The Training Process of Many Deep Networks Explores the Same Low-Dimensional Manifold

arXiv:2305.01604v3 Announce Type: replace
Abstract: We develop information-geometric techniques to analyze the trajectories of the predictions of deep networks during training. By examining the underlying high-dimensional probabilistic models, we reveal that the training process explores an effectively low-dimensional manifold. Networks with a wide range of architectures, sizes, trained using different optimization methods, regularization techniques, data augmentation techniques, and weight initializations lie on the same manifold in the prediction space. We study the details of this manifold to find that networks …

abstract analyze architectures arxiv cond-mat.dis-nn cs.lg information low manifold networks predictions process training type