{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:NOGDTPALKAUBE3ZOCHHL3D5HS3","short_pith_number":"pith:NOGDTPAL","canonical_record":{"source":{"id":"2109.06587","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2021-09-14T11:20:54Z","cross_cats_sorted":[],"title_canon_sha256":"0b36edeabb666e259f8e3de941abdd693457d31ccb2672a227e5635c5f934cdf","abstract_canon_sha256":"472130b3ee1f73dc51afb070ff329ffc2b1440858e940882ac46a2c03db5769e"},"schema_version":"1.0"},"canonical_sha256":"6b8c39bc0b5028126f2e11cebd8fa796f5e0fde9c569b9c7a78335d68e89066f","source":{"kind":"arxiv","id":"2109.06587","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.06587","created_at":"2026-07-05T03:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"2109.06587v1","created_at":"2026-07-05T03:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.06587","created_at":"2026-07-05T03:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"NOGDTPALKAUB","created_at":"2026-07-05T03:14:28Z"},{"alias_kind":"pith_short_16","alias_value":"NOGDTPALKAUBE3ZO","created_at":"2026-07-05T03:14:28Z"},{"alias_kind":"pith_short_8","alias_value":"NOGDTPAL","created_at":"2026-07-05T03:14:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:NOGDTPALKAUBE3ZOCHHL3D5HS3","target":"record","payload":{"canonical_record":{"source":{"id":"2109.06587","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2021-09-14T11:20:54Z","cross_cats_sorted":[],"title_canon_sha256":"0b36edeabb666e259f8e3de941abdd693457d31ccb2672a227e5635c5f934cdf","abstract_canon_sha256":"472130b3ee1f73dc51afb070ff329ffc2b1440858e940882ac46a2c03db5769e"},"schema_version":"1.0"},"canonical_sha256":"6b8c39bc0b5028126f2e11cebd8fa796f5e0fde9c569b9c7a78335d68e89066f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:14:28.323606Z","signature_b64":"sTy/lem18VvBnoRCbHbpJ9XodBQ+wNeGbWG0Xb99Q1rFp+lVhCfkXCwAJlTS4tRET9K/DDLbmLzvjAYz0HTuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b8c39bc0b5028126f2e11cebd8fa796f5e0fde9c569b9c7a78335d68e89066f","last_reissued_at":"2026-07-05T03:14:28.323169Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:14:28.323169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.06587","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JxDSMcnZHZWDAZWnxobvUjKrg6tFau/oapwO7oHmq3L8EJU5f2xF1qOolkQWwTlYNm6HgMWvy9VgW8xmO+c3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T14:57:56.796706Z"},"content_sha256":"1c018ac518d861bebcad6daaff7ddbd249e81de34b300612512997968024696e","schema_version":"1.0","event_id":"sha256:1c018ac518d861bebcad6daaff7ddbd249e81de34b300612512997968024696e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:NOGDTPALKAUBE3ZOCHHL3D5HS3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sum-Product-Attention Networks: Leveraging Self-Attention in Probabilistic Circuits","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Devendra Singh Dhami, Kristian Kersting, Zhongjie Yu","submitted_at":"2021-09-14T11:20:54Z","abstract_excerpt":"Probabilistic circuits (PCs) have become the de-facto standard for learning and inference in probabilistic modeling. We introduce Sum-Product-Attention Networks (SPAN), a new generative model that integrates probabilistic circuits with Transformers. SPAN uses self-attention to select the most relevant parts of a probabilistic circuit, here sum-product networks, to improve the modeling capability of the underlying sum-product network. We show that while modeling, SPAN focuses on a specific set of independent assumptions in every product layer of the sum-product network. Our empirical evaluation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.06587","kind":"arxiv","version":1},"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/2109.06587/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":"2026-07-05T03:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LFPSR9tKAWFum8rFpptCjHXC8KDIdsWlQyunLZWIjrNapKLWy+9rbWpT/R2caFDxwBGdkNtm2FeWem8i+2bFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T14:57:56.797064Z"},"content_sha256":"40ad6dfc4530298558f6e55d0e664ab7654f0586f40e12436ef91275e2af1e16","schema_version":"1.0","event_id":"sha256:40ad6dfc4530298558f6e55d0e664ab7654f0586f40e12436ef91275e2af1e16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NOGDTPALKAUBE3ZOCHHL3D5HS3/bundle.json","state_url":"https://pith.science/pith/NOGDTPALKAUBE3ZOCHHL3D5HS