{"paper":{"title":"SurReal: Fr\\'echet Mean and Distance Transform for Complex-Valued Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Jiayun Wang, Rudrasis Chakraborty, Stella X. Yu","submitted_at":"2019-06-24T16:12:31Z","abstract_excerpt":"We develop a novel deep learning architecture for naturally complex-valued data, which is often subject to complex scaling ambiguity. We treat each sample as a field in the space of complex numbers. With the polar form of a complex-valued number, the general group that acts in this space is the product of planar rotation and non-zero scaling. This perspective allows us to develop not only a novel convolution operator using weighted Fr\\'echet mean (wFM) on a Riemannian manifold, but also a novel fully connected layer operator using the distance to the wFM, with natural equivariant properties to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10048","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":""},"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"}