A pre-print of our paper “Probing the Compositionality of Intuitive Functions” is available on the Center for Brains, Minds & Machines page here
The paper contains a couple of experiments that we have run during my research stay at Harvard/MIT. These experiments tried to elicit whether human inductive biases of functions can be seen as compositional by nature.
For this, we assessed human intuitions of functions by a Gaussian Process regression framework, parameterized by three different kernels: a “one-size-fits-all” radial basis kernel, a “non-parametric all the way” spectral mixture kernel, and a compositional kernel made of different consecutive building blocks. We find that when choosing different extrapolations, when performing Markov chain Monte Carlo with people, when generating extrapolations manually as well as when deciding which functions are more predictable, people always seem to have a bias for the compositional kernel.
As compositionality speeds up intuitive inference, this might explain why participants are able to learn functions efficiently in the real world.