A Self-Supervised Framework for Function Learning and Extrapolation

Understanding how agents learn to generalize — and, in particular, to extrapolate — in high-dimensional, naturalistic environments remains a challenge for both machine learning and the study of biological agents. One approach to this has been the use of function learning paradigms, which allow agents’ empirical patterns of generalization for smooth scalar functions to be described precisely. However, to date, such work has not succeeded in identifying mechanisms that acquire the kinds of general purpose representations over which function learning can operate to exhibit the patterns of generalization observed in human empirical studies. Here, we present a framework for how a learner may acquire such representations, that then support generalization — and extrapolation in particular — in a few-shot fashion in the domain of scalar function learning. Taking inspiration from a classic theory of visual processing, we construct a self-supervised encoder that implements the basic inductive bias of invariance under topological distortions. We show the resulting representations outperform those from other models for unsupervised time series learning in several downstream function learning tasks, including extrapolation.