{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:LAPM4OIBXLBP4YDQCM76L2ZDHQ","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":"fa08f9162832804d02e3a3ff71dc48a3a2b751bf91141202b66021a078d2e08a","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-02-20T17:11:09Z","title_canon_sha256":"1585e02303092bc24e72c6c8050f5242440dc45f899fae0c9d98e28a29e658e3"},"schema_version":"1.0","source":{"id":"2002.08871","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.08871","created_at":"2026-07-05T01:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"2002.08871v2","created_at":"2026-07-05T01:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.08871","created_at":"2026-07-05T01:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"LAPM4OIBXLBP","created_at":"2026-07-05T01:14:38Z"},{"alias_kind":"pith_short_16","alias_value":"LAPM4OIBXLBP4YDQ","created_at":"2026-07-05T01:14:38Z"},{"alias_kind":"pith_short_8","alias_value":"LAPM4OIB","created_at":"2026-07-05T01:14:38Z"}],"graph_snapshots":[{"event_id":"sha256:17bdc9b044b0f7e72538df73e97d28e420c481ab6eb5df528cc467d1b9edbaf9","target":"graph","created_at":"2026-07-05T01:14:38Z","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/2002.08871/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Josip Djolonga, Mathieu Blondel, Olivier Teboul, Quentin Berthet","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-02-20T17:11:09Z","title":"Fast Differentiable Sorting and Ranking"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.08871","kind":"arxiv","version":2},"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":"sha256:863c5c97a856dc6f9bb6be2da113a2767b6af90df16dc6cd98997c5081faa929","target":"record","created_at":"2026-07-05T01:14:38Z","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":"fa08f9162832804d02e3a3ff71dc48a3a2b751bf91141202b66021a078d2e08a","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-02-20T17:11:09Z","title_canon_sha256":"1585e02303092bc24e72c6c8050f5242440dc45f899fae0c9d98e28a29e658e3"},"schema_version":"1.0","source":{"id":"2002.08871","kind":"arxiv","version":2}},"canonical_sha256":"581ece3901bac2fe6070133fe5eb233c37b08629ee9b75fab6caefeb10e676a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"581ece3901bac2fe6070133fe5eb233c37b08629ee9b75fab6caefeb10e676a3","first_computed_at":"2026-07-05T01:14:38.534171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:14:38.534171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Va9IhboivGjZAZW3105iKPfzhTWBzu8CfNVBgqyiVkjbNQ7AUpWs63A+3dM5YSxQ6plWsIHFZepNC4eSC+VMCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:14:38.534621Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.08871","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:863c5c97a856dc6f9bb6be2da113a2767b6af90df16dc6cd98997c5081faa929","sha256:17bdc9b044b0f7e72538df73e97d28e420c481ab6eb5df528cc467d1b9edbaf9"],"state_sha256":"575e4fb8889266807c77ec32565e26d81bba57bc176a271a986ba3b468807fb3"}