Exchangeability and Kernel Invariance in Trained MLPs

In the analysis of machine learning models, it is often convenient to assume that the parameters are IID. This assumption is not satisfied when the parameters are updated through training processes such as Stochastic Gradient Descent. A relaxation of the IID condition is a probabilistic symmetry known as exchangeability. We show the sense in which the weights in MLPs are exchangeable. This yields the result that in certain instances, the layer-wise kernel of fully-connected layers remains approximately constant during training. Our results shed light on such kernel properties throughout training while limiting the use of unrealistic assumptions.