{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TNSPLWAXCQM7WHFNBI3NUMIQ7Q","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":"2868ced2af0d679389848356f189234bd426ab88e86462d50c297b9b6282b978","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-05T18:55:03Z","title_canon_sha256":"14a1717bd039ead751343f9d4b08a277b75d84eb848ca6ad71990e0ea6c3e245"},"schema_version":"1.0","source":{"id":"2602.06021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.06021","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"arxiv_version","alias_value":"2602.06021v2","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.06021","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"pith_short_12","alias_value":"TNSPLWAXCQM7","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"TNSPLWAXCQM7WHFN","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"TNSPLWAX","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:a4839db26e35d6225dd7f0d767bf6af4c67060aa0f53f97dd42a09cece241453","target":"graph","created_at":"2026-05-18T02:44:31Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Our main result shows that generated samples evolve by a reach-align-slide mechanism: they first enter a neighborhood of the ridge, then their distance to the ridge is controlled by the normal component of training error, and finally their motion along the ridge is controlled by the tangential component."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the time-dependent family of log-density ridge manifolds constructed from the smoothed empirical distribution accurately captures the relevant geometry for characterizing reverse-time inference without introducing artifacts that alter the predicted reach-align-slide behavior."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Diffusion model generated samples follow a reach-align-slide path on data-dependent ridge manifolds, with normal and tangential training error components controlling distance to and motion along the ridge."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Diffusion model samples evolve by reaching a data ridge, then aligning via normal error and sliding via tangential error."}],"snapshot_sha256":"f513519951aeaf8f69ca7d2c998c616aedfa58643ae8a4cc4750831ed6efda4b"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"224a42f8476f963639b2ca8e99eba8fc9043750ec846e7eb9e4d192edf739c3e"},"paper":{"abstract_excerpt":"We study a data-dependent notion of diffusion-model generalization: when a model does not memorize the training set, where do its generated samples go relative to the geometry induced by the data? To answer this, we introduce a time-dependent family of log-density ridge manifolds constructed from the smoothed empirical distribution, and use it to characterize reverse-time inference. Our main result shows that generated samples evolve by a reach-align-slide mechanism: they first enter a neighborhood of the ridge, then their distance to the ridge is controlled by the normal component of training","authors_text":"Molei Tao, Ye He, Yitong Qiu","cross_cats":["cs.LG","cs.NA","math.NA","math.PR"],"headline":"Diffusion model samples evolve by reaching a data ridge, then aligning via normal error and sliding via tangential error.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-05T18:55:03Z","title":"Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.06021","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-16T06:37:14.804344Z","id":"7bf276d4-c72f-4b7e-8d5d-e5294e592970","model_set":{"reader":"grok-4.3"},"one_line_summary":"Diffusion model generated samples follow a reach-align-slide path on data-dependent ridge manifolds, with normal and tangential training error components controlling distance to and motion along the ridge.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Diffusion model samples evolve by reaching a data ridge, then aligning via normal error and sliding via tangential error.","strongest_claim":"Our main result shows that generated samples evolve by a reach-align-slide mechanism: they first enter a neighborhood of the ridge, then their distance to the ridge is controlled by the normal component of training error, and finally their motion along the ridge is controlled by the tangential component.","weakest_assumption":"That the time-dependent family of log-density ridge manifolds constructed from the smoothed empirical distribution accurately captures the relevant geometry for characterizing reverse-time inference without introducing artifacts that alter the predicted reach-align-slide behavior."}},"verdict_id":"7bf276d4-c72f-4b7e-8d5d-e5294e592970"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2f2d4822e216812f33085f953db41e3cdb60a2ce3e2f6eb37aec39a8a42228f6","target":"record","created_at":"2026-05-18T02:44:31Z","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":"2868ced2af0d679389848356f189234bd426ab88e86462d50c297b9b6282b978","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-05T18:55:03Z","title_canon_sha256":"14a1717bd039ead751343f9d4b08a277b75d84eb848ca6ad71990e0ea6c3e245"},"schema_version":"1.0","source":{"id":"2602.06021","kind":"arxiv","version":2}},"canonical_sha256":"9b64f5d8171419fb1cad0a36da3110fc0c6fca3823593454606fd49cb58962dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b64f5d8171419fb1cad0a36da3110fc0c6fca3823593454606fd49cb58962dd","first_computed_at":"2026-05-18T02:44:31.384415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:31.384415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R8rbGOSVjbYP5KWSpZWf9XZ+jHRDqa5Gm8xZfx7jAtT8BZbcSWcJ3SWWX5x0lT4B3wzeGe1bK1NaUmQhc2CrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:31.384943Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.06021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f2d4822e216812f33085f953db41e3cdb60a2ce3e2f6eb37aec39a8a42228f6","sha256:a4839db26e35d6225dd7f0d767bf6af4c67060aa0f53f97dd42a09cece241453"],"state_sha256":"a1713818f62a944ef751d1f903b5826f443185db8de0e893cbc09198fe668fff"}