From Dataset Spectral Geometry to Network Weights: A Geometry-Aware Initialization for Sigmoidal MLPs in Image Classification

Excerpt

arXiv:2606.28444v2 Announce Type: replace Abstract: Classical universal approximation theorems (UAT) establish the expressive power of sigmoidal multilayer perceptrons, but they do not specify how the weights should be initialized. We study a supervised, data-dependent, geometry-aware initialization for one-hidden-layer sigmoidal MLPs that compiles labeled class geometry into network weights. The construction starts from the idea that sigmoid units can act as smooth half-space gates. For each cl