{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:WAWF4GM2PSYYZXNOZTTR56WFTV","short_pith_number":"pith:WAWF4GM2","canonical_record":{"source":{"id":"2106.07832","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-15T01:35:17Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"2ca6e759590958222271894a8c4458afdf3c08f4eb8ab34152c1ec9270b47077","abstract_canon_sha256":"6fe163b32ca12b26862214888e4cc34c667884a4e216d3fd6d9788a6718c7f6a"},"schema_version":"1.0"},"canonical_sha256":"b02c5e199a7cb18cddaecce71efac59d553380abedb01baf6fc21c6b86ee5961","source":{"kind":"arxiv","id":"2106.07832","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.07832","created_at":"2026-07-05T03:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"2106.07832v2","created_at":"2026-07-05T03:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.07832","created_at":"2026-07-05T03:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"WAWF4GM2PSYY","created_at":"2026-07-05T03:01:36Z"},{"alias_kind":"pith_short_16","alias_value":"WAWF4GM2PSYYZXNO","created_at":"2026-07-05T03:01:36Z"},{"alias_kind":"pith_short_8","alias_value":"WAWF4GM2","created_at":"2026-07-05T03:01:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:WAWF4GM2PSYYZXNOZTTR56WFTV","target":"record","payload":{"canonical_record":{"source":{"id":"2106.07832","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-15T01:35:17Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"2ca6e759590958222271894a8c4458afdf3c08f4eb8ab34152c1ec9270b47077","abstract_canon_sha256":"6fe163b32ca12b26862214888e4cc34c667884a4e216d3fd6d9788a6718c7f6a"},"schema_version":"1.0"},"canonical_sha256":"b02c5e199a7cb18cddaecce71efac59d553380abedb01baf6fc21c6b86ee5961","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:01:36.517540Z","signature_b64":"4dNc3VGLfn8qBuukwwLQW6i85gMp6Iyg+3W+Xw5z5SEMd14kdf11Kl8Ccrp26HIWtg8KnRgQXUeIJvwLzGfhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b02c5e199a7cb18cddaecce71efac59d553380abedb01baf6fc21c6b86ee5961","last_reissued_at":"2026-07-05T03:01:36.517179Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:01:36.517179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.07832","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":"2026-07-05T03:01:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BROehDzFD+CxChhg3OLHbZ7ZQ0hgVaPfKFPAqHADNF06Uy8Rtfk7g/L4DpoqwhZTyEVaDp5Xi4ASz3kVkhHPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T23:34:28.705494Z"},"content_sha256":"b8eff30f99d0fd162f290930e8a2f26f9b0729f093909e1168e69e28035129a6","schema_version":"1.0","event_id":"sha256:b8eff30f99d0fd162f290930e8a2f26f9b0729f093909e1168e69e28035129a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:WAWF4GM2PSYYZXNOZTTR56WFTV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Lars Holdijk, Max Welling, Priyank Jaini","submitted_at":"2021-06-15T01:35:17Z","abstract_excerpt":"We focus on the problem of efficient sampling and learning of probability densities by incorporating symmetries in probabilistic models. We first introduce Equivariant Stein Variational Gradient Descent algorithm -- an equivariant sampling method based on Stein's identity for sampling from densities with symmetries. Equivariant SVGD explicitly incorporates symmetry information in a density through equivariant kernels which makes the resultant sampler efficient both in terms of sample complexity and the quality of generated samples. Subsequently, we define equivariant energy based models to mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.07832","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/2106.07832/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":"2026-07-05T03:01:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rvPQmrCCIF86IEsmMX9vtliAIhwl4xsnWG/d439tWi2ufq94Ql8tzrp/Au3I0ISoB1pvnpwVBX7JqFEKVEoWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T23:34:28.706012Z"},"content_sha256":"80eb08e58c720d245034c47ead91a42e50ce87087aa69080c56eedc682502521","schema_version":"1.0","event_id":"sha256:80eb08e58c720d245034c47ead91a42e50ce87087aa69080c56eedc682502521"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WAWF4GM2PSYYZXNOZTTR56WFTV/bundle.json","state_url":"https://pith.science/pith/WAWF4