{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:FPYEEFNZD4JENWV54MVLFZ6MTJ","short_pith_number":"pith:FPYEEFNZ","schema_version":"1.0","canonical_sha256":"2bf04215b91f1246dabde32ab2e7cc9a7b7677f83554312c45c866adf235f594","source":{"kind":"arxiv","id":"2606.30064","version":1},"attestation_state":"computed","paper":{"title":"Data-Driven Energy-Based Learning via Gibbs Measures on Hierarchical Structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.LG","authors_text":"F. Herrera, L.U. Abdullaev, M.V.Velasco, U.A. Rozikov","submitted_at":"2026-06-29T09:57:39Z","abstract_excerpt":"We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures. Unlike standard empirical risk minimization, where a dataset is used to identify a single optimal parameter, our approach transforms the empirical loss function into an interaction potential defining an energy-based model. The resulting Gibbs distribution describes a family of equilibrium learning states generated by the data.\n  We formulate the consistency conditions of the associated finite-volume distributions and derive nonlinear integral fixed-point equations whose s"},"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":"2606.30064","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T09:57:39Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"43ac202af63b5325d3896a70ed9bcc6b253b8eaf67cec5f916be280113b7678f","abstract_canon_sha256":"466457aaf777224ce5e8bff1e187250de5ae54b7b8f00215ab6bfc217d53e929"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:48.012809Z","signature_b64":"Qh6oH2ZzCl8TC+QS3yH/d4ZMqWANjIlb3JTizcIWu6jU2cAIbZNfm6LePJdts5Y/PLlxignHJ18cpu+bTfu4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bf04215b91f1246dabde32ab2e7cc9a7b7677f83554312c45c866adf235f594","last_reissued_at":"2026-06-30T02:17:48.012154Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:48.012154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Data-Driven Energy-Based Learning via Gibbs Measures on Hierarchical Structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.LG","authors_text":"F. Herrera, L.U. Abdullaev, M.V.Velasco, U.A. Rozikov","submitted_at":"2026-06-29T09:57:39Z","abstract_excerpt":"We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures. Unlike standard empirical risk minimization, where a dataset is used to identify a single optimal parameter, our approach transforms the empirical loss function into an interaction potential defining an energy-based model. The resulting Gibbs distribution describes a family of equilibrium learning states generated by the data.\n  We formulate the consistency conditions of the associated finite-volume distributions and derive nonlinear integral fixed-point equations whose s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30064","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/2606.30064/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":"2606.30064","created_at":"2026-06-30T02:17:48.012252+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.30064v1","created_at":"2026-06-30T02:17:48.012252+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30064","created_at":"2026-06-30T02:17:48.012252+00:00"},{"alias_kind":"pith_short_12","alias_value":"FPYEEFNZD4JE","created_at":"2026-06-30T02:17:48.012252+00:00"},{"alias_kind":"pith_short_16","alias_value":"FPYEEFNZD4JENWV5","created_at":"2026-06-30T02:17:48.012252+00:00"},{"alias_kind":"pith_short_8","alias_value":"FPYEEFNZ","created_at":"2026-06-30T02:17:48.012252+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/FPYEEFNZD4JENWV54MVLFZ6MTJ","json":"https://pith.science/pith/FPYEEFNZD4JENWV54MVLFZ6MTJ.json","graph_json":"https://pith.science/api/pith-number/FPYEEFNZD4JENWV54MVLFZ6MTJ/graph.json","events_json":"https://pith.science/api/pith-number/FPYEEFNZD4JENWV54MVLFZ6MTJ/events.json","paper":"https://pith.science/paper/FPYEEFNZ"},"agent_actions":{"view_html":"https://pith.science/pith/FPYEEFNZD4JENWV54MVLFZ6MTJ","download_json":"https://pith.science/pith/FPYEEFNZD4JENWV54MVLFZ6MTJ.json","view_paper":"https://pith.science/paper/FPYEEFNZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.30064&json=true","fetch_graph":"https://pith.science/api/pith-number/FPYEEFNZD4JENWV54MVLFZ6MTJ/graph.json","fetch_events":"https://pith.science/api/pith-number/FPYEEFNZD4JENWV54MVLFZ6MTJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FPYEEFNZD4JENWV54MVLFZ6MTJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FPYEEFNZD4JENWV54MVLFZ6MTJ/action/storage_attestation","attest_author":"https://pith.science/pith/FPYEEFNZD4JENWV54MVLFZ6MTJ/action/author_attestation","sign_citation":"https://pith.science/pith/FPYEEFNZD4JENWV54MVLFZ6MTJ/action/citation_signature","submit_replication":"https://pith.science/pith/FPYEEFNZD4JENWV54MVLFZ6MTJ/action/replication_record"}},"created_at":"2026-06-30T02:17:48.012252+00:00","updated_at":"2026-06-30T02:17:48.012252+00:00"}