{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:J5BHICDPOH5QMRPMMIKJZ2Z42O","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":"685dc26e4a2ecfccbf9c3e5159033e71d9493299a68de8f4b535e16a2facc7b2","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-17T20:13:17Z","title_canon_sha256":"5655aee7134cd55c92e67a364f53909367c968fdb9fd89dc3634e4fc6f3ddc2d"},"schema_version":"1.0","source":{"id":"1812.07035","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07035","created_at":"2026-07-05T01:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07035v4","created_at":"2026-07-05T01:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07035","created_at":"2026-07-05T01:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"J5BHICDPOH5Q","created_at":"2026-07-05T01:08:58Z"},{"alias_kind":"pith_short_16","alias_value":"J5BHICDPOH5QMRPM","created_at":"2026-07-05T01:08:58Z"},{"alias_kind":"pith_short_8","alias_value":"J5BHICDP","created_at":"2026-07-05T01:08:58Z"}],"graph_snapshots":[{"event_id":"sha256:3733f310a98e3654dc9a260272617ecc8d722ec75984057e2245a44995a11c00","target":"graph","created_at":"2026-07-05T01:08:58Z","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/1812.07035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In neural networks, it is often desirable to work with various representations of the same space. For example, 3D rotations can be represented with quaternions or Euler angles. In this paper, we advance a definition of a continuous representation, which can be helpful for training deep neural networks. We relate this to topological concepts such as homeomorphism and embedding. We then investigate what are continuous and discontinuous representations for 2D, 3D, and n-dimensional rotations. We demonstrate that for 3D rotations, all representations are discontinuous in the real Euclidean spaces ","authors_text":"Connelly Barnes, Hao Li, Jimei Yang, Jingwan Lu, Yi Zhou","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-17T20:13:17Z","title":"On the Continuity of Rotation Representations in Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07035","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":"sha256:4d180f038ddae7eb85526cffef4de7a6be81bdffc80b88269f3d39c19283187e","target":"record","created_at":"2026-07-05T01:08:58Z","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":"685dc26e4a2ecfccbf9c3e5159033e71d9493299a68de8f4b535e16a2facc7b2","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-17T20:13:17Z","title_canon_sha256":"5655aee7134cd55c92e67a364f53909367c968fdb9fd89dc3634e4fc6f3ddc2d"},"schema_version":"1.0","source":{"id":"1812.07035","kind":"arxiv","version":4}},"canonical_sha256":"4f4274086f71fb0645ec62149ceb3cd388cc161182abcf883d156db4847d5244","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f4274086f71fb0645ec62149ceb3cd388cc161182abcf883d156db4847d5244","first_computed_at":"2026-07-05T01:08:58.628340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:08:58.628340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CeKHdnNlp36SnmoNrqwPdNE8+Df7lvEvKbmm6rGYwjZzzlUezEKJZ60PIezxixPNQmKz+t1HiPUho/w9Eu5pBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:08:58.628738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.07035","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d180f038ddae7eb85526cffef4de7a6be81bdffc80b88269f3d39c19283187e","sha256:3733f310a98e3654dc9a260272617ecc8d722ec75984057e2245a44995a11c00"],"state_sha256":"ecd3401ccae6365567dce18fea08aa75cc4200eb60419c9ee393c13f855f6c2f"}