Deep Learning with Periodic Features and Applications in Particle Physics

Abstract

We introduce a periodic loss function and corresponding activation function, to be used for neural network regression and autoencoding task involving periodic targets. Such target features, typically represented in non-Cartesian coordinates, arise mainly from angular distributions, but also include repeating time series, e.g. 24-h cycles or seasonal intervals. To demonstrate the use of this loss function, two different use-cases within the context of high-energy physics are presented. The first is a simple regression network, trained to predict the angle between particles emerging from the decay of a heavier, unstable particle. Next, we look at the same particle decay, but train an autoencoder to reproduce all inputs, which include both cyclic and noncyclic features. All examples show that failing to incorporate the cyclic property of the targets into the loss and activation function significantly degrades the performance of the model predictions.