{"paper":{"title":"Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A neural network trained to satisfy the Ginsparg-Wilson relation as a soft constraint reproduces the overlap fermion operator to high accuracy without explicit sign-function approximations.","cross_cats":["hep-th"],"primary_cat":"hep-lat","authors_text":"Tatsuhiro Misumi","submitted_at":"2026-05-07T11:15:43Z","abstract_excerpt":"We propose a novel, machine-learning-based framework for constructing lattice fermions using Physics-Informed Neural Networks (PINNs). Our approach treats the formulation of the Dirac operator as an optimization problem guided by physical requirements, such as symmetries, locality and doubler-decoupling conditions. We first demonstrate that, when trained to satisfy the Ginsparg-Wilson (GW) relation as a soft constraint, a neural network reproduces the overlap fermion operator to high numerical accuracy and learns an effective sign-function mapping without explicitly using a prescribed polynomi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"when trained to satisfy the Ginsparg-Wilson (GW) relation as a soft constraint, a neural network reproduces the overlap fermion operator to high numerical accuracy and learns an effective sign-function mapping without explicitly using a prescribed polynomial or rational approximation. [...] by changing the initial search bias, the same framework also finds a distinct solution corresponding to a Fujikawa-type generalized GW relation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That training the neural network with the Ginsparg-Wilson relation as a soft constraint will lead to the physically correct continuum limit and correct behavior for all relevant momenta, without additional verification steps or hard enforcement of locality.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Physics-Informed Neural Networks construct lattice Dirac operators satisfying the Ginsparg-Wilson relation, reproducing overlap fermions to high accuracy and discovering a Fujikawa-type generalized relation via algebraic search.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A neural network trained to satisfy the Ginsparg-Wilson relation as a soft constraint reproduces the overlap fermion operator to high accuracy without explicit sign-function approximations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4b2f280cbec764d0634e3dcd48b68ac76394a713dc94613dd0c7a89b645a6357"},"source":{"id":"2605.06022","kind":"arxiv","version":3},"verdict":{"id":"ca289d94-7a83-45c0-8a1e-066309306e3e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T22:04:10.340964Z","strongest_claim":"when trained to satisfy the Ginsparg-Wilson (GW) relation as a soft constraint, a neural network reproduces the overlap fermion operator to high numerical accuracy and learns an effective sign-function mapping without explicitly using a prescribed polynomial or rational approximation. [...] by changing the initial search bias, the same framework also finds a distinct solution corresponding to a Fujikawa-type generalized GW relation.","one_line_summary":"Physics-Informed Neural Networks construct lattice Dirac operators satisfying the Ginsparg-Wilson relation, reproducing overlap fermions to high accuracy and discovering a Fujikawa-type generalized relation via algebraic search.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That training the neural network with the Ginsparg-Wilson relation as a soft constraint will lead to the physically correct continuum limit and correct behavior for all relevant momenta, without additional verification steps or hard enforcement of locality.","pith_extraction_headline":"A neural network trained to satisfy the Ginsparg-Wilson relation as a soft constraint reproduces the overlap fermion operator to high accuracy without explicit sign-function approximations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06022/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T13:22:04.336204Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T08:38:43.064538Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.177815Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T13:04:16.685439Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1632466a74e2d320e7496e451a376543359255f3296d2c936144c5b26bbf8b48"},"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"}