{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:5VBIKIIIOQDFXWBZ36UDC6OXR3","short_pith_number":"pith:5VBIKIII","schema_version":"1.0","canonical_sha256":"ed4285210874065bd839dfa83179d78edb3d5f9cd11d03b90bdc2f275e91219a","source":{"kind":"arxiv","id":"2410.14158","version":1},"attestation_state":"computed","paper":{"title":"A Mirror Descent Perspective of Smoothed Sign Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Diego Klabjan, Shuyang Wang","submitted_at":"2024-10-18T03:52:21Z","abstract_excerpt":"Recent work by Woodworth et al. (2020) shows that the optimization dynamics of gradient descent for overparameterized problems can be viewed as low-dimensional dual dynamics induced by a mirror map, explaining the implicit regularization phenomenon from the mirror descent perspective. However, the methodology does not apply to algorithms where update directions deviate from true gradients, such as ADAM. We use the mirror descent framework to study the dynamics of smoothed sign descent with a stability constant $\\varepsilon$ for regression problems. We propose a mirror map that establishes equi"},"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":"2410.14158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-18T03:52:21Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"77b1e946b930545880075a26760a5cbc811a4a035c0d8bfd20a24f6d2277ba30","abstract_canon_sha256":"5a10b38f0b6a8b6b0922273466b4a0be9cd5adff0960d9985f69875db1eeefc0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:22:28.118056Z","signature_b64":"cCdCGNV3qX9mLfFTTAri8/lm2cUD3kCvB2i7WAGd1C9QU6wS4MQYRZ9RM8O71Hp/BWIN1AINvcdQ040quiLWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed4285210874065bd839dfa83179d78edb3d5f9cd11d03b90bdc2f275e91219a","last_reissued_at":"2026-07-05T09:22:28.117644Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:22:28.117644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Mirror Descent Perspective of Smoothed Sign Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Diego Klabjan, Shuyang Wang","submitted_at":"2024-10-18T03:52:21Z","abstract_excerpt":"Recent work by Woodworth et al. (2020) shows that the optimization dynamics of gradient descent for overparameterized problems can be viewed as low-dimensional dual dynamics induced by a mirror map, explaining the implicit regularization phenomenon from the mirror descent perspective. However, the methodology does not apply to algorithms where update directions deviate from true gradients, such as ADAM. We use the mirror descent framework to study the dynamics of smoothed sign descent with a stability constant $\\varepsilon$ for regression problems. We propose a mirror map that establishes equi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.14158","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/2410.14158/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":"2410.14158","created_at":"2026-07-05T09:22:28.117705+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.14158v1","created_at":"2026-07-05T09:22:28.117705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.14158","created_at":"2026-07-05T09:22:28.117705+00:00"},{"alias_kind":"pith_short_12","alias_value":"5VBIKIIIOQDF","created_at":"2026-07-05T09:22:28.117705+00:00"},{"alias_kind":"pith_short_16","alias_value":"5VBIKIIIOQDFXWBZ","created_at":"2026-07-05T09:22:28.117705+00:00"},{"alias_kind":"pith_short_8","alias_value":"5VBIKIII","created_at":"2026-07-05T09:22:28.117705+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.13984","citing_title":"Mirror Descent Using the Tempesta Generalized Multi-parametric Logarithms","ref_index":37,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3","json":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3.json","graph_json":"https://pith.science/api/pith-number/5VBIKIIIOQDFXWBZ36UDC6OXR3/graph.json","events_json":"https://pith.science/api/pith-number/5VBIKIIIOQDFXWBZ36UDC6OXR3/events.json","paper":"https://pith.science/paper/5VBIKIII"},"agent_actions":{"view_html":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3","download_json":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3.json","view_paper":"https://pith.science/paper/5VBIKIII","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.14158&json=true","fetch_graph":"https://pith.science/api/pith-number/5VBIKIIIOQDFXWBZ36UDC6OXR3/graph.json","fetch_events":"https://pith.science/api/pith-number/5VBIKIIIOQDFXWBZ36UDC6OXR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/action/storage_attestation","attest_author":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/action/author_attestation","sign_citation":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/action/citation_signature","submit_replication":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/action/replication_record"}},"created_at":"2026-07-05T09:22:28.117705+00:00","updated_at":"2026-07-05T09:22:28.117705+00:00"}