{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OGSJUDJU2ORS6HR3BXR56TRYCA","short_pith_number":"pith:OGSJUDJU","canonical_record":{"source":{"id":"2411.00113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-10-31T18:09:01Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7bbd971bf5ef223cb42b1f1ba1e007fbeaacf73c4e6c24c6fb885b47ca18c15c","abstract_canon_sha256":"0d6cda8121d1b09abc8b4cd5b514e53907a2b4a5403353dc3812b0e50e7d462f"},"schema_version":"1.0"},"canonical_sha256":"71a49a0d34d3a32f1e3b0de3df4e38101ae9b1478dfa55a1abd55540e1af85ea","source":{"kind":"arxiv","id":"2411.00113","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.00113","created_at":"2026-07-05T10:30:02Z"},{"alias_kind":"arxiv_version","alias_value":"2411.00113v2","created_at":"2026-07-05T10:30:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.00113","created_at":"2026-07-05T10:30:02Z"},{"alias_kind":"pith_short_12","alias_value":"OGSJUDJU2ORS","created_at":"2026-07-05T10:30:02Z"},{"alias_kind":"pith_short_16","alias_value":"OGSJUDJU2ORS6HR3","created_at":"2026-07-05T10:30:02Z"},{"alias_kind":"pith_short_8","alias_value":"OGSJUDJU","created_at":"2026-07-05T10:30:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OGSJUDJU2ORS6HR3BXR56TRYCA","target":"record","payload":{"canonical_record":{"source":{"id":"2411.00113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-10-31T18:09:01Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7bbd971bf5ef223cb42b1f1ba1e007fbeaacf73c4e6c24c6fb885b47ca18c15c","abstract_canon_sha256":"0d6cda8121d1b09abc8b4cd5b514e53907a2b4a5403353dc3812b0e50e7d462f"},"schema_version":"1.0"},"canonical_sha256":"71a49a0d34d3a32f1e3b0de3df4e38101ae9b1478dfa55a1abd55540e1af85ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:30:02.686838Z","signature_b64":"+5F7yG9XNe1E821Mw3921n3ooqOcrdHs7Ou+LfMxxK039RAw7Axx2rpIoCkXerg3AvWxCEhZABrcRJm3i8GbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71a49a0d34d3a32f1e3b0de3df4e38101ae9b1478dfa55a1abd55540e1af85ea","last_reissued_at":"2026-07-05T10:30:02.686183Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:30:02.686183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.00113","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":"2026-07-05T10:30:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/DXnF6HPijcdpJrJIY4AwDQ+757hf3plPUh41UN1W5QhZsP1gu4p7/TWzWJvgYOGpGs/Jz1GSigoOmdly2w2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T10:29:18.029075Z"},"content_sha256":"ecd0300511f8e4a5774b4e61f44ac8947f8e94ea702777267d8e0a180f4686ae","schema_version":"1.0","event_id":"sha256:ecd0300511f8e4a5774b4e61f44ac8947f8e94ea702777267d8e0a180f4686ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OGSJUDJU2ORS6HR3BXR56TRYCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Geometric Framework for Understanding Memorization in Generative Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Brendan Leigh Ross, Gabriel Loaiza-Ganem, George Stein, Hamidreza Kamkari, Jesse C. Cresswell, Rasa Hosseinzadeh, Tongzi Wu, Zhaoyan Liu","submitted_at":"2024-10-31T18:09:01Z","abstract_excerpt":"As deep generative models have progressed, recent work has shown them to be capable of memorizing and reproducing training datapoints when deployed. These findings call into question the usability of generative models, especially in light of the legal and privacy risks brought about by memorization. To better understand this phenomenon, we propose the manifold memorization hypothesis (MMH), a geometric framework which leverages the manifold hypothesis into a clear language in which to reason about memorization. We propose to analyze memorization in terms of the relationship between the dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.00113","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/2411.00113/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":"2026-07-05T10:30:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eBxx9/Fla2N4kbALwVee6+pNcP1ejSvCgyzTNSq15nJ8rKdOBgXPxsUtb+gBQWJsULApMY8PpukZ0wEe3mA2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T10:29:18.029940Z"},"content_sha256":"dbc48462368a4c106f4aa5593c06d932f219ab4f901f59cdea8df73c98723688","schema_version":"1.0","event_id":"sha256:dbc48462368a4c106f4aa5593c06d932f219ab4f901f59cdea8df73c98723688"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGSJUDJU2ORS6HR3BXR56TRYCA/bundle.json","state_url":"https://pith.science