{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:FPT7FIAG5AMGDZO7HRRL6G664N","short_pith_number":"pith:FPT7FIAG","canonical_record":{"source":{"id":"2012.10885","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-20T11:02:49Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"4da6417018cf57fad92b1ae6ddab6d5574664f6933440d9407d4133131e45bec","abstract_canon_sha256":"3c98c25f13795a41badd748c789d16979cac58978ce273124a03b4c6d6ff2986"},"schema_version":"1.0"},"canonical_sha256":"2be7f2a006e81861e5df3c62bf1bdee379cb4424e0d6cd8594b390a997e9dffe","source":{"kind":"arxiv","id":"2012.10885","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.10885","created_at":"2026-07-05T02:49:52Z"},{"alias_kind":"arxiv_version","alias_value":"2012.10885v4","created_at":"2026-07-05T02:49:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.10885","created_at":"2026-07-05T02:49:52Z"},{"alias_kind":"pith_short_12","alias_value":"FPT7FIAG5AMG","created_at":"2026-07-05T02:49:52Z"},{"alias_kind":"pith_short_16","alias_value":"FPT7FIAG5AMGDZO7","created_at":"2026-07-05T02:49:52Z"},{"alias_kind":"pith_short_8","alias_value":"FPT7FIAG","created_at":"2026-07-05T02:49:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:FPT7FIAG5AMGDZO7HRRL6G664N","target":"record","payload":{"canonical_record":{"source":{"id":"2012.10885","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-20T11:02:49Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"4da6417018cf57fad92b1ae6ddab6d5574664f6933440d9407d4133131e45bec","abstract_canon_sha256":"3c98c25f13795a41badd748c789d16979cac58978ce273124a03b4c6d6ff2986"},"schema_version":"1.0"},"canonical_sha256":"2be7f2a006e81861e5df3c62bf1bdee379cb4424e0d6cd8594b390a997e9dffe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:49:52.206217Z","signature_b64":"HJV5DW/6Ax/+dA8xGlvH0crV5+/AE9aYhSrlqDvsBFWICBbkUfRaCsiTaQmg23iXdeJjf/T+vckzlg4vCkilAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2be7f2a006e81861e5df3c62bf1bdee379cb4424e0d6cd8594b390a997e9dffe","last_reissued_at":"2026-07-05T02:49:52.205727Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:49:52.205727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.10885","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":"2026-07-05T02:49:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6TIAX98nYalCGmA6WY+miDCUdRoJU5zRx7nZ8rNPt93S0aSkTpb2XKM1sw9iN8PLEjMvo2FmeX9KdYnJBopDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T11:37:09.397627Z"},"content_sha256":"f5d19413a4a80f2d42c0716f64c489cbdb54f1383e79a90742d63561d6505b28","schema_version":"1.0","event_id":"sha256:f5d19413a4a80f2d42c0716f64c489cbdb54f1383e79a90742d63561d6505b28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:FPT7FIAG5AMGDZO7HRRL6G664N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"LieTransformer: Equivariant self-attention for Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Charline Le Lan, Emilien Dupont, Hyunjik Kim, Michael Hutchinson, Sheheryar Zaidi, Yee Whye Teh","submitted_at":"2020-12-20T11:02:49Z","abstract_excerpt":"Group equivariant neural networks are used as building blocks of group invariant neural networks, which have been shown to improve generalisation performance and data efficiency through principled parameter sharing. Such works have mostly focused on group equivariant convolutions, building on the result that group equivariant linear maps are necessarily convolutions. In this work, we extend the scope of the literature to self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10885","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/2012.10885/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":"2026-07-05T02:49:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TwoHy14GtceSaBDpn1+Mgz1bHj8pgGXPywsAlnmKniOfGXDJpdtRZoyZPCFEIZ8qppCOuOWdEo39TOtpW5hQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T11:37:09.398155Z"},"content_sha256":"8823cd61d1606152b8dfbf115b679805693d82817254264a1adb437d09a15460","schema_version":"1.0","event_id":"sha256:8823cd61d1606152b8dfbf115b679805693d82817254264a1adb437d09a15460"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FPT7FIAG5AMGDZO7HRRL6G664N/bundle.json","state_url":"https://pith.science/pith/FPT7FIAG5