{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:5OMFNBJAV2AUC2UVDDFUB3HUXC","short_pith_number":"pith:5OMFNBJA","canonical_record":{"source":{"id":"2007.03317","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-07T10:05:01Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"238369117bf085ccb90f4e22a9a41ab6dc87f0f1a423eb7770a903ba4f0602f1","abstract_canon_sha256":"de01d35067604df57b2e86850e5561a07c04fc594bac09991b4dbbd8472f32a6"},"schema_version":"1.0"},"canonical_sha256":"eb98568520ae81416a9518cb40ecf4b8a8ac85e005fb0ad1c6e08f439f924330","source":{"kind":"arxiv","id":"2007.03317","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.03317","created_at":"2026-07-05T01:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"2007.03317v2","created_at":"2026-07-05T01:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.03317","created_at":"2026-07-05T01:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"5OMFNBJAV2AU","created_at":"2026-07-05T01:54:29Z"},{"alias_kind":"pith_short_16","alias_value":"5OMFNBJAV2AUC2UV","created_at":"2026-07-05T01:54:29Z"},{"alias_kind":"pith_short_8","alias_value":"5OMFNBJA","created_at":"2026-07-05T01:54:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:5OMFNBJAV2AUC2UVDDFUB3HUXC","target":"record","payload":{"canonical_record":{"source":{"id":"2007.03317","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-07T10:05:01Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"238369117bf085ccb90f4e22a9a41ab6dc87f0f1a423eb7770a903ba4f0602f1","abstract_canon_sha256":"de01d35067604df57b2e86850e5561a07c04fc594bac09991b4dbbd8472f32a6"},"schema_version":"1.0"},"canonical_sha256":"eb98568520ae81416a9518cb40ecf4b8a8ac85e005fb0ad1c6e08f439f924330","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:54:29.309410Z","signature_b64":"26Zgp33/GTp/ah+q5ayC1ANIAwKIfjIEUXmRf8XPFPhhpXtc5ffuSwy80mz6l0d8aSON4bXWUu58+mwe+MfiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb98568520ae81416a9518cb40ecf4b8a8ac85e005fb0ad1c6e08f439f924330","last_reissued_at":"2026-07-05T01:54:29.308963Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:54:29.308963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.03317","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":"2026-07-05T01:54:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3n8rPXbMrfAdZA9wjp9GmrTc1ZWXHfdMmpgc7c/OVja1Dzp0FgDGfj2COxlyhJXgLU0YhPnBI81zQyGjn7paCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T21:11:46.044885Z"},"content_sha256":"1a4f49332a613427b0eb3af4beb9b730df59e916bf2d32271e546094233611c3","schema_version":"1.0","event_id":"sha256:1a4f49332a613427b0eb3af4beb9b730df59e916bf2d32271e546094233611c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:5OMFNBJAV2AUC2UVDDFUB3HUXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Learning of Generative Models via Finite-Difference Score Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Chongxuan Li, Jun Zhu, Kun Xu, Stefano Ermon, Tianyu Pang, Yang Song","submitted_at":"2020-07-07T10:05:01Z","abstract_excerpt":"Several machine learning applications involve the optimization of higher-order derivatives (e.g., gradients of gradients) during training, which can be expensive in respect to memory and computation even with automatic differentiation. As a typical example in generative modeling, score matching (SM) involves the optimization of the trace of a Hessian. To improve computing efficiency, we rewrite the SM objective and its variants in terms of directional derivatives, and present a generic strategy to efficiently approximate any-order directional derivative with finite difference (FD). Our approxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.03317","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/2007.03317/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":"2026-07-05T01:54:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IRfZbAti/mjBKHBpv2ZpF7MmqantECDROWHaavbWyv2/BlN5ClFD5/NjOQaBXwhg2dLoUO+NO/gvD5Yq9yUyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T21:11:46.045658Z"},"content_sha256":"40b1f29d8af9f4325c2e1409d3c8adacc90ff993f322104e15fba9e954d67545","schema_version":"1.0","event_id":"sha256:40b1f29d8af9f4325c2e1409d3c8adacc90ff993f322104e15fba9e954d67545"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5OMFNBJAV2AUC2UVDDFUB3HUXC/bundle.json","state_url":"https://pith.science