{"paper":{"title":"Geometric and Information Compression of Representations in Deep Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.LG","authors_text":"Asja Fischer, Bernhard C. Geiger, Henning Petzka, Linara Adilova","submitted_at":"2026-06-19T16:49:50Z","abstract_excerpt":"Deep neural networks transform input data into latent representations that support a wide range of downstream tasks. These representations can be characterized along information-theoretic and geometric dimensions, but their relationship remains poorly understood. A central open question is whether low mutual information (MI) between inputs and representations necessarily implies geometrically compressed latent spaces and vice versa. We investigate this question using class-wise clustering as a measure of geometric compression and theoretically sound MI estimation in conditional entropy bottlen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21593","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/2606.21593/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"}