3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NOGDTPALKAUBE3ZOCHHL3D5HS3/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":"2026-07-13T14:57:56Z","links":{"resolver":"https://pith.science/pith/NOGDTPALKAUBE3ZOCHHL3D5HS3","bundle":"https://pith.science/pith/NOGDTPALKAUBE3ZOCHHL3D5HS3/bundle.json","state":"https://pith.science/pith/NOGDTPALKAUBE3ZOCHHL3D5HS3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NOGDTPALKAUBE3ZOCHHL3D5HS3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:NOGDTPALKAUBE3ZOCHHL3D5HS3","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":"472130b3ee1f73dc51afb070ff329ffc2b1440858e940882ac46a2c03db5769e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2021-09-14T11:20:54Z","title_canon_sha256":"0b36edeabb666e259f8e3de941abdd693457d31ccb2672a227e5635c5f934cdf"},"schema_version":"1.0","source":{"id":"2109.06587","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.06587","created_at":"2026-07-05T03:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"2109.06587v1","created_at":"2026-07-05T03:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.06587","created_at":"2026-07-05T03:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"NOGDTPALKAUB","created_at":"2026-07-05T03:14:28Z"},{"alias_kind":"pith_short_16","alias_value":"NOGDTPALKAUBE3ZO","created_at":"2026-07-05T03:14:28Z"},{"alias_kind":"pith_short_8","alias_value":"NOGDTPAL","created_at":"2026-07-05T03:14:28Z"}],"graph_snapshots":[{"event_id":"sha256:40ad6dfc4530298558f6e55d0e664ab7654f0586f40e12436ef91275e2af1e16","target":"graph","created_at":"2026-07-05T03:14:28Z","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/2109.06587/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Probabilistic circuits (PCs) have become the de-facto standard for learning and inference in probabilistic modeling. We introduce Sum-Product-Attention Networks (SPAN), a new generative model that integrates probabilistic circuits with Transformers. SPAN uses self-attention to select the most relevant parts of a probabilistic circuit, here sum-product networks, to improve the modeling capability of the underlying sum-product network. We show that while modeling, SPAN focuses on a specific set of independent assumptions in every product layer of the sum-product network. Our empirical evaluation","authors_text":"Devendra Singh Dhami, Kristian Kersting, Zhongjie Yu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2021-09-14T11:20:54Z","title":"Sum-Product-Attention Networks: Leveraging Self-Attention in Probabilistic Circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.06587","kind":"arxiv","version":1},"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":"sha256:1c018ac518d861bebcad6daaff7ddbd249e81de34b300612512997968024696e","target":"record","created_at":"2026-07-05T03:14:28Z","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":"472130b3ee1f73dc51afb070ff329ffc2b1440858e940882ac46a2c03db5769e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2021-09-14T11:20:54Z","title_canon_sha256":"0b36edeabb666e259f8e3de941abdd693457d31ccb2672a227e5635c5f934cdf"},"schema_version":"1.0","source":{"id":"2109.06587","kind":"arxiv","version":1}},"canonical_sha256":"6b8c39bc0b5028126f2e11cebd8fa796f5e0fde9c569b9c7a78335d68e89066f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b8c39bc0b5028126f2e11cebd8fa796f5e0fde9c569b9c7a78335d68e89066f","first_computed_at":"2026-07-05T03:14:28.323169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:14:28.323169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sTy/lem18VvBnoRCbHbpJ9XodBQ+wNeGbWG0Xb99Q1rFp+lVhCfkXCwAJlTS4tRET9K/DDLbmLzvjAYz0HTuDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:14:28.323606Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.06587","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c018ac518d861bebcad6daaff7ddbd249e81de34b300612512997968024696e","sha256:40ad6dfc4530298558f6e55d0e664ab7654f0586f40e12436ef91275e2af1e16"],"state_sha256":"3cd87214e3a8548adcd1868b8708d808fc9be323d253b034787b0d7a5568d7f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E5v6x2uXeCC9XHCbTqbvbuh/jO7cGRXE15zkB4IU3oyJYeVpj+p5XJG2iiPGt/BISoelvNfHCa9e3DzXyCMvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-13T14:57:56.799000Z","bundle_sha256":"32b031d12fb73d941192a34faf0050c5f490afad0ee373fa3342c475a0c393d0"}}