{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NIOML7QDNXYPWKYRVA6BYETNFA","short_pith_number":"pith:NIOML7QD","canonical_record":{"source":{"id":"2505.21423","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-27T16:51:06Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"afd9cd186b6f7da826fce3912e0e7ef2de511a35ef1ff9b17e59a9b3227699b7","abstract_canon_sha256":"3eb5115752cd7b627e3e6d17cf5871f2cc6dff04746733383ad667703a5675d0"},"schema_version":"1.0"},"canonical_sha256":"6a1cc5fe036df0fb2b11a83c1c126d283405e62750eafbff0d65ca77ec184367","source":{"kind":"arxiv","id":"2505.21423","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21423","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21423v3","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21423","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"pith_short_12","alias_value":"NIOML7QDNXYP","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"pith_short_16","alias_value":"NIOML7QDNXYPWKYR","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"pith_short_8","alias_value":"NIOML7QD","created_at":"2026-06-08T01:03:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NIOML7QDNXYPWKYRVA6BYETNFA","target":"record","payload":{"canonical_record":{"source":{"id":"2505.21423","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-27T16:51:06Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"afd9cd186b6f7da826fce3912e0e7ef2de511a35ef1ff9b17e59a9b3227699b7","abstract_canon_sha256":"3eb5115752cd7b627e3e6d17cf5871f2cc6dff04746733383ad667703a5675d0"},"schema_version":"1.0"},"canonical_sha256":"6a1cc5fe036df0fb2b11a83c1c126d283405e62750eafbff0d65ca77ec184367","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:03:45.204246Z","signature_b64":"HJAY5VJJxSAXyII36klj9tM0QQX9yPb6FzmK5JdYkzUe9nRIcbAojq/pl+7oNd9NnGzpU7xtbeNN9sTSa1lwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a1cc5fe036df0fb2b11a83c1c126d283405e62750eafbff0d65ca77ec184367","last_reissued_at":"2026-06-08T01:03:45.202913Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:03:45.202913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.21423","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":"2026-06-08T01:03:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IdmgDviXavM1waZXkxZpOAtjcC9rj0RRct0+No1QnNov04cKBjbYZOh7fwnP+M7u/mPDX5RYBykvA5QLJrmMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:21:14.430336Z"},"content_sha256":"8fa4f7eabd55897fe1383f8125592d3ff795a9572853f8312ef418eaf1218062","schema_version":"1.0","event_id":"sha256:8fa4f7eabd55897fe1383f8125592d3ff795a9572853f8312ef418eaf1218062"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NIOML7QDNXYPWKYRVA6BYETNFA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conflicting Biases at the Edge of Stability: Norm versus Sharpness Regularization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Gitta Kutyniok, Hung-Hsu Chou, Johannes Maly, Maria Matveev, Vit Fojtik","submitted_at":"2025-05-27T16:51:06Z","abstract_excerpt":"The remarkable generalization properties of overparameterized networks are often attributed to implicit biases, such as norm minimization at small learning rates and low sharpness in the Edge-of-Stability regime. In this work, we argue that a comprehensive understanding of the generalization performance of gradient descent requires analyzing the interaction between these various forms of implicit regularization. We empirically demonstrate that the learning rate interpolates between low parameter norm and low sharpness of the trained model. We furthermore prove that neither implicit bias alone "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21423","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/2505.21423/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":"2026-06-08T01:03:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ktAdvJZV5F89GtgXwRds7TSxNJfTCPZEOWQhrRiNFjOBQyqsakcYmr3HBroE3WkcmhN8DEIQy1YZg9hndWWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:21:14.430726Z"},"content_sha256":"319ea3c7e40525f4912cb19ea3a1d1866d6d203282d20e24fc699c2e3acf8fa2","schema_version":"1.0","event_id":"sha256:319ea3c7e40525f4912cb19ea3a1d1866d6d203282d20e24fc699c2e3acf8fa2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NIOML7QDNXYPWKYRVA6BYETNFA/bundle.json","state_url":"https://pith