On the Modeling of Error Functions as High Dimensional Landscapes for Weight Initialization in Learning Networks

Abstract: Next generation deep neural networks for classification hosted on embedded platforms will rely on fast, efficient, and accurate learning algorithms. Initialization of weights in learning networks has a great impact on the classification accuracy. In this paper we focus on deriving good initial weights by modeling the error function of a deep neural network as a high-dimensional landscape. We observe that due to the inherent complexity in its algebraic structure, such an error function may conform to general results of the statistics of large systems. To this end we apply some results from Random Matrix Theory to analyse these functions. We model the error function in terms of a Hamiltonian in N-dimensions and derive some theoretical results about its general behavior. These results are further used to make better initial guesses of weights for the learning algorithm.