{"paper":{"title":"LU-Net: Invertible Neural Networks Based on Matrix Factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE"],"primary_cat":"cs.LG","authors_text":"Hanno Gottschalk, Robin Chan, Sarina Penquitt","submitted_at":"2023-02-21T08:52:36Z","abstract_excerpt":"LU-Net is a simple and fast architecture for invertible neural networks (INN) that is based on the factorization of quadratic weight matrices $\\mathsf{A=LU}$, where $\\mathsf{L}$ is a lower triangular matrix with ones on the diagonal and $\\mathsf{U}$ an upper triangular matrix. Instead of learning a fully occupied matrix $\\mathsf{A}$, we learn $\\mathsf{L}$ and $\\mathsf{U}$ separately. If combined with an invertible activation function, such layers can easily be inverted whenever the diagonal entries of $\\mathsf{U}$ are different from zero. Also, the computation of the determinant of the Jacobia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.10524","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/2302.10524/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"}