Probing the Compositionality of Intuitive Functions

How do people learn about complex functional structure? Taking inspiration from other areas of cognitive science, we propose that this is accomplished by harnessing compositionality: complex structure is decomposed into simpler building blocks. We formalize this idea within the framework of Bayesian regression using a grammar over Gaussian process kernels. We show that participants prefer compositional over non-compositional function extrapolations, that samples from the human prior over functions are best described by a compositional model, and that people perceive compositional functions as more predictable than their non-compositional but otherwise similar counterparts. We argue that the compositional nature of intuitive functions is consistent with broad principles of human cognition. This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF 1231216. Probing the Compositionality of Intuitive Functions Eric Schulz Department of Experimental Psychology, University College London Joshua B. Tenenbaum Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology David Duvenaud School of Engineering and Applied Sciences, Harvard University Maarten Speekenbrink Department of Experimental Psychology, University College London Samuel J. Gershman Department of Psychology and Center for Brain Science, Harvard University Abstract How do people learn about complex functional structure? Taking inspiration from other areas of cognitive science, we propose that this is accomplished by harnessing compositionality: complex structure is decomposed into simpler building blocks. We formalize this idea within the framework of Bayesian regression using a grammar over Gaussian process kernels. We show that participants prefer compositional over non-compositional function extrapolations, that samples from the human prior over functions are best described by a compositional model, and that people perceive compositional functions as more predictable than their non-compositional but otherwise similar counterparts. We argue that the compositional nature of intuitive functions is consistent with broad principles of human cognition.