/pith/5OMFNBJAV2AUC2UVDDFUB3HUXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5OMFNBJAV2AUC2UVDDFUB3HUXC/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":"2026-08-15T21:11:46Z","links":{"resolver":"https://pith.science/pith/5OMFNBJAV2AUC2UVDDFUB3HUXC","bundle":"https://pith.science/pith/5OMFNBJAV2AUC2UVDDFUB3HUXC/bundle.json","state":"https://pith.science/pith/5OMFNBJAV2AUC2UVDDFUB3HUXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5OMFNBJAV2AUC2UVDDFUB3HUXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:5OMFNBJAV2AUC2UVDDFUB3HUXC","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":"de01d35067604df57b2e86850e5561a07c04fc594bac09991b4dbbd8472f32a6","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-07T10:05:01Z","title_canon_sha256":"238369117bf085ccb90f4e22a9a41ab6dc87f0f1a423eb7770a903ba4f0602f1"},"schema_version":"1.0","source":{"id":"2007.03317","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.03317","created_at":"2026-07-05T01:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"2007.03317v2","created_at":"2026-07-05T01:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.03317","created_at":"2026-07-05T01:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"5OMFNBJAV2AU","created_at":"2026-07-05T01:54:29Z"},{"alias_kind":"pith_short_16","alias_value":"5OMFNBJAV2AUC2UV","created_at":"2026-07-05T01:54:29Z"},{"alias_kind":"pith_short_8","alias_value":"5OMFNBJA","created_at":"2026-07-05T01:54:29Z"}],"graph_snapshots":[{"event_id":"sha256:40b1f29d8af9f4325c2e1409d3c8adacc90ff993f322104e15fba9e954d67545","target":"graph","created_at":"2026-07-05T01:54:29Z","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/2007.03317/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Several machine learning applications involve the optimization of higher-order derivatives (e.g., gradients of gradients) during training, which can be expensive in respect to memory and computation even with automatic differentiation. As a typical example in generative modeling, score matching (SM) involves the optimization of the trace of a Hessian. To improve computing efficiency, we rewrite the SM objective and its variants in terms of directional derivatives, and present a generic strategy to efficiently approximate any-order directional derivative with finite difference (FD). Our approxi","authors_text":"Chongxuan Li, Jun Zhu, Kun Xu, Stefano Ermon, Tianyu Pang, Yang Song","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-07T10:05:01Z","title":"Efficient Learning of Generative Models via Finite-Difference Score Matching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.03317","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":"sha256:1a4f49332a613427b0eb3af4beb9b730df59e916bf2d32271e546094233611c3","target":"record","created_at":"2026-07-05T01:54:29Z","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":"de01d35067604df57b2e86850e5561a07c04fc594bac09991b4dbbd8472f32a6","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-07T10:05:01Z","title_canon_sha256":"238369117bf085ccb90f4e22a9a41ab6dc87f0f1a423eb7770a903ba4f0602f1"},"schema_version":"1.0","source":{"id":"2007.03317","kind":"arxiv","version":2}},"canonical_sha256":"eb98568520ae81416a9518cb40ecf4b8a8ac85e005fb0ad1c6e08f439f924330","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb98568520ae81416a9518cb40ecf4b8a8ac85e005fb0ad1c6e08f439f924330","first_computed_at":"2026-07-05T01:54:29.308963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:54:29.308963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"26Zgp33/GTp/ah+q5ayC1ANIAwKIfjIEUXmRf8XPFPhhpXtc5ffuSwy80mz6l0d8aSON4bXWUu58+mwe+MfiAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:54:29.309410Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.03317","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a4f49332a613427b0eb3af4beb9b730df59e916bf2d32271e546094233611c3","sha256:40b1f29d8af9f4325c2e1409d3c8adacc90ff993f322104e15fba9e954d67545"],"state_sha256":"8581f4c159bc2d44ec1eb51a6153938bee0493d48bfd371dc8268c4df982c044"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T9s9Fs8HhRUmyS4gBzv7pZejD/Ju7WMBnoZoj7SeBcRPeSfr9oexX17Htmr3aPaElJExn8UAhYlecsUniqJ3AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T21:11:46.052527Z","bundle_sha256":"c6e73ec72e23dc90ed0408325cad284d0afac35a98476f6a13bdc7b30f77c19e"}}