.science/pith/NIOML7QDNXYPWKYRVA6BYETNFA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NIOML7QDNXYPWKYRVA6BYETNFA/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":"2026-06-26T01:21:14Z","links":{"resolver":"https://pith.science/pith/NIOML7QDNXYPWKYRVA6BYETNFA","bundle":"https://pith.science/pith/NIOML7QDNXYPWKYRVA6BYETNFA/bundle.json","state":"https://pith.science/pith/NIOML7QDNXYPWKYRVA6BYETNFA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NIOML7QDNXYPWKYRVA6BYETNFA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NIOML7QDNXYPWKYRVA6BYETNFA","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":"3eb5115752cd7b627e3e6d17cf5871f2cc6dff04746733383ad667703a5675d0","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-27T16:51:06Z","title_canon_sha256":"afd9cd186b6f7da826fce3912e0e7ef2de511a35ef1ff9b17e59a9b3227699b7"},"schema_version":"1.0","source":{"id":"2505.21423","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21423","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21423v3","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21423","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"pith_short_12","alias_value":"NIOML7QDNXYP","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"pith_short_16","alias_value":"NIOML7QDNXYPWKYR","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"pith_short_8","alias_value":"NIOML7QD","created_at":"2026-06-08T01:03:45Z"}],"graph_snapshots":[{"event_id":"sha256:319ea3c7e40525f4912cb19ea3a1d1866d6d203282d20e24fc699c2e3acf8fa2","target":"graph","created_at":"2026-06-08T01:03:45Z","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/2505.21423/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The remarkable generalization properties of overparameterized networks are often attributed to implicit biases, such as norm minimization at small learning rates and low sharpness in the Edge-of-Stability regime. In this work, we argue that a comprehensive understanding of the generalization performance of gradient descent requires analyzing the interaction between these various forms of implicit regularization. We empirically demonstrate that the learning rate interpolates between low parameter norm and low sharpness of the trained model. We furthermore prove that neither implicit bias alone ","authors_text":"Gitta Kutyniok, Hung-Hsu Chou, Johannes Maly, Maria Matveev, Vit Fojtik","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-27T16:51:06Z","title":"Conflicting Biases at the Edge of Stability: Norm versus Sharpness Regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21423","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":"sha256:8fa4f7eabd55897fe1383f8125592d3ff795a9572853f8312ef418eaf1218062","target":"record","created_at":"2026-06-08T01:03:45Z","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":"3eb5115752cd7b627e3e6d17cf5871f2cc6dff04746733383ad667703a5675d0","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-27T16:51:06Z","title_canon_sha256":"afd9cd186b6f7da826fce3912e0e7ef2de511a35ef1ff9b17e59a9b3227699b7"},"schema_version":"1.0","source":{"id":"2505.21423","kind":"arxiv","version":3}},"canonical_sha256":"6a1cc5fe036df0fb2b11a83c1c126d283405e62750eafbff0d65ca77ec184367","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a1cc5fe036df0fb2b11a83c1c126d283405e62750eafbff0d65ca77ec184367","first_computed_at":"2026-06-08T01:03:45.202913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:03:45.202913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HJAY5VJJxSAXyII36klj9tM0QQX9yPb6FzmK5JdYkzUe9nRIcbAojq/pl+7oNd9NnGzpU7xtbeNN9sTSa1lwDA==","signature_status":"signed_v1","signed_at":"2026-06-08T01:03:45.204246Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21423","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fa4f7eabd55897fe1383f8125592d3ff795a9572853f8312ef418eaf1218062","sha256:319ea3c7e40525f4912cb19ea3a1d1866d6d203282d20e24fc699c2e3acf8fa2"],"state_sha256":"ffde4b8181a70d146e47559f495e96148594aac00c9250c9f3b9d496c57d45c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vTT1sBs+v/Kcd5Ul1g0wBm9JB2jaCOmsy679A1zWPs1siv6p1MnWYutJeJVCP/P9BWP0jc/UE5B9yAvJlzvFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:21:14.432779Z","bundle_sha256":"6a578f5c43067f588579f764f02ad5d4a2801f38edfa475a413d6856477c573c"}}