{"paper":{"title":"Laplace--Fisher Gate Identities for Optimal Matrix-Gated Blended Score Estimation","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.LG","stat.TH"],"primary_cat":"math.ST","authors_text":"Alois Duston, Tan Bui Tanh","submitted_at":"2026-06-23T21:00:32Z","abstract_excerpt":"Sampling from an unnormalized target by reversing an Ornstein--Uhlenbeck diffusion requires the score of each noise-perturbed marginal. Tweedie's identity and a target-score identity give unbiased finite-reference estimators for this score. Scalar blends can reduce variance, but are too rigid for singular or strongly anisotropic targets. We cast blended score estimation as conditional risk minimization over matrix-valued blending coefficients, or gates, and derive the variance-optimal gate [\n\\Gstar(y,t)=\\alphat^2\\bigl(\\alphat^2 I_d+\\gammat,\\E[H_0(X_0)\\mid Y_t=y]\\bigr)^{-1},\\qquad H_0=-\\nabla^2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25169","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/2606.25169/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"}