{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:GAREWYTBYHQN5D5KPTC5UP2Q2M","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":"6ed5f095e35ed034439621d42df0aae9cf0e76fd27ff65aedd73f66b32d91630","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-21T18:59:47Z","title_canon_sha256":"460f5fe776a23e0b46eabdc6bef7439e4b3e8ed20c5763ddafd5f8ef4467ffa8"},"schema_version":"1.0","source":{"id":"2012.11589","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.11589","created_at":"2026-07-05T02:58:38Z"},{"alias_kind":"arxiv_version","alias_value":"2012.11589v3","created_at":"2026-07-05T02:58:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.11589","created_at":"2026-07-05T02:58:38Z"},{"alias_kind":"pith_short_12","alias_value":"GAREWYTBYHQN","created_at":"2026-07-05T02:58:38Z"},{"alias_kind":"pith_short_16","alias_value":"GAREWYTBYHQN5D5K","created_at":"2026-07-05T02:58:38Z"},{"alias_kind":"pith_short_8","alias_value":"GAREWYTB","created_at":"2026-07-05T02:58:38Z"}],"graph_snapshots":[{"event_id":"sha256:9d2069902231c0a7d8bb2a7c9b063ec9bce0753f83fe1c1bd1bfb6cc9e39912d","target":"graph","created_at":"2026-07-05T02:58:38Z","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/2012.11589/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can be fragile to outliers or noise, especially in high dimensions. Here, we introduce a new form of structured OT that simultaneously learns low-dimensional structure in data while leveraging this structure to solve the alignment task. Compared with OT, the resulting transport plan has better structural interpretability, highlighting the connections between ind","authors_text":"Chi-Heng Lin, Eva L. Dyer, Mehdi Azabou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-21T18:59:47Z","title":"Making transport more robust and interpretable by moving data through a small number of anchor points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.11589","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":"sha256:6e6ebb743c3825ddb069de02b968f1f2823cb4f311ab408c695f82179c6441ee","target":"record","created_at":"2026-07-05T02:58:38Z","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":"6ed5f095e35ed034439621d42df0aae9cf0e76fd27ff65aedd73f66b32d91630","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-21T18:59:47Z","title_canon_sha256":"460f5fe776a23e0b46eabdc6bef7439e4b3e8ed20c5763ddafd5f8ef4467ffa8"},"schema_version":"1.0","source":{"id":"2012.11589","kind":"arxiv","version":3}},"canonical_sha256":"30224b6261c1e0de8faa7cc5da3f50d302a757f3291513440c13a8bc31c50b60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30224b6261c1e0de8faa7cc5da3f50d302a757f3291513440c13a8bc31c50b60","first_computed_at":"2026-07-05T02:58:38.347145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:58:38.347145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lrCcA6Wrzn+W1WPmmadZSNKoMvTK5d7+0ICaNdB067MgPGnoi31b1SpLZJC8I5IR8Apy+RQCOWaOIzZ0V0gGAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:58:38.347537Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.11589","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e6ebb743c3825ddb069de02b968f1f2823cb4f311ab408c695f82179c6441ee","sha256:9d2069902231c0a7d8bb2a7c9b063ec9bce0753f83fe1c1bd1bfb6cc9e39912d"],"state_sha256":"078dbbbcca77ff6cbb203fc205356636fd9c713a4f5311c76366a1333b5a46b1"}