Preconditioned Spectral Descent for Deep Learning
A note about reviews: "heavy" review comments were provided by reviewers in the program committee as part of the evaluation process for NIPS 2015, along with posted responses during the author feedback period. Numerical scores from both "heavy" and "light" reviewers are not provided in the review link below.
Conference Event Type: Poster
Deep learning presents notorious computational challenges. These challenges include, but are not limited to, the non-convexity of learning objectives and estimating the quantities needed for optimization algorithms, such as gradients. While we do not address the non-convexity, we present an optimization solution that ex- ploits the so far unused “geometry” in the objective function in order to best make use of the estimated gradients. Previous work attempted similar goals with preconditioned methods in the Euclidean space, such as L-BFGS, RMSprop, and ADA-grad. In stark contrast, our approach combines a non-Euclidean gradient method with preconditioning. We provide evidence that this combination more accurately captures the geometry of the objective function compared to prior work. We theoretically formalize our arguments and derive novel preconditioned non-Euclidean algorithms. The results are promising in both computational time and quality when applied to Restricted Boltzmann Machines, Feedforward Neural Nets, and Convolutional Neural Nets.