{"paper":{"title":"Field Theory of Data: Anomaly Detection via the Functional Renormalization Group. The 2D Ising Model as a Benchmark","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Anomaly detection maps to renormalization group flows where the noise-to-signal ratio acts as temperature in an effective equilibrium field theory.","cross_cats":["cs.IT","hep-th","math.IT","stat.ME"],"primary_cat":"cond-mat.stat-mech","authors_text":"Dine Ousmane Samary, Parham Radpay, Riccardo Finotello, Vincent Lahoche","submitted_at":"2026-05-11T18:43:14Z","abstract_excerpt":"We establish a correspondence between anomaly detection in high-noise regimes and the renormalization group flow of non-equilibrium field theories. We provide a physical grounding for this framework by proving that the detection of phase transitions in interacting non-equilibrium systems maps to the study of an effective equilibrium field theory near its Gaussian fixed point, which we identify with the universal Marchenko-Pastur distribution. Applying the Functional Renormalization Group to the two-dimensional Model A, we demonstrate that the noise-to-signal ratio acts as a physical temperatur"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Applying the Functional Renormalization Group to the two-dimensional Model A, the noise-to-signal ratio acts as a physical temperature where the signal emerges as ordered domains, identifying critical thresholds with an error below 4% and outperforming Kullback-Leibler divergence.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the detection of phase transitions in interacting non-equilibrium systems maps to the study of an effective equilibrium field theory near its Gaussian fixed point, which is identified with the universal Marchenko-Pastur distribution.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Anomaly detection is mapped to the RG flow of a non-equilibrium field theory, with the 2D Ising model benchmark showing critical threshold identification error below 4% by treating noise-to-signal as effective temperature.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Anomaly detection maps to renormalization group flows where the noise-to-signal ratio acts as temperature in an effective equilibrium field theory.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fcb76bf656ac97176452d112f7de388c05a73e35492cd93dc7cba0da829a9e84"},"source":{"id":"2605.11138","kind":"arxiv","version":2},"verdict":{"id":"917eb344-bc9b-47a6-95b0-58199d54d97a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T00:55:21.140520Z","strongest_claim":"Applying the Functional Renormalization Group to the two-dimensional Model A, the noise-to-signal ratio acts as a physical temperature where the signal emerges as ordered domains, identifying critical thresholds with an error below 4% and outperforming Kullback-Leibler divergence.","one_line_summary":"Anomaly detection is mapped to the RG flow of a non-equilibrium field theory, with the 2D Ising model benchmark showing critical threshold identification error below 4% by treating noise-to-signal as effective temperature.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the detection of phase transitions in interacting non-equilibrium systems maps to the study of an effective equilibrium field theory near its Gaussian fixed point, which is identified with the universal Marchenko-Pastur distribution.","pith_extraction_headline":"Anomaly detection maps to renormalization group flows where the noise-to-signal ratio acts as temperature in an effective equilibrium field theory."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.11138/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T05:02:00.652609Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:34:44.758761Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T10:31:16.723425Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T08:45:14.151927Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"eedbc3895facb12dfb806c6e5f4738259c12e53347354e093c6dbe85a753ca89"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"6198ca22d693fdd82fb5fa3712d7f7daec142ba68f43be016a0fc204458a840a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}