/pith/OGSJUDJU2ORS6HR3BXR56TRYCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGSJUDJU2ORS6HR3BXR56TRYCA/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":"2026-08-09T10:29:18Z","links":{"resolver":"https://pith.science/pith/OGSJUDJU2ORS6HR3BXR56TRYCA","bundle":"https://pith.science/pith/OGSJUDJU2ORS6HR3BXR56TRYCA/bundle.json","state":"https://pith.science/pith/OGSJUDJU2ORS6HR3BXR56TRYCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGSJUDJU2ORS6HR3BXR56TRYCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OGSJUDJU2ORS6HR3BXR56TRYCA","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":"0d6cda8121d1b09abc8b4cd5b514e53907a2b4a5403353dc3812b0e50e7d462f","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-10-31T18:09:01Z","title_canon_sha256":"7bbd971bf5ef223cb42b1f1ba1e007fbeaacf73c4e6c24c6fb885b47ca18c15c"},"schema_version":"1.0","source":{"id":"2411.00113","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.00113","created_at":"2026-07-05T10:30:02Z"},{"alias_kind":"arxiv_version","alias_value":"2411.00113v2","created_at":"2026-07-05T10:30:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.00113","created_at":"2026-07-05T10:30:02Z"},{"alias_kind":"pith_short_12","alias_value":"OGSJUDJU2ORS","created_at":"2026-07-05T10:30:02Z"},{"alias_kind":"pith_short_16","alias_value":"OGSJUDJU2ORS6HR3","created_at":"2026-07-05T10:30:02Z"},{"alias_kind":"pith_short_8","alias_value":"OGSJUDJU","created_at":"2026-07-05T10:30:02Z"}],"graph_snapshots":[{"event_id":"sha256:dbc48462368a4c106f4aa5593c06d932f219ab4f901f59cdea8df73c98723688","target":"graph","created_at":"2026-07-05T10:30:02Z","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/2411.00113/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"As deep generative models have progressed, recent work has shown them to be capable of memorizing and reproducing training datapoints when deployed. These findings call into question the usability of generative models, especially in light of the legal and privacy risks brought about by memorization. To better understand this phenomenon, we propose the manifold memorization hypothesis (MMH), a geometric framework which leverages the manifold hypothesis into a clear language in which to reason about memorization. We propose to analyze memorization in terms of the relationship between the dimensi","authors_text":"Brendan Leigh Ross, Gabriel Loaiza-Ganem, George Stein, Hamidreza Kamkari, Jesse C. Cresswell, Rasa Hosseinzadeh, Tongzi Wu, Zhaoyan Liu","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-10-31T18:09:01Z","title":"A Geometric Framework for Understanding Memorization in Generative Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.00113","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:ecd0300511f8e4a5774b4e61f44ac8947f8e94ea702777267d8e0a180f4686ae","target":"record","created_at":"2026-07-05T10:30:02Z","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":"0d6cda8121d1b09abc8b4cd5b514e53907a2b4a5403353dc3812b0e50e7d462f","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-10-31T18:09:01Z","title_canon_sha256":"7bbd971bf5ef223cb42b1f1ba1e007fbeaacf73c4e6c24c6fb885b47ca18c15c"},"schema_version":"1.0","source":{"id":"2411.00113","kind":"arxiv","version":2}},"canonical_sha256":"71a49a0d34d3a32f1e3b0de3df4e38101ae9b1478dfa55a1abd55540e1af85ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71a49a0d34d3a32f1e3b0de3df4e38101ae9b1478dfa55a1abd55540e1af85ea","first_computed_at":"2026-07-05T10:30:02.686183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:30:02.686183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+5F7yG9XNe1E821Mw3921n3ooqOcrdHs7Ou+LfMxxK039RAw7Axx2rpIoCkXerg3AvWxCEhZABrcRJm3i8GbBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:30:02.686838Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.00113","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecd0300511f8e4a5774b4e61f44ac8947f8e94ea702777267d8e0a180f4686ae","sha256:dbc48462368a4c106f4aa5593c06d932f219ab4f901f59cdea8df73c98723688"],"state_sha256":"a961021d355db317243b1069e41b31821bff27c08a2245a7e94316f86e7ced71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ClYLObui2TVGT+1/WuBNMaHjA2swvYxGlgqUFRhpARYVelrNjGD0gSVqxAQnA/8/TBsXq+cqOvX8CXi1SP1jAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T10:29:18.036729Z","bundle_sha256":"fa45e0b5ce57eef5e6f41faaf6c76fab6cdb99d7ca4d152e121d5b0249a11eae"}}