The compositional nature of human function learning
Function learning lies at the core of everyday cognition. From learning which stimulus will lead to reward all the way to how other people's intentions influence their actions, almost any task requires the construction of mental representations that map inputs to outputs. Since the space of such mappings is infinite, inductive biases are necessary to constrain plausible inferences. What is the nature of the human inductive biases over functions? How do people deal with complex functions that are not easily captured by standard learning algorithms?Insight into this question is provided by the observation that many complex functions encountered in the real world can be broken down into compositions of simpler form. We pursue this idea theoretically and experimentally, by first defining a hypothetical compositional grammar for intuitive functions and then investigating whether this grammar quantitatively predicts human learning, pattern completion, and memory and change detection performance. We end by speculating that compositionality is a necessary requirement for intelligent behaviour.