{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:BKGIF5NLH7A2NRXV42HQK52GU3","short_pith_number":"pith:BKGIF5NL","schema_version":"1.0","canonical_sha256":"0a8c82f5ab3fc1a6c6f5e68f057746a6e649739b1cb583d0c9949fb8b9d113d8","source":{"kind":"arxiv","id":"2503.18754","version":2},"attestation_state":"computed","paper":{"title":"Dynamics of learning to integrate in linear recurrent neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","stat.ML"],"primary_cat":"q-bio.NC","authors_text":"Blake Bordelon, Cengiz Pehlevan, Jacob A. Zavatone-Veth, Jordan Cotler","submitted_at":"2025-03-24T15:03:23Z","abstract_excerpt":"Learning recurrent connectivity that supports memory over long intrinsic timescales is a basic problem in the theory of dynamical computation. While continuous attractor and integrator models describe how tuned recurrent circuits can maintain information, less is known about how such slow modes are acquired by gradient-based learning. Here we study this question in an analytically tractable setting: we build a mathematical theory of the learning dynamics of linear RNNs trained to integrate white noise. We show that when the initial recurrent weights are small, the dynamics of learning are desc"},"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":"2503.18754","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2025-03-24T15:03:23Z","cross_cats_sorted":["cond-mat.dis-nn","stat.ML"],"title_canon_sha256":"de768442cad4866aa1ab30cee72bbe4d10fc624f057a64ba2b59a9fa8cde71bb","abstract_canon_sha256":"c8fc5981472aef56520c0fa5a66286637ac1f40b331f4c237a98639679da5bb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:29.391113Z","signature_b64":"4CXv4+x3n9MkpMOpqmQ7xq2In2gQWraYBFJChT+yXT1yZfIlTYODxhzSGMT8KaJp4nDtx80QRzTOotbHqXxqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a8c82f5ab3fc1a6c6f5e68f057746a6e649739b1cb583d0c9949fb8b9d113d8","last_reissued_at":"2026-06-09T02:08:29.389934Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:29.389934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of learning to integrate in linear recurrent neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","stat.ML"],"primary_cat":"q-bio.NC","authors_text":"Blake Bordelon, Cengiz Pehlevan, Jacob A. Zavatone-Veth, Jordan Cotler","submitted_at":"2025-03-24T15:03:23Z","abstract_excerpt":"Learning recurrent connectivity that supports memory over long intrinsic timescales is a basic problem in the theory of dynamical computation. While continuous attractor and integrator models describe how tuned recurrent circuits can maintain information, less is known about how such slow modes are acquired by gradient-based learning. Here we study this question in an analytically tractable setting: we build a mathematical theory of the learning dynamics of linear RNNs trained to integrate white noise. We show that when the initial recurrent weights are small, the dynamics of learning are desc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.18754","kind":"arxiv","version":2},"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/2503.18754/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":"2503.18754","created_at":"2026-06-09T02:08:29.390121+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.18754v2","created_at":"2026-06-09T02:08:29.390121+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.18754","created_at":"2026-06-09T02:08:29.390121+00:00"},{"alias_kind":"pith_short_12","alias_value":"BKGIF5NLH7A2","created_at":"2026-06-09T02:08:29.390121+00:00"},{"alias_kind":"pith_short_16","alias_value":"BKGIF5NLH7A2NRXV","created_at":"2026-06-09T02:08:29.390121+00:00"},{"alias_kind":"pith_short_8","alias_value":"BKGIF5NL","created_at":"2026-06-09T02:08:29.390121+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.04115","citing_title":"Learning reveals invisible structure in low-rank RNNs","ref_index":25,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BKGIF5NLH7A2NRXV42HQK52GU3","json":"https://pith.science/pith/BKGIF5NLH7A2NRXV42HQK52GU3.json","graph_json":"https://pith.science/api/pith-number/BKGIF5NLH7A2NRXV42HQK52GU3/graph.json","events_json":"https://pith.science/api/pith-number/BKGIF5NLH7A2NRXV42HQK52GU3/events.json","paper":"https://pith.science/paper/BKGIF5NL"},"agent_actions":{"view_html":"https://pith.science/pith/BKGIF5NLH7A2NRXV42HQK52GU3","download_json":"https://pith.science/pith/BKGIF5NLH7A2NRXV42HQK52GU3.json","view_paper":"https://pith.science/paper/BKGIF5NL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.18754&json=true","fetch_graph":"https://pith.science/api/pith-number/BKGIF5NLH7A2NRXV42HQK52GU3/graph.json","fetch_events":"https://pith.science/api/pith-number/BKGIF5NLH7A2NRXV42HQK52GU3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BKGIF5NLH7A2NRXV42HQK52GU3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BKGIF5NLH7A2NRXV42HQK52GU3/action/storage_attestation","attest_author":"https://pith.science/pith/BKGIF5NLH7A2NRXV42HQK52GU3/action/author_attestation","sign_citation":"https://pith.science/pith/BKGIF5NLH7A2NRXV42HQK52GU3/action/citation_signature","submit_replication":"https://pith.science/pith/BKGIF5NLH7A2NRXV42HQK52GU3/action/replication_record"}},"created_at":"2026-06-09T02:08:29.390121+00:00","updated_at":"2026-06-09T02:08:29.390121+00:00"}