Efficient SGD Neural Network Training via Sublinear Activated Neuron Identification

Abstract: Deep learning has been widely used in many fields, but the model training process usually consumes massive computational resources and time. Therefore, designing an efficient neural network training method with a provable convergence guarantee is a fundamental and important research question. In this paper, we present a static half-space report data structure that consists of a fully connected two-layer neural network for shifted ReLU activation to enable activated neuron identification in sublinear time via geometric search. We also prove that our algorithm can converge in $O(M^2/\epsilon^2)$ time with network size quadratic in the coefficient norm upper bound $M$ and error term $\epsilon$.