{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XGV63IKGQILL4OSXIPJFL4ET4T","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":"c2410f2bd06eca92d599013b854ba0d48c9b99e660943f387d892c1ed1efb22b","cross_cats_sorted":["cs.CV","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-22T10:03:46Z","title_canon_sha256":"67bf803d1baa2669953b7403721e2a1d39a8ae3a022d228e7a5417ba338d93d2"},"schema_version":"1.0","source":{"id":"2605.23449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23449","created_at":"2026-05-25T02:01:54Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23449v1","created_at":"2026-05-25T02:01:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23449","created_at":"2026-05-25T02:01:54Z"},{"alias_kind":"pith_short_12","alias_value":"XGV63IKGQILL","created_at":"2026-05-25T02:01:54Z"},{"alias_kind":"pith_short_16","alias_value":"XGV63IKGQILL4OSX","created_at":"2026-05-25T02:01:54Z"},{"alias_kind":"pith_short_8","alias_value":"XGV63IKG","created_at":"2026-05-25T02:01:54Z"}],"graph_snapshots":[{"event_id":"sha256:746413e4031ce3b4adaa5f04bed888d67e50049687b61e214a4189737b59de5e","target":"graph","created_at":"2026-05-25T02:01:54Z","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/2605.23449/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Variational autoencoders (VAEs) often struggle to represent non-commutative structure in learned latent spaces. Symmetry-aware VAEs commonly address this issue by enforcing commutativity through algebraic regularization, which is appropriate for commutative transformation groups but can suppress meaningful non-commutative structure when it is intrinsic to the data. We argue that non-commutativity should instead be explicitly diagnosed and reflected in reconstruction behavior. We introduce a Lie Group VAE framework that combines geometric and algebraic perspectives on uncertainty while separati","authors_text":"Gabriel Eilertsen, Michael Felsberg, Tahereh Dehdarirad, Ziliang Xiong","cross_cats":["cs.CV","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-22T10:03:46Z","title":"Commutator-Induced Uncertainty in VAEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23449","kind":"arxiv","version":1},"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":"sha256:41ee8d93f7627575a629d2581bbcbdb862662be417561ac72bc797abfcf444af","target":"record","created_at":"2026-05-25T02:01:54Z","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":"c2410f2bd06eca92d599013b854ba0d48c9b99e660943f387d892c1ed1efb22b","cross_cats_sorted":["cs.CV","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-22T10:03:46Z","title_canon_sha256":"67bf803d1baa2669953b7403721e2a1d39a8ae3a022d228e7a5417ba338d93d2"},"schema_version":"1.0","source":{"id":"2605.23449","kind":"arxiv","version":1}},"canonical_sha256":"b9abeda1468216be3a5743d255f093e4f74b6a607d276d2e9ffdba3d94cae14d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9abeda1468216be3a5743d255f093e4f74b6a607d276d2e9ffdba3d94cae14d","first_computed_at":"2026-05-25T02:01:54.715470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:54.715470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rW/iO8PCS9b8wiORDC73nqTMrfeywh/ZljeJztgkDc7guNNohWAaEuAlgtxJ7nytCSOoQjUmwTTgixHBPNk0AQ==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:54.716228Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.23449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41ee8d93f7627575a629d2581bbcbdb862662be417561ac72bc797abfcf444af","sha256:746413e4031ce3b4adaa5f04bed888d67e50049687b61e214a4189737b59de5e"],"state_sha256":"dfddf134e289a1f0c78dbe35abeaf59ec44c2ca4b2821eac1e6c30eacae0e67e"}