Foothill: A Quasiconvex Regularization for Edge Computing of Deep Neural Networks

Deep neural networks (DNNs) have demonstrated success for many supervised learning tasks, ranging from voice recognition, object detection, to image classification. However, their increasing complexity might yield poor generalization error that make them hard to be deployed on edge devices. Quantization is an effective approach to compress DNNs in order to meet these constraints. Using a quasiconvex base function in order to construct a binary quantizer helps training binary neural networks (BNNs) and adding noise to the input data or using a concrete regularization function helps to improve generalization error. Here we introduce foothill function, an infinitely differentiable quasiconvex function. This regularizer is flexible enough to deform towards $L_1$ and $L_2$ penalties. Foothill can be used as a binary quantizer, as a regularizer, or as a loss. In particular, we show this regularizer reduces the accuracy gap between BNNs and their full-precision counterpart for image classification on ImageNet.Comment: Accepted in 16th International Conference of Image Analysis and Recognition (ICIAR 2019

On the Analysis of Trajectories of Gradient Descent in the Optimization of Deep Neural Networks

Theoretical analysis of the error landscape of deep neural networks has garnered significant interest in recent years. In this work, we theoretically study the importance of noise in the trajectories of gradient descent towards optimal solutions in multi-layer neural networks. We show that adding noise (in different ways) to a neural network while training increases the rank of the product of weight matrices of a multi-layer linear neural network. We thus study how adding noise can assist reaching a global optimum when the product matrix is full-rank (under certain conditions). We establish theoretical foundations between the noise induced into the neural network - either to the gradient, to the architecture, or to the input/output to a neural network - and the rank of product of weight matrices. We corroborate our theoretical findings with empirical results.Comment: 4 pages + 1 figure (main, excluding references), 5 pages + 4 figures (appendix