Geometric structure of shallow neural networks and constructive ${mathcal L}^2$ cost minimization
arXiv:2309.10370v4 Announce Type: replace-cross Abstract: In this paper, we approach the problem of cost (loss) minimization in underparametrized shallow ReLU networks through the explicit construction of upper bounds which appeal to the structure of classification data, without use of gradient descent. A key focus is on elucidating the geometric structure of approximate and precise minimizers. We consider an $L^2$ cost function, input space $mathbb{R}^M$, output space ${mathbb R}^Q$ with $Qleq M$, and training input sample size that can […]