{"paper":{"title":"What Your Model Threw Away and Why You'll Want It Back: Masking, Fingerprinting, and Privacy from Discarded Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.RT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Zachary P. Bradshaw","submitted_at":"2026-06-17T01:03:26Z","abstract_excerpt":"We develop a framework for the information discarded by machine learning models whose inputs carry a Lie group action. Given a representation $\\pi$ of a Lie group $G$ on a space $V$ and a learned function $f\\colon V \\to \\mathbb{R}$, we define two objects measuring the symmetry invisible to $f$. The null fiber at a point $x \\in V$ is the set $N_G(f,x) = \\{g \\in G : f(\\pi(g^{-1}) \\cdot x) = f(x)\\}$ of group elements whose inverse action on $x$ is undetectable by $f$. When $N_G(f,x)$ is independent of $x$, it coincides with the stabilizer $\\mathrm{Stab}_G(f)$, the largest subgroup of $G$ under wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13046","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/2607.13046/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"}