{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:AQH7M24EGQRJRUTIQLF5XKPGWX","short_pith_number":"pith:AQH7M24E","canonical_record":{"source":{"id":"2009.11162","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-23T14:17:53Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"269ffc95c23c902ccb99c58a50209729bf96471476f090818139453608b2cfd6","abstract_canon_sha256":"22fa6bbbd310e795a1540cabca779f163608de38ce438fab6de3071e2a285260"},"schema_version":"1.0"},"canonical_sha256":"040ff66b84342298d26882cbdba9e6b5e8451d38da196fb27266b8d98cb6537e","source":{"kind":"arxiv","id":"2009.11162","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.11162","created_at":"2026-07-05T04:41:09Z"},{"alias_kind":"arxiv_version","alias_value":"2009.11162v3","created_at":"2026-07-05T04:41:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.11162","created_at":"2026-07-05T04:41:09Z"},{"alias_kind":"pith_short_12","alias_value":"AQH7M24EGQRJ","created_at":"2026-07-05T04:41:09Z"},{"alias_kind":"pith_short_16","alias_value":"AQH7M24EGQRJRUTI","created_at":"2026-07-05T04:41:09Z"},{"alias_kind":"pith_short_8","alias_value":"AQH7M24E","created_at":"2026-07-05T04:41:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:AQH7M24EGQRJRUTIQLF5XKPGWX","target":"record","payload":{"canonical_record":{"source":{"id":"2009.11162","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-23T14:17:53Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"269ffc95c23c902ccb99c58a50209729bf96471476f090818139453608b2cfd6","abstract_canon_sha256":"22fa6bbbd310e795a1540cabca779f163608de38ce438fab6de3071e2a285260"},"schema_version":"1.0"},"canonical_sha256":"040ff66b84342298d26882cbdba9e6b5e8451d38da196fb27266b8d98cb6537e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:41:09.062338Z","signature_b64":"E0KLf91mL9CZniLo/XoMcTC0Thz/8RWQkBxmvqXP6xGjIQrDAWCLO4+WY4jJ+oan7duSUd/HNKj9BQRgmFmYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"040ff66b84342298d26882cbdba9e6b5e8451d38da196fb27266b8d98cb6537e","last_reissued_at":"2026-07-05T04:41:09.061866Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:41:09.061866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.11162","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:41:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vxg03XKVJ4nIerK7abEu6Lc3AlDeuDjGmTQDGZMZYnD22Yldm4Fgy8cfgCmFG/2m0sAMnccsOuAj+2yigL41Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:33:54.026290Z"},"content_sha256":"106d1e867976fb263108028cfb7943c86755382ae4ded47c2757083561e7f2f2","schema_version":"1.0","event_id":"sha256:106d1e867976fb263108028cfb7943c86755382ae4ded47c2757083561e7f2f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:AQH7M24EGQRJRUTIQLF5XKPGWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Implicit Gradient Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Benoit Dherin, David G.T. Barrett","submitted_at":"2020-09-23T14:17:53Z","abstract_excerpt":"Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient descent trajectories that have large loss gradients. We call this Implicit Gradient Regularization (IGR) and we use backward error analysis to calculate the size of this regularization. We confirm empirically that implicit gradient regularization biases gradient descent toward flat minima, where test errors are small and solutions are robust to noisy parameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11162","kind":"arxiv","version":3},"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/2009.11162/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":"2026-07-05T04:41:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HfPhNPpjNt9yreaO/pXJAGAUftLJy/LWYyXimNJzGwNbeInm7ZgyfbaTgX1cnGC20LC3akbrxpiAaPTSad/oCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:33:54.026784Z"},"content_sha256":"604558b7fbc068a27f51f40a9a6ef2612df5a9218289358a754bea7aa9427933","schema_version":"1.0","event_id":"sha256:604558b7fbc068a27f51f40a9a6ef2612df5a9218289358a754bea7aa9427933"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQH7M24EGQRJRUTIQLF5XKPGWX/bundle.json","state_url