Title: Training Deep Neural Networks via Optimization Over Graphs,
Abstract: In this work, we propose to train a deep neural network by distributed
optimization over a graph. Two nonlinear functions are considered: the
rectified linear unit (ReLU) and a linear unit with both lower and upper
cutoffs (DCutLU). The problem reformulation over a graph is realized by
explicitly representing ReLU or DCutLU using a set of slack variables. We then
apply the alternating direction method of multipliers (ADMM) to update the
weights of the network layerwise by solving subproblems of the reformulated
problem. Empirical results suggest that the ADMM-based method is less sensitive
to overfitting than the stochastic gradient descent (SGD) and Adam methods.