{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:2IGATDHYXG6PQG5F2HJEICVDCU","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":"405b9ebc263165f5140b6cd8b594a39a4bdd58e8fd4705d6af7f75be94e2209a","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-05T22:52:12Z","title_canon_sha256":"f9f7f4601f4502295bf2e64f7e72cd8431daf441ce3bf252f83acad214df8bbe"},"schema_version":"1.0","source":{"id":"2110.02393","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.02393","created_at":"2026-07-05T05:02:54Z"},{"alias_kind":"arxiv_version","alias_value":"2110.02393v2","created_at":"2026-07-05T05:02:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.02393","created_at":"2026-07-05T05:02:54Z"},{"alias_kind":"pith_short_12","alias_value":"2IGATDHYXG6P","created_at":"2026-07-05T05:02:54Z"},{"alias_kind":"pith_short_16","alias_value":"2IGATDHYXG6PQG5F","created_at":"2026-07-05T05:02:54Z"},{"alias_kind":"pith_short_8","alias_value":"2IGATDHY","created_at":"2026-07-05T05:02:54Z"}],"graph_snapshots":[{"event_id":"sha256:fe2d5ce858849a75c324d1ba48c02cb1f9158daf381fbbc38a221120840d4d19","target":"graph","created_at":"2026-07-05T05:02:54Z","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/2110.02393/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of geometric deep learning. Often problems in the physical sciences deal with relatively small sets of points in two- or three-dimensional space wherein translation, rotation, and permutation equivariance are important or even vital for models to be useful in practice. In this work, we present rotation- and permutation-equivariant architectures for deep learning on the","authors_text":"Matthew Spellings","cross_cats":["cs.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-05T22:52:12Z","title":"Geometric Algebra Attention Networks for Small Point Clouds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.02393","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:a765d059a3cfb97713428cdd04909641d33b227fac6ca6e7359cf13fbcaddd20","target":"record","created_at":"2026-07-05T05:02:54Z","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":"405b9ebc263165f5140b6cd8b594a39a4bdd58e8fd4705d6af7f75be94e2209a","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-05T22:52:12Z","title_canon_sha256":"f9f7f4601f4502295bf2e64f7e72cd8431daf441ce3bf252f83acad214df8bbe"},"schema_version":"1.0","source":{"id":"2110.02393","kind":"arxiv","version":2}},"canonical_sha256":"d20c098cf8b9bcf81ba5d1d2440aa315091007bea6aedb4207f5de4062dd18a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d20c098cf8b9bcf81ba5d1d2440aa315091007bea6aedb4207f5de4062dd18a0","first_computed_at":"2026-07-05T05:02:54.817141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:02:54.817141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MfE1tWP8RY8HMVrDVwQF2MNJhHq3btw4XyPIvYYdLXcpa2MYT/7OS9abE4zynNqFwQEygwPYijO8kMVgrLo8Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:02:54.817588Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.02393","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a765d059a3cfb97713428cdd04909641d33b227fac6ca6e7359cf13fbcaddd20","sha256:fe2d5ce858849a75c324d1ba48c02cb1f9158daf381fbbc38a221120840d4d19"],"state_sha256":"38c69e2e30c629d9053eda15973a0a3c65dc6920fec26abb5f96a24df510a79f"}