{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2ED3UQKGAMSK2N357SDNAYYWHD","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":"24f1866f6cdd0f57af746087d6e385bd640bddc7f5622df9ce272c65e33e6ebf","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-09T23:02:00Z","title_canon_sha256":"3d0a651ffc6c9d8735f6be7f83ee9fb103ec2b5ffcb8cef870775a2e12d68547"},"schema_version":"1.0","source":{"id":"2410.07476","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.07476","created_at":"2026-07-05T10:05:13Z"},{"alias_kind":"arxiv_version","alias_value":"2410.07476v3","created_at":"2026-07-05T10:05:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.07476","created_at":"2026-07-05T10:05:13Z"},{"alias_kind":"pith_short_12","alias_value":"2ED3UQKGAMSK","created_at":"2026-07-05T10:05:13Z"},{"alias_kind":"pith_short_16","alias_value":"2ED3UQKGAMSK2N35","created_at":"2026-07-05T10:05:13Z"},{"alias_kind":"pith_short_8","alias_value":"2ED3UQKG","created_at":"2026-07-05T10:05:13Z"}],"graph_snapshots":[{"event_id":"sha256:3ae76ffdb348d69c999ea829997b6205025532ea7b32dc439383e767e6218844","target":"graph","created_at":"2026-07-05T10:05:13Z","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/2410.07476/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A recent line of work in mechanistic interpretability has focused on reverse-engineering the computation performed by neural networks trained on the binary operation of finite groups. We investigate the internals of one-hidden-layer neural networks trained on this task, revealing previously unidentified structure and producing a more complete description of such models in a step towards unifying the explanations of previous works (Chughtai et al., 2023; Stander et al., 2024). Notably, these models approximate equivariance in each input argument. We verify that our explanation applies to a larg","authors_text":"Jacob Drori, Jason Gross, Louis Jaburi, Wilson Wu","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-09T23:02:00Z","title":"Towards a unified and verified understanding of group-operation networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.07476","kind":"arxiv","version":3},"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":"sha256:629b0f42327dfa93ec54734ab357e83d13043898811492f86f04e69b1a0a067a","target":"record","created_at":"2026-07-05T10:05:13Z","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":"24f1866f6cdd0f57af746087d6e385bd640bddc7f5622df9ce272c65e33e6ebf","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-09T23:02:00Z","title_canon_sha256":"3d0a651ffc6c9d8735f6be7f83ee9fb103ec2b5ffcb8cef870775a2e12d68547"},"schema_version":"1.0","source":{"id":"2410.07476","kind":"arxiv","version":3}},"canonical_sha256":"d107ba41460324ad377dfc86d0631638f9a7e7b77d649e148ec6b51d486731ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d107ba41460324ad377dfc86d0631638f9a7e7b77d649e148ec6b51d486731ff","first_computed_at":"2026-07-05T10:05:13.337233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:05:13.337233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OtWaVfL3NtWeYo2SpfGvHMf6+GxVe3InNirs7CO/qprE+s6XpkPuQ5+CGzcK7RHE0XzC6utcM+CU61pEfOerDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:05:13.337731Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.07476","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:629b0f42327dfa93ec54734ab357e83d13043898811492f86f04e69b1a0a067a","sha256:3ae76ffdb348d69c999ea829997b6205025532ea7b32dc439383e767e6218844"],"state_sha256":"b10b10f1a3ecb9f92c5be53f94346506f57b7f9a45a771069052b53dd7c333d5"}