{"paper":{"title":"Contextuality, Holonomy and Discrete Fiber Bundles in Group-Valued Boltzmann Machines","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.data-an","quant-ph"],"primary_cat":"cs.LG","authors_text":"Jean-Pierre Magnot","submitted_at":"2025-09-05T15:07:54Z","abstract_excerpt":"We propose a geometric extension of restricted Boltzmann machines (RBMs) by allowing weights to take values in abstract groups such as \\( \\mathrm{GL}_n(\\mathbb{R}) \\), \\( \\mathrm{SU}(2) \\), or even infinite-dimensional operator groups. This generalization enables the modeling of complex relational structures, including projective transformations, spinor dynamics, and functional symmetries, with direct applications to vision, language, and quantum learning.\n  A central contribution of this work is the introduction of a \\emph{contextuality index} based on group-valued holonomies computed along c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.10536","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/2509.10536/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"}