{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UT4ND4DDGOQW5PWCCHYYTXNCEB","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":"d37ab7e0a4e41d91fcd0592bfc250222d07828627a99164bccc7c73f6722d961","cross_cats_sorted":["cs.CV","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-17T19:36:41Z","title_canon_sha256":"881137350ef609860f5a95ca5e8a56742e2e7d1fe896637430a86c21638753aa"},"schema_version":"1.0","source":{"id":"1506.05439","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05439","created_at":"2026-05-18T01:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05439v3","created_at":"2026-05-18T01:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05439","created_at":"2026-05-18T01:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"UT4ND4DDGOQW","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UT4ND4DDGOQW5PWC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UT4ND4DD","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:c17f4313e93854941ee9e28ba7effa901bf1633984949fbf63789e90f83cc137","target":"graph","created_at":"2026-05-18T01:23:38Z","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"},"paper":{"abstract_excerpt":"Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The Wasserstein distance provides a natural notion of dissimilarity for probability measures. Although optimizing with respect to the exact Wasserstein distance is costly, recent work has described a regularized approximation that is efficiently computed. We describe an efficient learning algorithm based on this regularization, as well a","authors_text":"Charlie Frogner, Chiyuan Zhang, Hossein Mobahi, Mauricio Araya-Polo, Tomaso Poggio","cross_cats":["cs.CV","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-17T19:36:41Z","title":"Learning with a Wasserstein Loss"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05439","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":"sha256:3cd0fea8d38848b3206e11d5027a5b44ac80c103836b3c8e83f974ee8189f208","target":"record","created_at":"2026-05-18T01:23:38Z","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":"d37ab7e0a4e41d91fcd0592bfc250222d07828627a99164bccc7c73f6722d961","cross_cats_sorted":["cs.CV","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-17T19:36:41Z","title_canon_sha256":"881137350ef609860f5a95ca5e8a56742e2e7d1fe896637430a86c21638753aa"},"schema_version":"1.0","source":{"id":"1506.05439","kind":"arxiv","version":3}},"canonical_sha256":"a4f8d1f06333a16ebec211f189dda2205e06a811987759da3abbf900e06ed62e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4f8d1f06333a16ebec211f189dda2205e06a811987759da3abbf900e06ed62e","first_computed_at":"2026-05-18T01:23:38.213026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:38.213026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b6Tu/6L7pxXkA/CL7SJNNLJbbRBa0Ie5KzUeyw7NICBRZCqS4oDIlnOox7kJASDnCru/m0EPKVLTgMatLNCnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:38.213614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.05439","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cd0fea8d38848b3206e11d5027a5b44ac80c103836b3c8e83f974ee8189f208","sha256:c17f4313e93854941ee9e28ba7effa901bf1633984949fbf63789e90f83cc137"],"state_sha256":"a79941b065a548c6df7d2aac4016417843c0ed5af6296636af1c4d76b10d5802"}