{"paper":{"title":"Transformationally Identical and Invariant Convolutional Neural Networks through Symmetric Element Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Matthew T. Freedman, Seong K. Mun, Shih Chung B. Lo, Shuo Gu","submitted_at":"2018-06-10T11:16:36Z","abstract_excerpt":"Mathematically speaking, a transformationally invariant operator, such as a transformationally identical (TI) matrix kernel (i.e., K= T{K}), commutes with the transformation (T{.}) itself when they operate on the first operand matrix. We found that by consistently applying the same type of TI kernels in a convolutional neural networks (CNN) system, the commutative property holds throughout all layers of convolution processes with and without involving an activation function and/or a 1D convolution across channels within a layer. We further found that any CNN possessing the same TI kernel prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03636","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}