{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:THMQMLW6SLVDBAADGMCINR7RHR","short_pith_number":"pith:THMQMLW6","canonical_record":{"source":{"id":"2202.03599","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-02-08T02:03:45Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"079481177164e31e7a3861f6d4eb2c5c77a4ee212aa91221959ca70a1daefdda","abstract_canon_sha256":"2dac719e4aebefe3448a0873d326c23601a3889b5b6c96fc7dc8a16e469733e1"},"schema_version":"1.0"},"canonical_sha256":"99d9062ede92ea308003330486c7f13c789d89c376452792baeaf3887c3fbaea","source":{"kind":"arxiv","id":"2202.03599","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.03599","created_at":"2026-07-05T04:34:50Z"},{"alias_kind":"arxiv_version","alias_value":"2202.03599v3","created_at":"2026-07-05T04:34:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.03599","created_at":"2026-07-05T04:34:50Z"},{"alias_kind":"pith_short_12","alias_value":"THMQMLW6SLVD","created_at":"2026-07-05T04:34:50Z"},{"alias_kind":"pith_short_16","alias_value":"THMQMLW6SLVDBAAD","created_at":"2026-07-05T04:34:50Z"},{"alias_kind":"pith_short_8","alias_value":"THMQMLW6","created_at":"2026-07-05T04:34:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:THMQMLW6SLVDBAADGMCINR7RHR","target":"record","payload":{"canonical_record":{"source":{"id":"2202.03599","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-02-08T02:03:45Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"079481177164e31e7a3861f6d4eb2c5c77a4ee212aa91221959ca70a1daefdda","abstract_canon_sha256":"2dac719e4aebefe3448a0873d326c23601a3889b5b6c96fc7dc8a16e469733e1"},"schema_version":"1.0"},"canonical_sha256":"99d9062ede92ea308003330486c7f13c789d89c376452792baeaf3887c3fbaea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:34:50.617030Z","signature_b64":"zMB/bkBQJdkrGwu9Z46clq4AN+GkEGN9Dt71is2ujNQuCk7qBUBPJmcEXcaxR8QRwVWx0KLVFhUwVKHganICAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99d9062ede92ea308003330486c7f13c789d89c376452792baeaf3887c3fbaea","last_reissued_at":"2026-07-05T04:34:50.616396Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:34:50.616396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.03599","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":"2026-07-05T04:34:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JZQ0+n/ebxVzSKP7rIFb17hoEZTja8l2un7/fcM95gkoyErTO2CeFDZkaH4MNJmieNUdUSVOR/Vn4jQLbUpJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:47:51.411459Z"},"content_sha256":"5b78c6bfb70f099c5149f64e4efc9d350b703ba8676c07ed9c8e09a2436581f2","schema_version":"1.0","event_id":"sha256:5b78c6bfb70f099c5149f64e4efc9d350b703ba8676c07ed9c8e09a2436581f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:THMQMLW6SLVDBAADGMCINR7RHR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Penalizing Gradient Norm for Efficiently Improving Generalization in Deep Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Hao Zhang, Xiuyuan Hu, Yang Zhao","submitted_at":"2022-02-08T02:03:45Z","abstract_excerpt":"How to train deep neural networks (DNNs) to generalize well is a central concern in deep learning, especially for severely overparameterized networks nowadays. In this paper, we propose an effective method to improve the model generalization by additionally penalizing the gradient norm of loss function during optimization. We demonstrate that confining the gradient norm of loss function could help lead the optimizers towards finding flat minima. We leverage the first-order approximation to efficiently implement the corresponding gradient to fit well in the gradient descent framework. In our ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.03599","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/2202.03599/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":"2026-07-05T04:34:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jdh5/5sCVWmHrJwxnEir/95Na6sfr4b7x1/3QnjzKeJugJpbNM9w0ZvlQCxgvqHE+WM6ggymMnpsExOMAaQ2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:47:51.411838Z"},"content_sha256":"ef40358946b9ec39c65d1b0dda9c8732e29fa134546818309830f609e3d40f1f","schema_version":"1.0","event_id":"sha256:ef40358946b9ec39c65d1b0dda9c8732e29fa134546818309830f609e3d40f1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/THMQMLW6SLVDBAADGMCINR7RHR/bundle.json","state_url":"https://pith.science