  Recent seminal work at the intersection of deep neural networks practice and
random matrix theory has linked the convergence speed and robustness of these
networks with the combination of random weight initialization and nonlinear
activation function in use. Building on those principles, we introduce a
process to transform an existing activation function into another one with
better properties. We term such transform \emph{static activation
normalization}. More specifically we focus on this normalization applied to the
ReLU unit, and show empirically that it significantly promotes convergence
robustness, maximum training depth, and anytime performance. We verify these
claims by examining empirical eigenvalue distributions of networks trained with
those activations. Our static activation normalization provides a first step
towards giving benefits similar in spirit to schemes like batch normalization,
but without computational cost.
