{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:X6K6BOHM2TCBFDFDXJOMUX3YKK","short_pith_number":"pith:X6K6BOHM","canonical_record":{"source":{"id":"2407.18609","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-07-26T09:00:18Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"da5c877599bc87018b737111b9eb484cb8e4ccf0cabe12e579d403201498631c","abstract_canon_sha256":"76f1973869c44f34a37b3b533effa1b814198c2508d12f3ba4e3c77f6853dd5b"},"schema_version":"1.0"},"canonical_sha256":"bf95e0b8ecd4c4128ca3ba5cca5f78528793229cef574a06ec386e4d17fc1718","source":{"kind":"arxiv","id":"2407.18609","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.18609","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"2407.18609v4","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.18609","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"X6K6BOHM2TCB","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"pith_short_16","alias_value":"X6K6BOHM2TCBFDFD","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"pith_short_8","alias_value":"X6K6BOHM","created_at":"2026-07-05T11:22:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:X6K6BOHM2TCBFDFDXJOMUX3YKK","target":"record","payload":{"canonical_record":{"source":{"id":"2407.18609","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-07-26T09:00:18Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"da5c877599bc87018b737111b9eb484cb8e4ccf0cabe12e579d403201498631c","abstract_canon_sha256":"76f1973869c44f34a37b3b533effa1b814198c2508d12f3ba4e3c77f6853dd5b"},"schema_version":"1.0"},"canonical_sha256":"bf95e0b8ecd4c4128ca3ba5cca5f78528793229cef574a06ec386e4d17fc1718","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:31.453065Z","signature_b64":"xpudcQlxOLMS86NQjVhjmHv5zoS9XhXcwVAvhUjP9SbBWXLM19L/DgrFBy8aAG89TAWy+eXl3WmMLhBxBkTfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf95e0b8ecd4c4128ca3ba5cca5f78528793229cef574a06ec386e4d17fc1718","last_reissued_at":"2026-07-05T11:22:31.452500Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:31.452500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.18609","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:22:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XdSwJLoRLm7HMTbT43B7L6J6Gjtz/W2Iyg00bMph6gDUcRpx5zr9tywfg9ZOr2HidTe69/DHkojic91UU7frCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:49:45.746380Z"},"content_sha256":"4fecb7d73d738f08c3ec8dbba2ddeb0b3daef6db097a09ccff1e1850df68d7d9","schema_version":"1.0","event_id":"sha256:4fecb7d73d738f08c3ec8dbba2ddeb0b3daef6db097a09ccff1e1850df68d7d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:X6K6BOHM2TCBFDFDXJOMUX3YKK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heavy-Tailed Diffusion with Denoising L\\'evy Probabilistic Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Alain Durmus, Dario Shariatian, Umut Simsekli","submitted_at":"2024-07-26T09:00:18Z","abstract_excerpt":"Exploring noise distributions beyond Gaussian in diffusion models remains an open challenge. While Gaussian-based models succeed within a unified SDE framework, recent studies suggest that heavy-tailed noise distributions, like $\\alpha$-stable distributions, may better handle mode collapse and effectively manage datasets exhibiting class imbalance, heavy tails, or prominent outliers. Recently, Yoon et al.\\ (NeurIPS 2023), presented the L\\'evy-It\\^o model (LIM), directly extending the SDE-based framework to a class of heavy-tailed SDEs, where the injected noise followed an $\\alpha$-stable distr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.18609","kind":"arxiv","version":4},"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/2407.18609/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":"2026-07-05T11:22:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WKjr//TugLZv08sxqrPpG6+jhL86MTVKDB2U63Om215o/IGvQOpfroGDdD9wnzzzHRO+g32SWIeVhWF3hx3zAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:49:45.746910Z"},"content_sha256":"9a95f22770d9534c3476ac9a9649dfbb0bd442d9f1f22a09d998df540ce42e7b","schema_version":"1.0","event_id":"sha256:9a95f22770d9534c3476ac9a9649dfbb0bd442d9f1f22a09d998df540ce42e7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X6K6BOHM2TCBFDFDXJOMUX3YKK/bundle.json","state_url":"https://pith.science/pith/X6K6BOHM2TCBFDFDXJOMUX3YKK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X6K6BOHM2TCBFDFDXJOMUX3YKK/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":"2026-08-04T16:49:45Z","links":{"resolver":"https://pith.science/pith/X6K6BOHM2TCBFDFDXJOMUX3YKK","bundle":"https://pith.science/pith/X6K6BOHM2TCBFDFDXJOMUX3YKK/bundle.json","state":"https://pith.science/pith/X6K6BOHM2TCBFDFDXJOMUX3YKK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X6K6BOHM2TCBFDFDXJOMUX3YKK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:X6K6BOHM2TCBFDFDXJOMUX3YKK","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":"76f1973869c44f34a37b3b533effa1b814198c2508d12f3ba4e3c77f6853dd5b","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-07-26T09:00:18Z","title_canon_sha256":"da5c877599bc87018b737111b9eb484cb8e4ccf0cabe12e579d403201498631c"},"schema_version":"1.0","source":{"id":"2407.18609","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.18609","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"2407.18609v4","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.18609","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"X6K6BOHM2TCB","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"pith_short_16","alias_value":"X6K6BOHM2TCBFDFD","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"pith_short_8","alias_value":"X6K6BOHM","created_at":"2026-07-05T11:22:31Z"}],"graph_snapshots":[{"event_id":"sha256:9a95f22770d9534c3476ac9a9649dfbb0bd442d9f1f22a09d998df540ce42e7b","target":"graph","created_at":"2026-07-05T11:22:31Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.18609/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Exploring noise distributions beyond Gaussian in diffusion models remains an open challenge. While Gaussian-based models succeed within a unified SDE framework, recent studies suggest that heavy-tailed noise distributions, like $\\alpha$-stable distributions, may better handle mode collapse and effectively manage datasets exhibiting class imbalance, heavy tails, or prominent outliers. Recently, Yoon et al.\\ (NeurIPS 2023), presented the L\\'evy-It\\^o model (LIM), directly extending the SDE-based framework to a class of heavy-tailed SDEs, where the injected noise followed an $\\alpha$-stable distr","authors_text":"Alain Durmus, Dario Shariatian, Umut Simsekli","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-07-26T09:00:18Z","title":"Heavy-Tailed Diffusion with Denoising L\\'evy Probabilistic Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.18609","kind":"arxiv","version":4},"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":"sha256:4fecb7d73d738f08c3ec8dbba2ddeb0b3daef6db097a09ccff1e1850df68d7d9","target":"record","created_at":"2026-07-05T11:22:31Z","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":"76f1973869c44f34a37b3b533effa1b814198c2508d12f3ba4e3c77f6853dd5b","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-07-26T09:00:18Z","title_canon_sha256":"da5c877599bc87018b737111b9eb484cb8e4ccf0cabe12e579d403201498631c"},"schema_version":"1.0","source":{"id":"2407.18609","kind":"arxiv","version":4}},"canonical_sha256":"bf95e0b8ecd4c4128ca3ba5cca5f78528793229cef574a06ec386e4d17fc1718","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf95e0b8ecd4c4128ca3ba5cca5f78528793229cef574a06ec386e4d17fc1718","first_computed_at":"2026-07-05T11:22:31.452500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:22:31.452500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xpudcQlxOLMS86NQjVhjmHv5zoS9XhXcwVAvhUjP9SbBWXLM19L/DgrFBy8aAG89TAWy+eXl3WmMLhBxBkTfCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:22:31.453065Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.18609","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fecb7d73d738f08c3ec8dbba2ddeb0b3daef6db097a09ccff1e1850df68d7d9","sha256:9a95f22770d9534c3476ac9a9649dfbb0bd442d9f1f22a09d998df540ce42e7b"],"state_sha256":"1b241887a80cbd388294f32f15350ec144b5ccc9f2a84624cf56f86d4989b46d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tytXY/ZS+qHNIBc1YByxIodqI4ebjbQzO2wQV4MX9QHk0WVkhcvLZehOmKxjzWUZH6PLDJeOy7prXYIuEfsmBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T16:49:45.750544Z","bundle_sha256":"0254b0b5868eb8acb5798f0ceebd98921f8ceaa0337a38252d9e8983ee740034"}}