{"paper":{"title":"Injectivity of ReLU networks: perspectives from statistical physics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","stat.ML"],"primary_cat":"cond-mat.dis-nn","authors_text":"Afonso S. Bandeira, Antoine Maillard, David Belius, Ivan Dokmani\\'c, Shuta Nakajima","submitted_at":"2023-02-27T19:51:42Z","abstract_excerpt":"When can the input of a ReLU neural network be inferred from its output? In other words, when is the network injective? We consider a single layer, $x \\mapsto \\mathrm{ReLU}(Wx)$, with a random Gaussian $m \\times n$ matrix $W$, in a high-dimensional setting where $n, m \\to \\infty$. Recent work connects this problem to spherical integral geometry giving rise to a conjectured sharp injectivity threshold for $\\alpha = \\frac{m}{n}$ by studying the expected Euler characteristic of a certain random set. We adopt a different perspective and show that injectivity is equivalent to a property of the grou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.14112","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/2302.14112/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"}