Spatially Embedded Neural Networks: Proving Non-Increasing MSE under Bayesian Updating

The purpose of this research note is to examine Bayesian updates to the prior distribution in a spatially embedded, parameter-conditioned network. This note shows that if the Rao-Blackwell inequality applies, Bayesian updating weakly reduces the network’s expected training error. This result strengthens the rationale for applying Bayesian updates to spatially embedded neural networks. Mean squared error loss is used