Numerical Exploration of Training Loss Level-Sets in Deep Neural Networks

We present a computational method for empirically characterizing the training\nloss level-sets of deep neural networks. Our method numerically constructs a\npath in parameter space that is constrained to a set with a fixed near-zero\ntraining loss. By measuring regularization functions and test loss at different\npoints within this path, we examine how different points in the parameter space\nwith the same fixed training loss compare in terms of generalization ability.\nWe also compare this method for finding regularized points with the more\ntypical method, that uses objective functions which are weighted sums of\ntraining loss and regularization terms. We apply dimensionality reduction to\nthe traversed paths in order to visualize the loss level sets in a\nwell-regularized region of parameter space. Our results provide new information\nabout the loss landscape of deep neural networks, as well as a new strategy for\nreducing test loss.\n