{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:6DEEYRGVMWBUPTGGTH2HZU3WWL","short_pith_number":"pith:6DEEYRGV","schema_version":"1.0","canonical_sha256":"f0c84c44d5658347ccc699f47cd376b2db0d381f9d6be5e1d3f42552c87a6434","source":{"kind":"arxiv","id":"2304.14165","version":1},"attestation_state":"computed","paper":{"title":"An Algorithm for Computing with Brauer's Group Equivariant Neural Network Layers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.RT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Edward Pearce-Crump","submitted_at":"2023-04-27T13:06:07Z","abstract_excerpt":"The learnable, linear neural network layers between tensor power spaces of $\\mathbb{R}^{n}$ that are equivariant to the orthogonal group, $O(n)$, the special orthogonal group, $SO(n)$, and the symplectic group, $Sp(n)$, were characterised in arXiv:2212.08630. We present an algorithm for multiplying a vector by any weight matrix for each of these groups, using category theoretic constructions to implement the procedure. We achieve a significant reduction in computational cost compared with a naive implementation by making use of Kronecker product matrices to perform the multiplication. We show "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2304.14165","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-27T13:06:07Z","cross_cats_sorted":["math.CO","math.RT","stat.ML"],"title_canon_sha256":"b546eede33a263b780b3194832f3867335a665fffb2b83daff8eefeaf8fc07b7","abstract_canon_sha256":"a5aa65d0ea2d43d8159519bb4e02035b1b09ecf8d7eea4bd341436195ef00ba9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:05:01.649678Z","signature_b64":"3+0vdySfnJ2A1btTbY+rNrbiZAL9oA/FKVfx+UXuctjYaXJYI/Lfykfn2nz1hn8b9vvsuq4/8eyP047Mdtc6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0c84c44d5658347ccc699f47cd376b2db0d381f9d6be5e1d3f42552c87a6434","last_reissued_at":"2026-07-05T06:05:01.649244Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:05:01.649244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Algorithm for Computing with Brauer's Group Equivariant Neural Network Layers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.RT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Edward Pearce-Crump","submitted_at":"2023-04-27T13:06:07Z","abstract_excerpt":"The learnable, linear neural network layers between tensor power spaces of $\\mathbb{R}^{n}$ that are equivariant to the orthogonal group, $O(n)$, the special orthogonal group, $SO(n)$, and the symplectic group, $Sp(n)$, were characterised in arXiv:2212.08630. We present an algorithm for multiplying a vector by any weight matrix for each of these groups, using category theoretic constructions to implement the procedure. We achieve a significant reduction in computational cost compared with a naive implementation by making use of Kronecker product matrices to perform the multiplication. We show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.14165","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/2304.14165/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2304.14165","created_at":"2026-07-05T06:05:01.649309+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.14165v1","created_at":"2026-07-05T06:05:01.649309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.14165","created_at":"2026-07-05T06:05:01.649309+00:00"},{"alias_kind":"pith_short_12","alias_value":"6DEEYRGVMWBU","created_at":"2026-07-05T06:05:01.649309+00:00"},{"alias_kind":"pith_short_16","alias_value":"6DEEYRGVMWBUPTGG","created_at":"2026-07-05T06:05:01.649309+00:00"},{"alias_kind":"pith_short_8","alias_value":"6DEEYRGV","created_at":"2026-07-05T06:05:01.649309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.18263","citing_title":"High-Rank Irreducible Cartesian Tensor Decomposition and Bases of Equivariant Spaces","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6DEEYRGVMWBUPTGGTH2HZU3WWL","json":"https://pith.science/pith/6DEEYRGVMWBUPTGGTH2HZU3WWL.json","graph_json":"https://pith.science/api/pith-number/6DEEYRGVMWBUPTGGTH2HZU3WWL/graph.json","events_json":"https://pith.science/api/pith-number/6DEEYRGVMWBUPTGGTH2HZU3WWL/events.json","paper":"https://pith.science/paper/6DEEYRGV"},"agent_actions":{"view_html":"https://pith.science/pith/6DEEYRGVMWBUPTGGTH2HZU3WWL","download_json":"https://pith.science/pith/6DEEYRGVMWBUPTGGTH2HZU3WWL.json","view_paper":"https://pith.science/paper/6DEEYRGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.14165&json=true","fetch_graph":"https://pith.science/api/pith-number/6DEEYRGVMWBUPTGGTH2HZU3WWL/graph.json","fetch_events":"https://pith.science/api/pith-number/6DEEYRGVMWBUPTGGTH2HZU3WWL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6DEEYRGVMWBUPTGGTH2HZU3WWL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6DEEYRGVMWBUPTGGTH2HZU3WWL/action/storage_attestation","attest_author":"https://pith.science/pith/6DEEYRGVMWBUPTGGTH2HZU3WWL/action/author_attestation","sign_citation":"https://pith.science/pith/6DEEYRGVMWBUPTGGTH2HZU3WWL/action/citation_signature","submit_replication":"https://pith.science/pith/6DEEYRGVMWBUPTGGTH2HZU3WWL/action/replication_record"}},"created_at":"2026-07-05T06:05:01.649309+00:00","updated_at":"2026-07-05T06:05:01.649309+00:00"}