{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4VFVH7RT7NIJEDZMB6SEQLAGC4","short_pith_number":"pith:4VFVH7RT","schema_version":"1.0","canonical_sha256":"e54b53fe33fb50920f2c0fa4482c06172be583716132f5e9a0791c79b77db38f","source":{"kind":"arxiv","id":"2502.17340","version":2},"attestation_state":"computed","paper":{"title":"Low-rank bias, weight decay, and model merging in neural networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ilja Kuzborskij, Yasin Abbasi Yadkori","submitted_at":"2025-02-24T17:17:00Z","abstract_excerpt":"We explore the low-rank structure of the weight matrices in neural networks at the stationary points (limiting solutions of optimization algorithms) with $L2$ regularization (also known as weight decay). We show several properties of such deep neural networks, induced by $L2$ regularization. In particular, for a stationary point we show alignment of the parameters and the gradient, norm preservation across layers, and low-rank bias: properties previously known in the context of solution of gradient descent/flow type algorithms. Experiments show that the assumptions made in the analysis only mi"},"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":"2502.17340","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-24T17:17:00Z","cross_cats_sorted":[],"title_canon_sha256":"9c1ed96083b3b6cf186aa633fa15a4371bb61075e4623a294840adafd038c686","abstract_canon_sha256":"7cc3fc016401abf0399020c0b1493040f54619430ec61dc64abc398fb7f1ff90"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:17.780083Z","signature_b64":"jPthw0K9gw4YAc17VTQWlb6xXWseoK0c7oGXEjfcVJ40altkkcWbdbzkHv3y9pQLETNcVBKziRS2ExaJst+5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e54b53fe33fb50920f2c0fa4482c06172be583716132f5e9a0791c79b77db38f","last_reissued_at":"2026-07-05T11:56:17.779346Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:17.779346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low-rank bias, weight decay, and model merging in neural networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ilja Kuzborskij, Yasin Abbasi Yadkori","submitted_at":"2025-02-24T17:17:00Z","abstract_excerpt":"We explore the low-rank structure of the weight matrices in neural networks at the stationary points (limiting solutions of optimization algorithms) with $L2$ regularization (also known as weight decay). We show several properties of such deep neural networks, induced by $L2$ regularization. In particular, for a stationary point we show alignment of the parameters and the gradient, norm preservation across layers, and low-rank bias: properties previously known in the context of solution of gradient descent/flow type algorithms. Experiments show that the assumptions made in the analysis only mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.17340","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/2502.17340/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":"2502.17340","created_at":"2026-07-05T11:56:17.779442+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.17340v2","created_at":"2026-07-05T11:56:17.779442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.17340","created_at":"2026-07-05T11:56:17.779442+00:00"},{"alias_kind":"pith_short_12","alias_value":"4VFVH7RT7NIJ","created_at":"2026-07-05T11:56:17.779442+00:00"},{"alias_kind":"pith_short_16","alias_value":"4VFVH7RT7NIJEDZM","created_at":"2026-07-05T11:56:17.779442+00:00"},{"alias_kind":"pith_short_8","alias_value":"4VFVH7RT","created_at":"2026-07-05T11:56:17.779442+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.05863","citing_title":"Deciphering Two Training Clocks in Grokking via Deep Linear Network Theory with Conditional ReLU Reduction","ref_index":60,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4VFVH7RT7NIJEDZMB6SEQLAGC4","json":"https://pith.science/pith/4VFVH7RT7NIJEDZMB6SEQLAGC4.json","graph_json":"https://pith.science/api/pith-number/4VFVH7RT7NIJEDZMB6SEQLAGC4/graph.json","events_json":"https://pith.science/api/pith-number/4VFVH7RT7NIJEDZMB6SEQLAGC4/events.json","paper":"https://pith.science/paper/4VFVH7RT"},"agent_actions":{"view_html":"https://pith.science/pith/4VFVH7RT7NIJEDZMB6SEQLAGC4","download_json":"https://pith.science/pith/4VFVH7RT7NIJEDZMB6SEQLAGC4.json","view_paper":"https://pith.science/paper/4VFVH7RT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.17340&json=true","fetch_graph":"https://pith.science/api/pith-number/4VFVH7RT7NIJEDZMB6SEQLAGC4/graph.json","fetch_events":"https://pith.science/api/pith-number/4VFVH7RT7NIJEDZMB6SEQLAGC4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4VFVH7RT7NIJEDZMB6SEQLAGC4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4VFVH7RT7NIJEDZMB6SEQLAGC4/action/storage_attestation","attest_author":"https://pith.science/pith/4VFVH7RT7NIJEDZMB6SEQLAGC4/action/author_attestation","sign_citation":"https://pith.science/pith/4VFVH7RT7NIJEDZMB6SEQLAGC4/action/citation_signature","submit_replication":"https://pith.science/pith/4VFVH7RT7NIJEDZMB6SEQLAGC4/action/replication_record"}},"created_at":"2026-07-05T11:56:17.779442+00:00","updated_at":"2026-07-05T11:56:17.779442+00:00"}