{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GLI32OL74OYXXBEXPXEKY4SHK3","short_pith_number":"pith:GLI32OL7","schema_version":"1.0","canonical_sha256":"32d1bd397fe3b17b84977dc8ac724756d54b15925febd40c64f3b22558512266","source":{"kind":"arxiv","id":"2505.11664","version":1},"attestation_state":"computed","paper":{"title":"A Local Polyak-Lojasiewicz and Descent Lemma of Gradient Descent For Overparametrized Linear Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Enrique Mallada, Hancheng Min, Rene Vidal, Salma Tarmoun, Ziqing Xu","submitted_at":"2025-05-16T19:57:22Z","abstract_excerpt":"Most prior work on the convergence of gradient descent (GD) for overparameterized neural networks relies on strong assumptions on the step size (infinitesimal), the hidden-layer width (infinite), or the initialization (large, spectral, balanced). Recent efforts to relax these assumptions focus on two-layer linear networks trained with the squared loss. In this work, we derive a linear convergence rate for training two-layer linear neural networks with GD for general losses and under relaxed assumptions on the step size, width, and initialization. A key challenge in deriving this result is that"},"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":"2505.11664","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-16T19:57:22Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"339613fa38584a84baff1409057656692bb1aa04766255aba88af76405c0cbe1","abstract_canon_sha256":"787b667d612d7d3707e65335e2f204376dd361779eabad1e29ccd94088ee2505"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:04:25.086611Z","signature_b64":"XP9BHMCTSbmV/s5Y7CX3NYdrEZZxA1IynDy4MAHaWbi/UMKYKXTUPyz+TvM8jN3U4tK8sY+FbWff83hs7XtEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32d1bd397fe3b17b84977dc8ac724756d54b15925febd40c64f3b22558512266","last_reissued_at":"2026-07-05T11:04:25.086043Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:04:25.086043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Local Polyak-Lojasiewicz and Descent Lemma of Gradient Descent For Overparametrized Linear Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Enrique Mallada, Hancheng Min, Rene Vidal, Salma Tarmoun, Ziqing Xu","submitted_at":"2025-05-16T19:57:22Z","abstract_excerpt":"Most prior work on the convergence of gradient descent (GD) for overparameterized neural networks relies on strong assumptions on the step size (infinitesimal), the hidden-layer width (infinite), or the initialization (large, spectral, balanced). Recent efforts to relax these assumptions focus on two-layer linear networks trained with the squared loss. In this work, we derive a linear convergence rate for training two-layer linear neural networks with GD for general losses and under relaxed assumptions on the step size, width, and initialization. A key challenge in deriving this result is that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.11664","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/2505.11664/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":"2505.11664","created_at":"2026-07-05T11:04:25.086106+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.11664v1","created_at":"2026-07-05T11:04:25.086106+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.11664","created_at":"2026-07-05T11:04:25.086106+00:00"},{"alias_kind":"pith_short_12","alias_value":"GLI32OL74OYX","created_at":"2026-07-05T11:04:25.086106+00:00"},{"alias_kind":"pith_short_16","alias_value":"GLI32OL74OYXXBEX","created_at":"2026-07-05T11:04:25.086106+00:00"},{"alias_kind":"pith_short_8","alias_value":"GLI32OL7","created_at":"2026-07-05T11:04:25.086106+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GLI32OL74OYXXBEXPXEKY4SHK3","json":"https://pith.science/pith/GLI32OL74OYXXBEXPXEKY4SHK3.json","graph_json":"https://pith.science/api/pith-number/GLI32OL74OYXXBEXPXEKY4SHK3/graph.json","events_json":"https://pith.science/api/pith-number/GLI32OL74OYXXBEXPXEKY4SHK3/events.json","paper":"https://pith.science/paper/GLI32OL7"},"agent_actions":{"view_html":"https://pith.science/pith/GLI32OL74OYXXBEXPXEKY4SHK3","download_json":"https://pith.science/pith/GLI32OL74OYXXBEXPXEKY4SHK3.json","view_paper":"https://pith.science/paper/GLI32OL7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.11664&json=true","fetch_graph":"https://pith.science/api/pith-number/GLI32OL74OYXXBEXPXEKY4SHK3/graph.json","fetch_events":"https://pith.science/api/pith-number/GLI32OL74OYXXBEXPXEKY4SHK3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GLI32OL74OYXXBEXPXEKY4SHK3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GLI32OL74OYXXBEXPXEKY4SHK3/action/storage_attestation","attest_author":"https://pith.science/pith/GLI32OL74OYXXBEXPXEKY4SHK3/action/author_attestation","sign_citation":"https://pith.science/pith/GLI32OL74OYXXBEXPXEKY4SHK3/action/citation_signature","submit_replication":"https://pith.science/pith/GLI32OL74OYXXBEXPXEKY4SHK3/action/replication_record"}},"created_at":"2026-07-05T11:04:25.086106+00:00","updated_at":"2026-07-05T11:04:25.086106+00:00"}