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

תקציר מקורי באנגליתarXiv:2606.28444v2 Announce Type: replace-cross 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 class, we center the training samples at their mean, apply SVD to estimate principal directions and spectral scales, select retained directions by an energy threshold, and represent each retained direction by a pair of sigmoid slab gates. These class-specific gates are then concatenated into a s