Training a Two Layer ReLU Network Analytically
This work addresses the challenge of efficiently training neural networks for practitioners, though it is incremental as it builds on prior theoretical insights about critical points in such networks.
The authors tackled the problem of training two-layer ReLU networks by developing an analytical algorithm that finds critical points without relying on gradient descent, resulting in deeper optima and significantly smaller training loss on four out of five real datasets, with faster performance and fewer tuning parameters.
Neural networks are usually trained with different variants of gradient descent based optimization algorithms such as stochastic gradient descent or the Adam optimizer. Recent theoretical work states that the critical points (where the gradient of the loss is zero) of two-layer ReLU networks with the square loss are not all local minima. However, in this work we will explore an algorithm for training two-layer neural networks with ReLU-like activation and the square loss that alternatively finds the critical points of the loss function analytically for one layer while keeping the other layer and the neuron activation pattern fixed. Experiments indicate that this simple algorithm can find deeper optima than Stochastic Gradient Descent or the Adam optimizer, obtaining significantly smaller training loss values on four out of the five real datasets evaluated. Moreover, the method is faster than the gradient descent methods and has virtually no tuning parameters.