{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UDZUPLVENXEAONEKMCIZM5UI7B","short_pith_number":"pith:UDZUPLVE","schema_version":"1.0","canonical_sha256":"a0f347aea46dc807348a6091967688f8781add47494a5ac49ecc77d13f63bc26","source":{"kind":"arxiv","id":"1710.05488","version":2},"attestation_state":"computed","paper":{"title":"A Geometric View of Optimal Transportation and Generative Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"David Xianfeng Gu, Kehua Su, Li Cui, Na Lei, Shing-Tung Yau","submitted_at":"2017-10-16T03:30:09Z","abstract_excerpt":"In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. This leads to a geometric interpretation to generative models, and leads to a novel framework for generative models. By using the optimal transportation view of GAN model, we show that the discriminator computes the Kantorovich potential, the generator calculates the transportation map. For a large class of transportation costs, the Kantorovich potential can giv"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.05488","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-16T03:30:09Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"9ab2abf7839be5b7b9158785dabe5b766f595a4b06f2d8da3c57360a895565eb","abstract_canon_sha256":"79c0c7ef31742bfd0b7c9ee1ac91e3d9e0c633028b7e00e96e3d486305b74e5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:42.684543Z","signature_b64":"1zVdlDqqnHFuPKhrATa80LXyzlvza5Mv7pJUXaN07p6ezYYYcyzWqM6xBdBWXViO8LYDljJamqhr9aaPfR0hDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0f347aea46dc807348a6091967688f8781add47494a5ac49ecc77d13f63bc26","last_reissued_at":"2026-05-18T00:27:42.683912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:42.683912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Geometric View of Optimal Transportation and Generative Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"David Xianfeng Gu, Kehua Su, Li Cui, Na Lei, Shing-Tung Yau","submitted_at":"2017-10-16T03:30:09Z","abstract_excerpt":"In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. This leads to a geometric interpretation to generative models, and leads to a novel framework for generative models. By using the optimal transportation view of GAN model, we show that the discriminator computes the Kantorovich potential, the generator calculates the transportation map. For a large class of transportation costs, the Kantorovich potential can giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05488","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.05488","created_at":"2026-05-18T00:27:42.683999+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.05488v2","created_at":"2026-05-18T00:27:42.683999+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05488","created_at":"2026-05-18T00:27:42.683999+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDZUPLVENXEA","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDZUPLVENXEAONEK","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDZUPLVE","created_at":"2026-05-18T12:31:46.661854+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.09691","citing_title":"Adversarial Computation of Optimal Transport Maps","ref_index":19,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UDZUPLVENXEAONEKMCIZM5UI7B","json":"https://pith.science/pith/UDZUPLVENXEAONEKMCIZM5UI7B.json","graph_json":"https://pith.science/api/pith-number/UDZUPLVENXEAONEKMCIZM5UI7B/graph.json","events_json":"https://pith.science/api/pith-number/UDZUPLVENXEAONEKMCIZM5UI7B/events.json","paper":"https://pith.science/paper/UDZUPLVE"},"agent_actions":{"view_html":"https://pith.science/pith/UDZUPLVENXEAONEKMCIZM5UI7B","download_json":"https://pith.science/pith/UDZUPLVENXEAONEKMCIZM5UI7B.json","view_paper":"https://pith.science/paper/UDZUPLVE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.05488&json=true","fetch_graph":"https://pith.science/api/pith-number/UDZUPLVENXEAONEKMCIZM5UI7B/graph.json","fetch_events":"https://pith.science/api/pith-number/UDZUPLVENXEAONEKMCIZM5UI7B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDZUPLVENXEAONEKMCIZM5UI7B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDZUPLVENXEAONEKMCIZM5UI7B/action/storage_attestation","attest_author":"https://pith.science/pith/UDZUPLVENXEAONEKMCIZM5UI7B/action/author_attestation","sign_citation":"https://pith.science/pith/UDZUPLVENXEAONEKMCIZM5UI7B/action/citation_signature","submit_replication":"https://pith.science/pith/UDZUPLVENXEAONEKMCIZM5UI7B/action/replication_record"}},"created_at":"2026-05-18T00:27:42.683999+00:00","updated_at":"2026-05-18T00:27:42.683999+00:00"}