From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford's Geometric Algebra and Convexity

arXiv:2309.16512v3 Announce Type: replace
Abstract: In this paper, we introduce a novel analysis of neural networks based on geometric (Clifford) algebra and convex optimization. We show that optimal weights of deep ReLU neural networks are given by the wedge product of training samples when trained with standard regularized loss. Furthermore, the training problem reduces to convex optimization over wedge product features, which encode the geometric structure of the training dataset. This structure is given in terms of signed volumes of …

abstract algebra analysis arxiv complexity cs.ai cs.lg cs.ne deep neural network math.oc network networks neural network neural networks novel optimization paper product relu samples show stat.ml training type via