{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:LAPM4OIBXLBP4YDQCM76L2ZDHQ","short_pith_number":"pith:LAPM4OIB","schema_version":"1.0","canonical_sha256":"581ece3901bac2fe6070133fe5eb233c37b08629ee9b75fab6caefeb10e676a3","source":{"kind":"arxiv","id":"2002.08871","version":2},"attestation_state":"computed","paper":{"title":"Fast Differentiable Sorting and Ranking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Josip Djolonga, Mathieu Blondel, Olivier Teboul, Quentin Berthet","submitted_at":"2020-02-20T17:11:09Z","abstract_excerpt":"The sorting operation is one of the most commonly used building blocks in computer programming. In machine learning, it is often used for robust statistics. However, seen as a function, it is piecewise linear and as a result includes many kinks where it is non-differentiable. More problematic is the related ranking operator, often used for order statistics and ranking metrics. It is a piecewise constant function, meaning that its derivatives are null or undefined. While numerous works have proposed differentiable proxies to sorting and ranking, they do not achieve the $O(n \\log n)$ time comple"},"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":"2002.08871","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-02-20T17:11:09Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1585e02303092bc24e72c6c8050f5242440dc45f899fae0c9d98e28a29e658e3","abstract_canon_sha256":"fa08f9162832804d02e3a3ff71dc48a3a2b751bf91141202b66021a078d2e08a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:14:38.534621Z","signature_b64":"Va9IhboivGjZAZW3105iKPfzhTWBzu8CfNVBgqyiVkjbNQ7AUpWs63A+3dM5YSxQ6plWsIHFZepNC4eSC+VMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"581ece3901bac2fe6070133fe5eb233c37b08629ee9b75fab6caefeb10e676a3","last_reissued_at":"2026-07-05T01:14:38.534171Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:14:38.534171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast Differentiable Sorting and Ranking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Josip Djolonga, Mathieu Blondel, Olivier Teboul, Quentin Berthet","submitted_at":"2020-02-20T17:11:09Z","abstract_excerpt":"The sorting operation is one of the most commonly used building blocks in computer programming. In machine learning, it is often used for robust statistics. However, seen as a function, it is piecewise linear and as a result includes many kinks where it is non-differentiable. More problematic is the related ranking operator, often used for order statistics and ranking metrics. It is a piecewise constant function, meaning that its derivatives are null or undefined. While numerous works have proposed differentiable proxies to sorting and ranking, they do not achieve the $O(n \\log n)$ time comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.08871","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.08871/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":"2002.08871","created_at":"2026-07-05T01:14:38.534228+00:00"},{"alias_kind":"arxiv_version","alias_value":"2002.08871v2","created_at":"2026-07-05T01:14:38.534228+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.08871","created_at":"2026-07-05T01:14:38.534228+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAPM4OIBXLBP","created_at":"2026-07-05T01:14:38.534228+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAPM4OIBXLBP4YDQ","created_at":"2026-07-05T01:14:38.534228+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAPM4OIB","created_at":"2026-07-05T01:14:38.534228+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.02294","citing_title":"Regularized Large Neighborhood Search","ref_index":11,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LAPM4OIBXLBP4YDQCM76L2ZDHQ","json":"https://pith.science/pith/LAPM4OIBXLBP4YDQCM76L2ZDHQ.json","graph_json":"https://pith.science/api/pith-number/LAPM4OIBXLBP4YDQCM76L2ZDHQ/graph.json","events_json":"https://pith.science/api/pith-number/LAPM4OIBXLBP4YDQCM76L2ZDHQ/events.json","paper":"https://pith.science/paper/LAPM4OIB"},"agent_actions":{"view_html":"https://pith.science/pith/LAPM4OIBXLBP4YDQCM76L2ZDHQ","download_json":"https://pith.science/pith/LAPM4OIBXLBP4YDQCM76L2ZDHQ.json","view_paper":"https://pith.science/paper/LAPM4OIB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2002.08871&json=true","fetch_graph":"https://pith.science/api/pith-number/LAPM4OIBXLBP4YDQCM76L2ZDHQ/graph.json","fetch_events":"https://pith.science/api/pith-number/LAPM4OIBXLBP4YDQCM76L2ZDHQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAPM4OIBXLBP4YDQCM76L2ZDHQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAPM4OIBXLBP4YDQCM76L2ZDHQ/action/storage_attestation","attest_author":"https://pith.science/pith/LAPM4OIBXLBP4YDQCM76L2ZDHQ/action/author_attestation","sign_citation":"https://pith.science/pith/LAPM4OIBXLBP4YDQCM76L2ZDHQ/action/citation_signature","submit_replication":"https://pith.science/pith/LAPM4OIBXLBP4YDQCM76L2ZDHQ/action/replication_record"}},"created_at":"2026-07-05T01:14:38.534228+00:00","updated_at":"2026-07-05T01:14:38.534228+00:00"}