GM2PSYYZXNOZTTR56WFTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WAWF4GM2PSYYZXNOZTTR56WFTV/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":"2026-08-04T23:34:28Z","links":{"resolver":"https://pith.science/pith/WAWF4GM2PSYYZXNOZTTR56WFTV","bundle":"https://pith.science/pith/WAWF4GM2PSYYZXNOZTTR56WFTV/bundle.json","state":"https://pith.science/pith/WAWF4GM2PSYYZXNOZTTR56WFTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WAWF4GM2PSYYZXNOZTTR56WFTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:WAWF4GM2PSYYZXNOZTTR56WFTV","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":"6fe163b32ca12b26862214888e4cc34c667884a4e216d3fd6d9788a6718c7f6a","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-15T01:35:17Z","title_canon_sha256":"2ca6e759590958222271894a8c4458afdf3c08f4eb8ab34152c1ec9270b47077"},"schema_version":"1.0","source":{"id":"2106.07832","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.07832","created_at":"2026-07-05T03:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"2106.07832v2","created_at":"2026-07-05T03:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.07832","created_at":"2026-07-05T03:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"WAWF4GM2PSYY","created_at":"2026-07-05T03:01:36Z"},{"alias_kind":"pith_short_16","alias_value":"WAWF4GM2PSYYZXNO","created_at":"2026-07-05T03:01:36Z"},{"alias_kind":"pith_short_8","alias_value":"WAWF4GM2","created_at":"2026-07-05T03:01:36Z"}],"graph_snapshots":[{"event_id":"sha256:80eb08e58c720d245034c47ead91a42e50ce87087aa69080c56eedc682502521","target":"graph","created_at":"2026-07-05T03:01:36Z","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/2106.07832/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We focus on the problem of efficient sampling and learning of probability densities by incorporating symmetries in probabilistic models. We first introduce Equivariant Stein Variational Gradient Descent algorithm -- an equivariant sampling method based on Stein's identity for sampling from densities with symmetries. Equivariant SVGD explicitly incorporates symmetry information in a density through equivariant kernels which makes the resultant sampler efficient both in terms of sample complexity and the quality of generated samples. Subsequently, we define equivariant energy based models to mod","authors_text":"Lars Holdijk, Max Welling, Priyank Jaini","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-15T01:35:17Z","title":"Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.07832","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:b8eff30f99d0fd162f290930e8a2f26f9b0729f093909e1168e69e28035129a6","target":"record","created_at":"2026-07-05T03:01:36Z","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":"6fe163b32ca12b26862214888e4cc34c667884a4e216d3fd6d9788a6718c7f6a","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-15T01:35:17Z","title_canon_sha256":"2ca6e759590958222271894a8c4458afdf3c08f4eb8ab34152c1ec9270b47077"},"schema_version":"1.0","source":{"id":"2106.07832","kind":"arxiv","version":2}},"canonical_sha256":"b02c5e199a7cb18cddaecce71efac59d553380abedb01baf6fc21c6b86ee5961","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b02c5e199a7cb18cddaecce71efac59d553380abedb01baf6fc21c6b86ee5961","first_computed_at":"2026-07-05T03:01:36.517179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:01:36.517179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4dNc3VGLfn8qBuukwwLQW6i85gMp6Iyg+3W+Xw5z5SEMd14kdf11Kl8Ccrp26HIWtg8KnRgQXUeIJvwLzGfhDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:01:36.517540Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.07832","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8eff30f99d0fd162f290930e8a2f26f9b0729f093909e1168e69e28035129a6","sha256:80eb08e58c720d245034c47ead91a42e50ce87087aa69080c56eedc682502521"],"state_sha256":"fc41ca1ccf4dca3d2464265235c80b4eecdef6e69e618035e4870c047bc30e1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7gaGpTPZ5P8GINyjorRVYZ9JcxvYFCv6siVZ1yei55DdEBxSprFzeBvbmxIO9smBfe7n9yU4tX45qLNMmfcKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T23:34:28.711008Z","bundle_sha256":"88875bdfcc707ec46067f60b0df924e1880655666cea18d4e119f6c8b97dccfe"}}