{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:ELPGKYK4RK6DX6T57J2UBABHO7","short_pith_number":"pith:ELPGKYK4","schema_version":"1.0","canonical_sha256":"22de65615c8abc3bfa7dfa7540802777e40de48ddfbc7e2235daf300e88d3eed","source":{"kind":"arxiv","id":"2006.12065","version":4},"attestation_state":"computed","paper":{"title":"A Trainable Optimal Transport Embedding for Feature Aggregation and its Relationship to Attention","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Alexandre d'Aspremont, Dexiong Chen, Gr\\'egoire Mialon, Julien Mairal","submitted_at":"2020-06-22T08:35:58Z","abstract_excerpt":"We address the problem of learning on sets of features, motivated by the need of performing pooling operations in long biological sequences of varying sizes, with long-range dependencies, and possibly few labeled data. To address this challenging task, we introduce a parametrized representation of fixed size, which embeds and then aggregates elements from a given input set according to the optimal transport plan between the set and a trainable reference. Our approach scales to large datasets and allows end-to-end training of the reference, while also providing a simple unsupervised learning me"},"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":"2006.12065","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-22T08:35:58Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"f2085031414a8cc52e624f3fd38d8e861a56745577356135bc7f33bf26a6637f","abstract_canon_sha256":"e4acc1704bbfaca98ba008de729a4394055f67b64350f98d6557a9face565a1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:14:10.200761Z","signature_b64":"hX73oidFK3zrAy8rYkUj67xkkv9w8n2G6TBgDVq5i3niSFg8yCEYyg+ybX4KpMzfmqtndILN7ZUYcoNAQwOMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22de65615c8abc3bfa7dfa7540802777e40de48ddfbc7e2235daf300e88d3eed","last_reissued_at":"2026-07-05T02:14:10.200355Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:14:10.200355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Trainable Optimal Transport Embedding for Feature Aggregation and its Relationship to Attention","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Alexandre d'Aspremont, Dexiong Chen, Gr\\'egoire Mialon, Julien Mairal","submitted_at":"2020-06-22T08:35:58Z","abstract_excerpt":"We address the problem of learning on sets of features, motivated by the need of performing pooling operations in long biological sequences of varying sizes, with long-range dependencies, and possibly few labeled data. To address this challenging task, we introduce a parametrized representation of fixed size, which embeds and then aggregates elements from a given input set according to the optimal transport plan between the set and a trainable reference. Our approach scales to large datasets and allows end-to-end training of the reference, while also providing a simple unsupervised learning me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.12065","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.12065/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2006.12065","created_at":"2026-07-05T02:14:10.200403+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.12065v4","created_at":"2026-07-05T02:14:10.200403+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.12065","created_at":"2026-07-05T02:14:10.200403+00:00"},{"alias_kind":"pith_short_12","alias_value":"ELPGKYK4RK6D","created_at":"2026-07-05T02:14:10.200403+00:00"},{"alias_kind":"pith_short_16","alias_value":"ELPGKYK4RK6DX6T5","created_at":"2026-07-05T02:14:10.200403+00:00"},{"alias_kind":"pith_short_8","alias_value":"ELPGKYK4","created_at":"2026-07-05T02:14:10.200403+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ELPGKYK4RK6DX6T57J2UBABHO7","json":"https://pith.science/pith/ELPGKYK4RK6DX6T57J2UBABHO7.json","graph_json":"https://pith.science/api/pith-number/ELPGKYK4RK6DX6T57J2UBABHO7/graph.json","events_json":"https://pith.science/api/pith-number/ELPGKYK4RK6DX6T57J2UBABHO7/events.json","paper":"https://pith.science/paper/ELPGKYK4"},"agent_actions":{"view_html":"https://pith.science/pith/ELPGKYK4RK6DX6T57J2UBABHO7","download_json":"https://pith.science/pith/ELPGKYK4RK6DX6T57J2UBABHO7.json","view_paper":"https://pith.science/paper/ELPGKYK4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.12065&json=true","fetch_graph":"https://pith.science/api/pith-number/ELPGKYK4RK6DX6T57J2UBABHO7/graph.json","fetch_events":"https://pith.science/api/pith-number/ELPGKYK4RK6DX6T57J2UBABHO7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ELPGKYK4RK6DX6T57J2UBABHO7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ELPGKYK4RK6DX6T57J2UBABHO7/action/storage_attestation","attest_author":"https://pith.science/pith/ELPGKYK4RK6DX6T57J2UBABHO7/action/author_attestation","sign_citation":"https://pith.science/pith/ELPGKYK4RK6DX6T57J2UBABHO7/action/citation_signature","submit_replication":"https://pith.science/pith/ELPGKYK4RK6DX6T57J2UBABHO7/action/replication_record"}},"created_at":"2026-07-05T02:14:10.200403+00:00","updated_at":"2026-07-05T02:14:10.200403+00:00"}