{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:6V2PXPY6CTMTTVTWVWQVE7VZ3J","short_pith_number":"pith:6V2PXPY6","schema_version":"1.0","canonical_sha256":"f574fbbf1e14d939d676ada1527eb9da574d83d35235ccc5f2e8f9be422ebbbb","source":{"kind":"arxiv","id":"2412.21149","version":1},"attestation_state":"computed","paper":{"title":"Functional Risk Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Clement Gehring, Ferran Alet, Joshua B. Tenenbaum, Kenji Kawaguchi, Leslie Pack Kaelbling, Tom\\'as Lozano-P\\'erez","submitted_at":"2024-12-30T18:29:48Z","abstract_excerpt":"The field of Machine Learning has changed significantly since the 1970s. However, its most basic principle, Empirical Risk Minimization (ERM), remains unchanged. We propose Functional Risk Minimization~(FRM), a general framework where losses compare functions rather than outputs. This results in better performance in supervised, unsupervised, and RL experiments. In the FRM paradigm, for each data point $(x_i,y_i)$ there is function $f_{\\theta_i}$ that fits it: $y_i = f_{\\theta_i}(x_i)$. This allows FRM to subsume ERM for many common loss functions and to capture more realistic noise processes."},"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":"2412.21149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-30T18:29:48Z","cross_cats_sorted":[],"title_canon_sha256":"a078ba2a76cd9a28f294f536e1137b49001cac89c03ec243b54cb48c5b30539a","abstract_canon_sha256":"bed2a781ef26ae73e03dff0d525f4ccb548152b6033acf4e5bcabcc7b650bcdd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:27.825445Z","signature_b64":"UuzyzoCyTygs0H/FDwlmGWwCHP1T43+WwQbrp3KGRC3dqOEGhs1MCrW6kclX6yiXv/266r6ia/LMvJpUNNqzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f574fbbf1e14d939d676ada1527eb9da574d83d35235ccc5f2e8f9be422ebbbb","last_reissued_at":"2026-07-05T09:55:27.824936Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:27.824936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional Risk Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Clement Gehring, Ferran Alet, Joshua B. Tenenbaum, Kenji Kawaguchi, Leslie Pack Kaelbling, Tom\\'as Lozano-P\\'erez","submitted_at":"2024-12-30T18:29:48Z","abstract_excerpt":"The field of Machine Learning has changed significantly since the 1970s. However, its most basic principle, Empirical Risk Minimization (ERM), remains unchanged. We propose Functional Risk Minimization~(FRM), a general framework where losses compare functions rather than outputs. This results in better performance in supervised, unsupervised, and RL experiments. In the FRM paradigm, for each data point $(x_i,y_i)$ there is function $f_{\\theta_i}$ that fits it: $y_i = f_{\\theta_i}(x_i)$. This allows FRM to subsume ERM for many common loss functions and to capture more realistic noise processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.21149","kind":"arxiv","version":1},"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/2412.21149/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":"2412.21149","created_at":"2026-07-05T09:55:27.824996+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.21149v1","created_at":"2026-07-05T09:55:27.824996+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.21149","created_at":"2026-07-05T09:55:27.824996+00:00"},{"alias_kind":"pith_short_12","alias_value":"6V2PXPY6CTMT","created_at":"2026-07-05T09:55:27.824996+00:00"},{"alias_kind":"pith_short_16","alias_value":"6V2PXPY6CTMTTVTW","created_at":"2026-07-05T09:55:27.824996+00:00"},{"alias_kind":"pith_short_8","alias_value":"6V2PXPY6","created_at":"2026-07-05T09:55:27.824996+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.19642","citing_title":"Rigorous uncertainty quantification of probabilistic AI weather forecasts with conformal prediction","ref_index":117,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6V2PXPY6CTMTTVTWVWQVE7VZ3J","json":"https://pith.science/pith/6V2PXPY6CTMTTVTWVWQVE7VZ3J.json","graph_json":"https://pith.science/api/pith-number/6V2PXPY6CTMTTVTWVWQVE7VZ3J/graph.json","events_json":"https://pith.science/api/pith-number/6V2PXPY6CTMTTVTWVWQVE7VZ3J/events.json","paper":"https://pith.science/paper/6V2PXPY6"},"agent_actions":{"view_html":"https://pith.science/pith/6V2PXPY6CTMTTVTWVWQVE7VZ3J","download_json":"https://pith.science/pith/6V2PXPY6CTMTTVTWVWQVE7VZ3J.json","view_paper":"https://pith.science/paper/6V2PXPY6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.21149&json=true","fetch_graph":"https://pith.science/api/pith-number/6V2PXPY6CTMTTVTWVWQVE7VZ3J/graph.json","fetch_events":"https://pith.science/api/pith-number/6V2PXPY6CTMTTVTWVWQVE7VZ3J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6V2PXPY6CTMTTVTWVWQVE7VZ3J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6V2PXPY6CTMTTVTWVWQVE7VZ3J/action/storage_attestation","attest_author":"https://pith.science/pith/6V2PXPY6CTMTTVTWVWQVE7VZ3J/action/author_attestation","sign_citation":"https://pith.science/pith/6V2PXPY6CTMTTVTWVWQVE7VZ3J/action/citation_signature","submit_replication":"https://pith.science/pith/6V2PXPY6CTMTTVTWVWQVE7VZ3J/action/replication_record"}},"created_at":"2026-07-05T09:55:27.824996+00:00","updated_at":"2026-07-05T09:55:27.824996+00:00"}