Superspace extrapolation reveals inductive biases in function learning

We introduce a new approach for exploring how humans learn and represent functional relationships based on limited observations. We focus on a problem called superspace extrapolation, where learners observe training examples drawn from an n-dimensional space and must extrapolate to an n+1-dimensional superspace of the training examples. Many existing psychological models predict that superspace extrapolation should be fundamentally underdetermined, but we show that humans are able to extrapolate both linear and non-linear functions under these conditions. We also show that a Bayesian model can account for our results given a hypothesis space that includes families of simple functional relationships.