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In the analysis of machine learning models, it is often convenient to assumethat the parameters are IID. This assumption is not satisfied when theparameters are updated through training processes such as SGD. A relaxation ofthe IID condition is a probabilistic symmetry known as exchangeability. We showthe sense in which the weights in MLPs are exchangeable. This yields the resultthat in certain instances, the layer-wise kernel of fully-connected layersremains approximately constant during training. We identify a sharp change inthe macroscopic behavior of networks as the covariance between weights changesfrom zero.

Exchangeability and Kernel Invariance in Trained MLPs