{"paper":{"title":"Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ronald Katende","submitted_at":"2025-11-04T11:33:54Z","abstract_excerpt":"We study latent geometry as an explicit component of representation quality in data-scarce learning. For an encoder (\\phi), we define (Q_{\\beta,\\gamma}(\\phi)=I(\\phi(X);Y)-\\beta\\mathcal C(\\phi)-\\gamma d_{\\mathrm{int}}(\\phi)), combining task-relevant information with penalties for curvature and intrinsic latent dimension. Thus geometry becomes part of the bottleneck criterion, not only a post hoc diagnostic.\n  Under smooth-manifold, loss-transfer, and estimator-concentration assumptions, we derive non-asymptotic low-label generalization bounds where intrinsic dimension and covering complexity en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.02496","kind":"arxiv","version":2},"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/2511.02496/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"}