Block-diagonal Hessian-free Optimization for Training Neural Networks

Abstract

Second-order methods for neural network optimization have several advantages over methods based on first-order gradient descent, including better scaling to large mini-batch sizes and fewer updates needed for convergence. But they are rarely applied to deep learning in practice because of high computational cost and the need for model-dependent algorithmic variations. We introduce a variant of the Hessian-free method that leverages a block-diagonal approximation of the generalized Gauss-Newton matrix. Our method computes the curvature approximation matrix only for pairs of parameters from the same layer or block of the neural network and performs conjugate gradient updates independently for each block. Experiments on deep autoencoders, deep convolutional networks, and multilayer LSTMs demonstrate better convergence and generalization compared to the original Hessian-free approach and the Adam method.

10 pages, 3 figures

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• DeepOBS: A Deep Learning Optimizer Benchmark Suite
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• Train Feedfoward Neural Network with Layer-wise Adaptive Rate via Approximating Back-matching Propagation
• Whitening and second order optimization both make information in the dataset unusable during training, and can reduce or prevent generalization