{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:MWH6BAJCAFJTWTFNX43XXIGGIG","short_pith_number":"pith:MWH6BAJC","canonical_record":{"source":{"id":"2110.03128","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-07T00:53:33Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"7409115b3e9a299c34ebd1196629ec511efbb58323025103fb181ab210792f37","abstract_canon_sha256":"fdddae878fb379e3c531a7621cd79e9de555b8d0ded57e27b29461739b9abb36"},"schema_version":"1.0"},"canonical_sha256":"658fe0812201533b4cadbf377ba0c6419736f9a6bab42d8547f26463eeba0a96","source":{"kind":"arxiv","id":"2110.03128","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.03128","created_at":"2026-07-05T04:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"2110.03128v2","created_at":"2026-07-05T04:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.03128","created_at":"2026-07-05T04:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"MWH6BAJCAFJT","created_at":"2026-07-05T04:06:45Z"},{"alias_kind":"pith_short_16","alias_value":"MWH6BAJCAFJTWTFN","created_at":"2026-07-05T04:06:45Z"},{"alias_kind":"pith_short_8","alias_value":"MWH6BAJC","created_at":"2026-07-05T04:06:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:MWH6BAJCAFJTWTFNX43XXIGGIG","target":"record","payload":{"canonical_record":{"source":{"id":"2110.03128","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-07T00:53:33Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"7409115b3e9a299c34ebd1196629ec511efbb58323025103fb181ab210792f37","abstract_canon_sha256":"fdddae878fb379e3c531a7621cd79e9de555b8d0ded57e27b29461739b9abb36"},"schema_version":"1.0"},"canonical_sha256":"658fe0812201533b4cadbf377ba0c6419736f9a6bab42d8547f26463eeba0a96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:06:45.567377Z","signature_b64":"awiuIzW4oEV+BecdEu4yof2zl98wpkWzyIswEu0ZsMfC0y1Djjc9z+0/QNapogAV9Y5dqkiX/BgECnL66UQkDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"658fe0812201533b4cadbf377ba0c6419736f9a6bab42d8547f26463eeba0a96","last_reissued_at":"2026-07-05T04:06:45.566929Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:06:45.566929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.03128","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:06:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3nziPD0rV1E67PJ5If1QIw86uGF6nWiVbIFxl+uBkITb347ZKZneN8TE7sK0QN+k+pkLI88Oapfy1w+UZt3hBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T18:05:20.441826Z"},"content_sha256":"94034a7ff6d3b5dab28fecfecba84b2f03ac6a793461389838e61c1a3faad205","schema_version":"1.0","event_id":"sha256:94034a7ff6d3b5dab28fecfecba84b2f03ac6a793461389838e61c1a3faad205"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:MWH6BAJCAFJTWTFNX43XXIGGIG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Generalization of Models Trained with SGD: Information-Theoretic Bounds and Implications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.LG","authors_text":"Yongyi Mao, Ziqiao Wang","submitted_at":"2021-10-07T00:53:33Z","abstract_excerpt":"This paper follows up on a recent work of Neu et al. (2021) and presents some new information-theoretic upper bounds for the generalization error of machine learning models, such as neural networks, trained with SGD. We apply these bounds to analyzing the generalization behaviour of linear and two-layer ReLU networks. Experimental study of these bounds provide some insights on the SGD training of neural networks. They also point to a new and simple regularization scheme which we show performs comparably to the current state of the art."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.03128","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/2110.03128/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":"2026-07-05T04:06:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a8Brne1QzqJpliDMFhUEYudE9vveTzi9u6dVT4U4vgdlsIoj+CJwEEmOUpSHmqTbcZ/hBuN+DiIzOeHyRTeGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T18:05:20.442833Z"},"content_sha256":"4dc74b2051f7c3fa80b47a662aabd8c220f60e8e2f97afd336b73c7886bb4852","schema_version":"1.0","event_id":"sha256:4dc74b2051f7c3fa80b47a662aabd8c220f60e8e2f97afd336b73c7886bb4852"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWH6BAJCAFJTWTFNX43XXIGGIG/bundle.json","state_url":"https://pith.science