AMGDZO7HRRL6G664N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FPT7FIAG5AMGDZO7HRRL6G664N/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":"2026-08-07T11:37:09Z","links":{"resolver":"https://pith.science/pith/FPT7FIAG5AMGDZO7HRRL6G664N","bundle":"https://pith.science/pith/FPT7FIAG5AMGDZO7HRRL6G664N/bundle.json","state":"https://pith.science/pith/FPT7FIAG5AMGDZO7HRRL6G664N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FPT7FIAG5AMGDZO7HRRL6G664N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:FPT7FIAG5AMGDZO7HRRL6G664N","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":"3c98c25f13795a41badd748c789d16979cac58978ce273124a03b4c6d6ff2986","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-20T11:02:49Z","title_canon_sha256":"4da6417018cf57fad92b1ae6ddab6d5574664f6933440d9407d4133131e45bec"},"schema_version":"1.0","source":{"id":"2012.10885","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.10885","created_at":"2026-07-05T02:49:52Z"},{"alias_kind":"arxiv_version","alias_value":"2012.10885v4","created_at":"2026-07-05T02:49:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.10885","created_at":"2026-07-05T02:49:52Z"},{"alias_kind":"pith_short_12","alias_value":"FPT7FIAG5AMG","created_at":"2026-07-05T02:49:52Z"},{"alias_kind":"pith_short_16","alias_value":"FPT7FIAG5AMGDZO7","created_at":"2026-07-05T02:49:52Z"},{"alias_kind":"pith_short_8","alias_value":"FPT7FIAG","created_at":"2026-07-05T02:49:52Z"}],"graph_snapshots":[{"event_id":"sha256:8823cd61d1606152b8dfbf115b679805693d82817254264a1adb437d09a15460","target":"graph","created_at":"2026-07-05T02:49:52Z","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/2012.10885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Group equivariant neural networks are used as building blocks of group invariant neural networks, which have been shown to improve generalisation performance and data efficiency through principled parameter sharing. Such works have mostly focused on group equivariant convolutions, building on the result that group equivariant linear maps are necessarily convolutions. In this work, we extend the scope of the literature to self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that","authors_text":"Charline Le Lan, Emilien Dupont, Hyunjik Kim, Michael Hutchinson, Sheheryar Zaidi, Yee Whye Teh","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-20T11:02:49Z","title":"LieTransformer: Equivariant self-attention for Lie Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10885","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:f5d19413a4a80f2d42c0716f64c489cbdb54f1383e79a90742d63561d6505b28","target":"record","created_at":"2026-07-05T02:49:52Z","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":"3c98c25f13795a41badd748c789d16979cac58978ce273124a03b4c6d6ff2986","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-20T11:02:49Z","title_canon_sha256":"4da6417018cf57fad92b1ae6ddab6d5574664f6933440d9407d4133131e45bec"},"schema_version":"1.0","source":{"id":"2012.10885","kind":"arxiv","version":4}},"canonical_sha256":"2be7f2a006e81861e5df3c62bf1bdee379cb4424e0d6cd8594b390a997e9dffe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2be7f2a006e81861e5df3c62bf1bdee379cb4424e0d6cd8594b390a997e9dffe","first_computed_at":"2026-07-05T02:49:52.205727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:49:52.205727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HJV5DW/6Ax/+dA8xGlvH0crV5+/AE9aYhSrlqDvsBFWICBbkUfRaCsiTaQmg23iXdeJjf/T+vckzlg4vCkilAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:49:52.206217Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.10885","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5d19413a4a80f2d42c0716f64c489cbdb54f1383e79a90742d63561d6505b28","sha256:8823cd61d1606152b8dfbf115b679805693d82817254264a1adb437d09a15460"],"state_sha256":"5bd665b775ad88432293a87ef512c8ad5488d1f23f2f8ce42f9f238f528b2508"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cnp6aT3DcTxPqqVFhBfsvnw/j1LeN5Lbj6BXnYeMy9U3mSg9bwSYxmYVmH/3nStlK4pumoDrSW5w0lAyxATADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T11:37:09.402941Z","bundle_sha256":"9eb8a2fe44281c12c90a0b86c8b213570d78008d64aecf1c6e6ae9a134fa30e4"}}