":"https://pith.science/pith/AQH7M24EGQRJRUTIQLF5XKPGWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQH7M24EGQRJRUTIQLF5XKPGWX/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":"2026-08-03T16:33:54Z","links":{"resolver":"https://pith.science/pith/AQH7M24EGQRJRUTIQLF5XKPGWX","bundle":"https://pith.science/pith/AQH7M24EGQRJRUTIQLF5XKPGWX/bundle.json","state":"https://pith.science/pith/AQH7M24EGQRJRUTIQLF5XKPGWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQH7M24EGQRJRUTIQLF5XKPGWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:AQH7M24EGQRJRUTIQLF5XKPGWX","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":"22fa6bbbd310e795a1540cabca779f163608de38ce438fab6de3071e2a285260","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-23T14:17:53Z","title_canon_sha256":"269ffc95c23c902ccb99c58a50209729bf96471476f090818139453608b2cfd6"},"schema_version":"1.0","source":{"id":"2009.11162","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.11162","created_at":"2026-07-05T04:41:09Z"},{"alias_kind":"arxiv_version","alias_value":"2009.11162v3","created_at":"2026-07-05T04:41:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.11162","created_at":"2026-07-05T04:41:09Z"},{"alias_kind":"pith_short_12","alias_value":"AQH7M24EGQRJ","created_at":"2026-07-05T04:41:09Z"},{"alias_kind":"pith_short_16","alias_value":"AQH7M24EGQRJRUTI","created_at":"2026-07-05T04:41:09Z"},{"alias_kind":"pith_short_8","alias_value":"AQH7M24E","created_at":"2026-07-05T04:41:09Z"}],"graph_snapshots":[{"event_id":"sha256:604558b7fbc068a27f51f40a9a6ef2612df5a9218289358a754bea7aa9427933","target":"graph","created_at":"2026-07-05T04:41:09Z","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/2009.11162/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient descent trajectories that have large loss gradients. We call this Implicit Gradient Regularization (IGR) and we use backward error analysis to calculate the size of this regularization. We confirm empirically that implicit gradient regularization biases gradient descent toward flat minima, where test errors are small and solutions are robust to noisy parameter","authors_text":"Benoit Dherin, David G.T. Barrett","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-23T14:17:53Z","title":"Implicit Gradient Regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11162","kind":"arxiv","version":3},"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":"sha256:106d1e867976fb263108028cfb7943c86755382ae4ded47c2757083561e7f2f2","target":"record","created_at":"2026-07-05T04:41:09Z","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":"22fa6bbbd310e795a1540cabca779f163608de38ce438fab6de3071e2a285260","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-23T14:17:53Z","title_canon_sha256":"269ffc95c23c902ccb99c58a50209729bf96471476f090818139453608b2cfd6"},"schema_version":"1.0","source":{"id":"2009.11162","kind":"arxiv","version":3}},"canonical_sha256":"040ff66b84342298d26882cbdba9e6b5e8451d38da196fb27266b8d98cb6537e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"040ff66b84342298d26882cbdba9e6b5e8451d38da196fb27266b8d98cb6537e","first_computed_at":"2026-07-05T04:41:09.061866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:41:09.061866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E0KLf91mL9CZniLo/XoMcTC0Thz/8RWQkBxmvqXP6xGjIQrDAWCLO4+WY4jJ+oan7duSUd/HNKj9BQRgmFmYAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:41:09.062338Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.11162","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:106d1e867976fb263108028cfb7943c86755382ae4ded47c2757083561e7f2f2","sha256:604558b7fbc068a27f51f40a9a6ef2612df5a9218289358a754bea7aa9427933"],"state_sha256":"6446e70e86ba9375fd151de7565662ec91288922964869fd357633e0c60ec345"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UtnADrFmxnNxWMka7NW8Rz4PXFWpNbNVEppioab1Hpd7qZ6cl0d3Gd4sMhnvBZhpA+8ireGfakw761w0K3g0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:33:54.030329Z","bundle_sha256":"0854fbe6afb387e1a457b1f1267e9570784036d7b42a9c7110dad3d39cb8f3c0"}}