/pith/MWH6BAJCAFJTWTFNX43XXIGGIG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWH6BAJCAFJTWTFNX43XXIGGIG/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":"2026-08-09T18:05:20Z","links":{"resolver":"https://pith.science/pith/MWH6BAJCAFJTWTFNX43XXIGGIG","bundle":"https://pith.science/pith/MWH6BAJCAFJTWTFNX43XXIGGIG/bundle.json","state":"https://pith.science/pith/MWH6BAJCAFJTWTFNX43XXIGGIG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWH6BAJCAFJTWTFNX43XXIGGIG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:MWH6BAJCAFJTWTFNX43XXIGGIG","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":"fdddae878fb379e3c531a7621cd79e9de555b8d0ded57e27b29461739b9abb36","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-07T00:53:33Z","title_canon_sha256":"7409115b3e9a299c34ebd1196629ec511efbb58323025103fb181ab210792f37"},"schema_version":"1.0","source":{"id":"2110.03128","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.03128","created_at":"2026-07-05T04:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"2110.03128v2","created_at":"2026-07-05T04:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.03128","created_at":"2026-07-05T04:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"MWH6BAJCAFJT","created_at":"2026-07-05T04:06:45Z"},{"alias_kind":"pith_short_16","alias_value":"MWH6BAJCAFJTWTFN","created_at":"2026-07-05T04:06:45Z"},{"alias_kind":"pith_short_8","alias_value":"MWH6BAJC","created_at":"2026-07-05T04:06:45Z"}],"graph_snapshots":[{"event_id":"sha256:4dc74b2051f7c3fa80b47a662aabd8c220f60e8e2f97afd336b73c7886bb4852","target":"graph","created_at":"2026-07-05T04:06:45Z","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/2110.03128/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper follows up on a recent work of Neu et al. (2021) and presents some new information-theoretic upper bounds for the generalization error of machine learning models, such as neural networks, trained with SGD. We apply these bounds to analyzing the generalization behaviour of linear and two-layer ReLU networks. Experimental study of these bounds provide some insights on the SGD training of neural networks. They also point to a new and simple regularization scheme which we show performs comparably to the current state of the art.","authors_text":"Yongyi Mao, Ziqiao Wang","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-07T00:53:33Z","title":"On the Generalization of Models Trained with SGD: Information-Theoretic Bounds and Implications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.03128","kind":"arxiv","version":2},"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":"sha256:94034a7ff6d3b5dab28fecfecba84b2f03ac6a793461389838e61c1a3faad205","target":"record","created_at":"2026-07-05T04:06:45Z","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":"fdddae878fb379e3c531a7621cd79e9de555b8d0ded57e27b29461739b9abb36","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-07T00:53:33Z","title_canon_sha256":"7409115b3e9a299c34ebd1196629ec511efbb58323025103fb181ab210792f37"},"schema_version":"1.0","source":{"id":"2110.03128","kind":"arxiv","version":2}},"canonical_sha256":"658fe0812201533b4cadbf377ba0c6419736f9a6bab42d8547f26463eeba0a96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"658fe0812201533b4cadbf377ba0c6419736f9a6bab42d8547f26463eeba0a96","first_computed_at":"2026-07-05T04:06:45.566929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:06:45.566929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"awiuIzW4oEV+BecdEu4yof2zl98wpkWzyIswEu0ZsMfC0y1Djjc9z+0/QNapogAV9Y5dqkiX/BgECnL66UQkDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:06:45.567377Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.03128","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94034a7ff6d3b5dab28fecfecba84b2f03ac6a793461389838e61c1a3faad205","sha256:4dc74b2051f7c3fa80b47a662aabd8c220f60e8e2f97afd336b73c7886bb4852"],"state_sha256":"db095102350f614c2021ee102cf0cb4868abea266f4dea4acedbdea81195a1c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3H7egR5xAwJXwL8jFlubs7R73K+NNjSfE82oH0mZ8kP/KHGWg6Z3xzxTgumAiYk/G2sBFQxMaG7rvL2EEyXTDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T18:05:20.449434Z","bundle_sha256":"662854c0ea85b561379b526e29af4f7e9343b805452287addf3563ca468b6e58"}}