S-GAI: Spectral Geometry-Aware Initialization for Sigmoidal MLPs -- From Dataset Geometry to Network Weights

arXiv:2606.28444v1 Announce Type: new Abstract: Classical universal approximation theorems establish the expressive power of sigmoidal multilayer perceptrons, but they do not prescribe how initial weights should encode the geometry of a data distribution. We propose S-GAI, a spectral geometry-aware initialization framework for one-hidden-layer sigmoidal MLPs. Starting from the constructive idea that sigmoid units can act as smooth half-space gates, we move from hand-specified planar geometry to ...