/pith/THMQMLW6SLVDBAADGMCINR7RHR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/THMQMLW6SLVDBAADGMCINR7RHR/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":"2026-07-06T15:47:51Z","links":{"resolver":"https://pith.science/pith/THMQMLW6SLVDBAADGMCINR7RHR","bundle":"https://pith.science/pith/THMQMLW6SLVDBAADGMCINR7RHR/bundle.json","state":"https://pith.science/pith/THMQMLW6SLVDBAADGMCINR7RHR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/THMQMLW6SLVDBAADGMCINR7RHR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:THMQMLW6SLVDBAADGMCINR7RHR","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":"2dac719e4aebefe3448a0873d326c23601a3889b5b6c96fc7dc8a16e469733e1","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-02-08T02:03:45Z","title_canon_sha256":"079481177164e31e7a3861f6d4eb2c5c77a4ee212aa91221959ca70a1daefdda"},"schema_version":"1.0","source":{"id":"2202.03599","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.03599","created_at":"2026-07-05T04:34:50Z"},{"alias_kind":"arxiv_version","alias_value":"2202.03599v3","created_at":"2026-07-05T04:34:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.03599","created_at":"2026-07-05T04:34:50Z"},{"alias_kind":"pith_short_12","alias_value":"THMQMLW6SLVD","created_at":"2026-07-05T04:34:50Z"},{"alias_kind":"pith_short_16","alias_value":"THMQMLW6SLVDBAAD","created_at":"2026-07-05T04:34:50Z"},{"alias_kind":"pith_short_8","alias_value":"THMQMLW6","created_at":"2026-07-05T04:34:50Z"}],"graph_snapshots":[{"event_id":"sha256:ef40358946b9ec39c65d1b0dda9c8732e29fa134546818309830f609e3d40f1f","target":"graph","created_at":"2026-07-05T04:34:50Z","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/2202.03599/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"How to train deep neural networks (DNNs) to generalize well is a central concern in deep learning, especially for severely overparameterized networks nowadays. In this paper, we propose an effective method to improve the model generalization by additionally penalizing the gradient norm of loss function during optimization. We demonstrate that confining the gradient norm of loss function could help lead the optimizers towards finding flat minima. We leverage the first-order approximation to efficiently implement the corresponding gradient to fit well in the gradient descent framework. In our ex","authors_text":"Hao Zhang, Xiuyuan Hu, Yang Zhao","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-02-08T02:03:45Z","title":"Penalizing Gradient Norm for Efficiently Improving Generalization in Deep Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.03599","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":"sha256:5b78c6bfb70f099c5149f64e4efc9d350b703ba8676c07ed9c8e09a2436581f2","target":"record","created_at":"2026-07-05T04:34:50Z","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":"2dac719e4aebefe3448a0873d326c23601a3889b5b6c96fc7dc8a16e469733e1","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-02-08T02:03:45Z","title_canon_sha256":"079481177164e31e7a3861f6d4eb2c5c77a4ee212aa91221959ca70a1daefdda"},"schema_version":"1.0","source":{"id":"2202.03599","kind":"arxiv","version":3}},"canonical_sha256":"99d9062ede92ea308003330486c7f13c789d89c376452792baeaf3887c3fbaea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99d9062ede92ea308003330486c7f13c789d89c376452792baeaf3887c3fbaea","first_computed_at":"2026-07-05T04:34:50.616396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:34:50.616396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zMB/bkBQJdkrGwu9Z46clq4AN+GkEGN9Dt71is2ujNQuCk7qBUBPJmcEXcaxR8QRwVWx0KLVFhUwVKHganICAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:34:50.617030Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.03599","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b78c6bfb70f099c5149f64e4efc9d350b703ba8676c07ed9c8e09a2436581f2","sha256:ef40358946b9ec39c65d1b0dda9c8732e29fa134546818309830f609e3d40f1f"],"state_sha256":"7296e1859376a7b789fbdd073a194222a24de4f76179c07658ecbf58c3e3faaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/UpEBcb7iymt5994otl/c/1wTAf/vyMwMDSVYpy4PViR2sNEzdZaaa8RpSZAklS1pKGFjxFwpYsIecLJf1+yCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T15:47:51.413860Z","bundle_sha256":"4ac3007d4c34f16042875c826f6d4a50897c3ea973d5b07c63f1a2526a4971c0"}}