Periodic Extrapolative Generalisation in Neural Networks

TL;DR

This paper investigates the ability of various neural network architectures to generalize periodically beyond training data, revealing limitations of current models and providing a benchmarking toolkit for future research.

Contribution

It formalizes the problem of extrapolative generalization for periodic signals and systematically evaluates different architectures, highlighting their shortcomings and introducing PerKit for benchmarking.

Findings

Classical and snake activation functions fail at periodic extrapolation.

Traditional sequential models outperform recent extrapolation-specific architectures.

Population-based training surpasses other methods in generalization ability.

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, available and easily accessible to facilitate future work in the area.