{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5VBIKIIIOQDFXWBZ36UDC6OXR3","short_pith_number":"pith:5VBIKIII","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"},"canonical_sha256":"ed4285210874065bd839dfa83179d78edb3d5f9cd11d03b90bdc2f275e91219a","source":{"kind":"arxiv","id":"2410.14158","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.14158","created_at":"2026-07-05T09:22:28Z"},{"alias_kind":"arxiv_version","alias_value":"2410.14158v1","created_at":"2026-07-05T09:22:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.14158","created_at":"2026-07-05T09:22:28Z"},{"alias_kind":"pith_short_12","alias_value":"5VBIKIIIOQDF","created_at":"2026-07-05T09:22:28Z"},{"alias_kind":"pith_short_16","alias_value":"5VBIKIIIOQDFXWBZ","created_at":"2026-07-05T09:22:28Z"},{"alias_kind":"pith_short_8","alias_value":"5VBIKIII","created_at":"2026-07-05T09:22:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5VBIKIIIOQDFXWBZ36UDC6OXR3","target":"record","payload":{"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"},"canonical_sha256":"ed4285210874065bd839dfa83179d78edb3d5f9cd11d03b90bdc2f275e91219a","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"},"source_kind":"arxiv","source_id":"2410.14158","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:22:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"687e49lPajPG6NRu1dxbEn9XE9w+vxem4XeUAMQELGtaO3mKSqTJcbU1aErsnLDQ1lHelYfg9uMPdStxYBHvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:28:26.569978Z"},"content_sha256":"8a9b9acd9ed0f4d3e9efc59e7143eed01ad4b86f326657a9d886f776e8793d7f","schema_version":"1.0","event_id":"sha256:8a9b9acd9ed0f4d3e9efc59e7143eed01ad4b86f326657a9d886f776e8793d7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5VBIKIIIOQDFXWBZ36UDC6OXR3","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:22:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H5wQOW1hm8PoA/vJJsJqm8rCp1yn1ihlRNHzvoXten2VSECZySHx9Kr4TPkDq6PF7DJEGGrsIAX9RBAv1QWqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:28:26.570492Z"},"content_sha256":"94ea87fc8588dbbe3d1a1fe8d0440002226aba15716220a282bed55690554c9e","schema_version":"1.0","event_id":"sha256:94ea87fc8588dbbe3d1a1fe8d0440002226aba15716220a282bed55690554c9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/bundle.json","state_url":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T14:28:26Z","links":{"resolver":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3","bundle":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/bundle.json","state":"https://pith.science/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5VBIKIIIOQDFXWBZ36UDC6OXR3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5VBIKIIIOQDFXWBZ36UDC6OXR3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5a10b38f0b6a8b6b0922273466b4a0be9cd5adff0960d9985f69875db1eeefc0","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-18T03:52:21Z","title_canon_sha256":"77b1e946b930545880075a26760a5cbc811a4a035c0d8bfd20a24f6d2277ba30"},"schema_version":"1.0","source":{"id":"2410.14158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.14158","created_at":"2026-07-05T09:22:28Z"},{"alias_kind":"arxiv_version","alias_value":"2410.14158v1","created_at":"2026-07-05T09:22:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.14158","created_at":"2026-07-05T09:22:28Z"},{"alias_kind":"pith_short_12","alias_value":"5VBIKIIIOQDF","created_at":"2026-07-05T09:22:28Z"},{"alias_kind":"pith_short_16","alias_value":"5VBIKIIIOQDFXWBZ","created_at":"2026-07-05T09:22:28Z"},{"alias_kind":"pith_short_8","alias_value":"5VBIKIII","created_at":"2026-07-05T09:22:28Z"}],"graph_snapshots":[{"event_id":"sha256:94ea87fc8588dbbe3d1a1fe8d0440002226aba15716220a282bed55690554c9e","target":"graph","created_at":"2026-07-05T09:22:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.14158/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Diego Klabjan, Shuyang Wang","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-18T03:52:21Z","title":"A Mirror Descent Perspective of Smoothed Sign Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.14158","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8a9b9acd9ed0f4d3e9efc59e7143eed01ad4b86f326657a9d886f776e8793d7f","target":"record","created_at":"2026-07-05T09:22:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5a10b38f0b6a8b6b0922273466b4a0be9cd5adff0960d9985f69875db1eeefc0","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-18T03:52:21Z","title_canon_sha256":"77b1e946b930545880075a26760a5cbc811a4a035c0d8bfd20a24f6d2277ba30"},"schema_version":"1.0","source":{"id":"2410.14158","kind":"arxiv","version":1}},"canonical_sha256":"ed4285210874065bd839dfa83179d78edb3d5f9cd11d03b90bdc2f275e91219a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed4285210874065bd839dfa83179d78edb3d5f9cd11d03b90bdc2f275e91219a","first_computed_at":"2026-07-05T09:22:28.117644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:22:28.117644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cCdCGNV3qX9mLfFTTAri8/lm2cUD3kCvB2i7WAGd1C9QU6wS4MQYRZ9RM8O71Hp/BWIN1AINvcdQ040quiLWBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:22:28.118056Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.14158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a9b9acd9ed0f4d3e9efc59e7143eed01ad4b86f326657a9d886f776e8793d7f","sha256:94ea87fc8588dbbe3d1a1fe8d0440002226aba15716220a282bed55690554c9e"],"state_sha256":"e57417f4fa66022de9ab44b0e8443b0ce36f31008de22e796ef05d46cbec39a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uJ3rcFq84uHZPhK6fe6QCl+qyGIF1hQqDpRW/6CQH8+eJtDpoTx+ng06TZ+yx7pPyafxErYcpLF+M0ncR1hnBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T14:28:26.575754Z","bundle_sha256":"cc83c34bb73e5ae5b2d12233ac2776fb9a829c71093837dd39eada594482f5de"}}