Newton Losses: Efficiently Including Second-Order Information into Gradient Descent

Felix Petersen, Christian Borgelt, Tobias Sutter, Hilde Kuehne, Oliver Deussen

Keywords: differentiable algorithms, backpropagation, differentiable

TL;DR: Applying Newton to the loss and gradient descent to the neural network.

Abstract: We present Newton losses, a method for incorporating second-order information of losses by approximating them with quadratic functions. The presented method is applied only to the loss function and allows training the neural network with gradient descent. As loss functions are usually substantially cheaper to compute than the neural network, Newton losses can be used at a relatively small additional cost. We find that they yield superior performance, especially when applied to non-convex and hard-to-optimize loss functions such as algorithmic losses, which have been popularized in recent research.

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