{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PAB5S5ELBB7D24QJIAVDWHKW6Y","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":"8a377e3b4c250f4b6e671ed294c26543c5cc1c6ab6a77f4ca9d5ab5a08595001","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-05T22:46:17Z","title_canon_sha256":"5d502ba0895164f36f474120d67f85accccfae3c62356d43a2e8b24f0b2ffa99"},"schema_version":"1.0","source":{"id":"2607.04535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04535","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04535v1","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04535","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"PAB5S5ELBB7D","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"pith_short_16","alias_value":"PAB5S5ELBB7D24QJ","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"pith_short_8","alias_value":"PAB5S5EL","created_at":"2026-07-07T02:19:23Z"}],"graph_snapshots":[{"event_id":"sha256:7866ce9668b1155a875d014f6913bc4c842cd876881c1e3765f28f172058467e","target":"graph","created_at":"2026-07-07T02:19:23Z","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/2607.04535/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Orthogonal and Stiefel layers give neural weights exact spectral control, but they also impose a strong modeling constraint: all represented singular values are fixed at one. Many settings that benefit from an orthonormal basis still need direction-dependent attenuation or amplification. We introduce ManifoldFlow, a minimal relaxation of a fixed-spectrum Stiefel layer that keeps the basis on the Stiefel manifold while learning a bounded positive spectrum through W = Q S^{1/2}, with Q^T Q = I and S positive definite. Since W^T W = S, the eigenvalues of S are exactly the squared singular values ","authors_text":"Haiwen Yi, Xinyuan Song","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-05T22:46:17Z","title":"ManifoldFlow: SPD-Relaxed Stiefel Layers with Learnable Singular Spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04535","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":"sha256:63bb74085d5ee1c7da5b5cd2ecdd1be46eefc66ceea331452867df1f7700b59c","target":"record","created_at":"2026-07-07T02:19:23Z","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":"8a377e3b4c250f4b6e671ed294c26543c5cc1c6ab6a77f4ca9d5ab5a08595001","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-05T22:46:17Z","title_canon_sha256":"5d502ba0895164f36f474120d67f85accccfae3c62356d43a2e8b24f0b2ffa99"},"schema_version":"1.0","source":{"id":"2607.04535","kind":"arxiv","version":1}},"canonical_sha256":"7803d9748b087e3d7209402a3b1d56f60022b58f465311e0f16fcfbcc300a8d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7803d9748b087e3d7209402a3b1d56f60022b58f465311e0f16fcfbcc300a8d9","first_computed_at":"2026-07-07T02:19:23.586676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:19:23.586676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b/IkbOocXWIhfBNvEMlMAtU4VysgVzZpB9La8sUv0/cWjA61rYnHXHExPJSRCNZgLMHhR5rIGIPiHISSObyMBQ==","signature_status":"signed_v1","signed_at":"2026-07-07T02:19:23.587443Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.04535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63bb74085d5ee1c7da5b5cd2ecdd1be46eefc66ceea331452867df1f7700b59c","sha256:7866ce9668b1155a875d014f6913bc4c842cd876881c1e3765f28f172058467e"],"state_sha256":"5bc95f3bfb69ee2c908be31f43748cd2f1316403a6eef7f9617bbb7f7b43a745"}