Notes on the Symmetries of 2-Layer ReLU-Networks.

Symmetries in neural networks allow different weight configurations leading to the same network function. For odd activation functions, the set of transformations mapping between such configurations have been studied extensively, but less is known for neural networks with ReLU activation functions. We give a complete characterization for fully-connected networks with two layers. Apart from two well-known transformations, only degenerated situations allow additional transformations that leave the network function unchanged. Reduction steps can remove only part of the degenerated cases. Finally, we present a non-degenerate situation for deep neural networks leading to new transformations leaving the network function intact.