This paper studies and confirms the effectiveness of compositionality through human experiments from data generated by gaussian processes regression, supporting it’s case that human learning is inherently compositional.
TLDR
This paper uses eight carefully designed experiments to probe whether an inductive bias for compositionality exists in human learning
Two class of theories around function learning exist: rule-based, parametric, strong inductive bias vs. similarity-based non-parametric, weak inductive bias
rule-based are limited to linear combinations of a fixed set of parametric functions
similarity-based are theoretically unlimited
A Gaussian Processes is used to model both learning theories, and test the effectiveness of compositionality by running human experiments.
Data is generated for specific tasks using non-compositional structured kernels that are flexible in their parameters, and compositional kernels that are additive and multiplicative of a primitive set of kernels
Question: Is this a linear model of nonlinear functions?
Experiments include predicting a function, change detection, judging predictability, short-term memory
Bonus Tangents/Papers
Comparisons to functional programming language/category theory!
Inferring the human kernel. The case for studying rationality, forecasting, decision-making. This is a systematic framework for doing so which is exciting.
Note: This paper is over 80 pages long, but so interesting I barely noticed. I will write a follow-up more detailed spoon-feed analysis
