Periodic Extrapolative Generalisation in Neural Networks

Peter Belcak, Roger Wattenhofer

Abstract: The learning of the simplest possible computational pattern - periodicity - is an open problem in the research of strong generalisation in neural networks. We formalise the problem of extrapolative generalisation for periodic signals and systematically investigate the generalisation abilities of classical, population-based, and recently proposed periodic architectures on a set of benchmarking tasks. We find that periodic and “snake” activation functions consistently fail at periodic extrapolation, regardless of the trainability of their periodicity parameters. Further, our results show that traditional sequential models still outperform the novel architectures designed specifically for extrapolation, and that these are in turn trumped by population-based training. We make our benchmarking and evaluation toolkit, Perkit <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> PERKIT: A toolkit for the study of periodicity in neural networks. Available at hups://github.com/pbelcakiperkit., available and easily accessible to facilitate future work in the area.