{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4NRIEDQWKUEN2TEXIBM2X4NHWK","short_pith_number":"pith:4NRIEDQW","canonical_record":{"source":{"id":"2605.18022","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T08:12:45Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"a5f0d4c35c84587b9318b7471ca79d2862839013b7da656c7fe764d47ebddee7","abstract_canon_sha256":"2a0de5d6455a852c65afd21f29e5e3585d57a8d56f4430131ade16be9bbfad80"},"schema_version":"1.0"},"canonical_sha256":"e362820e165508dd4c974059abf1a7b2aba4fb1703beb87c2922dedbc3faf165","source":{"kind":"arxiv","id":"2605.18022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18022","created_at":"2026-05-20T00:05:11Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18022v1","created_at":"2026-05-20T00:05:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18022","created_at":"2026-05-20T00:05:11Z"},{"alias_kind":"pith_short_12","alias_value":"4NRIEDQWKUEN","created_at":"2026-05-20T00:05:11Z"},{"alias_kind":"pith_short_16","alias_value":"4NRIEDQWKUEN2TEX","created_at":"2026-05-20T00:05:11Z"},{"alias_kind":"pith_short_8","alias_value":"4NRIEDQW","created_at":"2026-05-20T00:05:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4NRIEDQWKUEN2TEXIBM2X4NHWK","target":"record","payload":{"canonical_record":{"source":{"id":"2605.18022","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T08:12:45Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"a5f0d4c35c84587b9318b7471ca79d2862839013b7da656c7fe764d47ebddee7","abstract_canon_sha256":"2a0de5d6455a852c65afd21f29e5e3585d57a8d56f4430131ade16be9bbfad80"},"schema_version":"1.0"},"canonical_sha256":"e362820e165508dd4c974059abf1a7b2aba4fb1703beb87c2922dedbc3faf165","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:11.711397Z","signature_b64":"11OEtkj+4d8cas6Bx/72jHDyY7fxTuS7aG8M5HomiwprO/mBCTdCNjqY9Lzl4n9lhFUf0aojtq2OveDJDwt0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e362820e165508dd4c974059abf1a7b2aba4fb1703beb87c2922dedbc3faf165","last_reissued_at":"2026-05-20T00:05:11.710410Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:11.710410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.18022","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":"2026-05-20T00:05:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6XQAntKwMhbU2UDgYI0oEp57FR19Pz+ccQWWJCQ9mP1NRMcgwC6Dhd17VmuwnzrPNuwEy+oZu7oIJgxS//iPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:06:18.366345Z"},"content_sha256":"1a54ec609c902c4143d6fa37259e8d06e3c22e6984028cae63bf710bdc5fd31b","schema_version":"1.0","event_id":"sha256:1a54ec609c902c4143d6fa37259e8d06e3c22e6984028cae63bf710bdc5fd31b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4NRIEDQWKUEN2TEXIBM2X4NHWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unveiling Memorization-Generalization Coexistence: A Case Study on Arithmetic Tasks with Label Noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Linyu Liu, Pinyan Lu","submitted_at":"2026-05-18T08:12:45Z","abstract_excerpt":"Highly over-parameterized models can simultaneously memorize noisy labels and generalize well, yet how these behaviors coexist remains poorly understood. In this work, we investigate the underlying mechanisms of this coexistence using modular arithmetic tasks under heavy label noise. Through extensive experiments on two-layer neural networks, we find that larger models tend to generalize better under appropriate optimization and model configurations, while noisy labels are memorized faster than clean data. Over-parameterized models internally form a generalization structure, but its expression"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18022","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/2605.18022/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.517994Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"a37b0454e33b2ca0d35c944f37dbef1378c92aab5ddc05b20f0135967d81ecb4"},"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":"2026-05-20T00:05:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mcYZpR7Fn70GpxWQgCCOeuAwP5qMZ1urRIENteCg/nYwWzEdQV31jzAEb9bVITTbcQqn7q54wjiBCk7SEYCECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:06:18.366985Z"},"content_sha256":"075c7da785d300ff0688bdd21fd97c459572cc99ab8430e66876bbf67e0b313e","schema_version":"1.0","event_id":"sha256:075c7da785d300ff0688bdd21fd97c459572cc99ab8430e66876bbf67e0b313e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NRIEDQWKUEN2TEXIBM2X4NHWK/bundle.json","state_url":"https://pith.science/pith/4NRIEDQWKUEN2TEXIBM2X4NHWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NRIEDQWKUEN2TEXIBM2X4NHWK/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":"2026-05-28T21:06:18Z","links":{"resolver":"https://pith.science/pith/4NRIEDQWKUEN2TEXIBM2X4NHWK","bundle":"https://pith.science/pith/4NRIEDQWKUEN2TEXIBM2X4NHWK/bundle.json","state":"https://pith.science/pith/4NRIEDQWKUEN2TEXIBM2X4NHWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NRIEDQWKUEN2TEXIBM2X4NHWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4NRIEDQWKUEN2TEXIBM2X4NHWK","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":"2a0de5d6455a852c65afd21f29e5e3585d57a8d56f4430131ade16be9bbfad80","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T08:12:45Z","title_canon_sha256":"a5f0d4c35c84587b9318b7471ca79d2862839013b7da656c7fe764d47ebddee7"},"schema_version":"1.0","source":{"id":"2605.18022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18022","created_at":"2026-05-20T00:05:11Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18022v1","created_at":"2026-05-20T00:05:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18022","created_at":"2026-05-20T00:05:11Z"},{"alias_kind":"pith_short_12","alias_value":"4NRIEDQWKUEN","created_at":"2026-05-20T00:05:11Z"},{"alias_kind":"pith_short_16","alias_value":"4NRIEDQWKUEN2TEX","created_at":"2026-05-20T00:05:11Z"},{"alias_kind":"pith_short_8","alias_value":"4NRIEDQW","created_at":"2026-05-20T00:05:11Z"}],"graph_snapshots":[{"event_id":"sha256:075c7da785d300ff0688bdd21fd97c459572cc99ab8430e66876bbf67e0b313e","target":"graph","created_at":"2026-05-20T00:05:11Z","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":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.517994Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.18022/integrity.json","findings":[],"snapshot_sha256":"a37b0454e33b2ca0d35c944f37dbef1378c92aab5ddc05b20f0135967d81ecb4","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Highly over-parameterized models can simultaneously memorize noisy labels and generalize well, yet how these behaviors coexist remains poorly understood. In this work, we investigate the underlying mechanisms of this coexistence using modular arithmetic tasks under heavy label noise. Through extensive experiments on two-layer neural networks, we find that larger models tend to generalize better under appropriate optimization and model configurations, while noisy labels are memorized faster than clean data. Over-parameterized models internally form a generalization structure, but its expression","authors_text":"Linyu Liu, Pinyan Lu","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T08:12:45Z","title":"Unveiling Memorization-Generalization Coexistence: A Case Study on Arithmetic Tasks with Label Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18022","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":"sha256:1a54ec609c902c4143d6fa37259e8d06e3c22e6984028cae63bf710bdc5fd31b","target":"record","created_at":"2026-05-20T00:05:11Z","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":"2a0de5d6455a852c65afd21f29e5e3585d57a8d56f4430131ade16be9bbfad80","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T08:12:45Z","title_canon_sha256":"a5f0d4c35c84587b9318b7471ca79d2862839013b7da656c7fe764d47ebddee7"},"schema_version":"1.0","source":{"id":"2605.18022","kind":"arxiv","version":1}},"canonical_sha256":"e362820e165508dd4c974059abf1a7b2aba4fb1703beb87c2922dedbc3faf165","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e362820e165508dd4c974059abf1a7b2aba4fb1703beb87c2922dedbc3faf165","first_computed_at":"2026-05-20T00:05:11.710410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:11.710410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"11OEtkj+4d8cas6Bx/72jHDyY7fxTuS7aG8M5HomiwprO/mBCTdCNjqY9Lzl4n9lhFUf0aojtq2OveDJDwt0Cw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:11.711397Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.18022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a54ec609c902c4143d6fa37259e8d06e3c22e6984028cae63bf710bdc5fd31b","sha256:075c7da785d300ff0688bdd21fd97c459572cc99ab8430e66876bbf67e0b313e"],"state_sha256":"95c7b31a72d48f80bb1298e7ca837231a44037e57078840f90d34df994c666fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5vOOS4TEj8SYGQQqs2Yjck+fTB+qXQIphqNcLFyBvEldJz650fpmTEqdmM3AprrqsZHgw3R38MLNatAtTgsUCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:06:18.370198Z","bundle_sha256":"e76dd56742f492c3a6a24da6ba71c613ee05a85f344b19472844ce0ec125453d"}}