},"created_at":"2026-07-05T11:28:10.643138+00:00","updated_at":"2026-07-05T11:28:10.643138+00:00"}