  Many aspects of human learning have been proposed as a process of
constructing mental programs: from acquiring symbolic number representations to
intuitive theories about the world. In parallel, there is a long-tradition of
using information processing to model human cognition through Rate Distortion
Theory (RDT). Yet, it is still poorly understood how to apply RDT when mental
representations take the form of programs. In this work, we adapt RDT by
proposing a three way trade-off among rate (description length), distortion
(error), and computational costs (search budget). We use simulations on a
melody task to study the implications of this trade-off, and show that
constructing a shared program library across tasks provides global benefits.
However, this comes at the cost of sensitivity to curricula, which is also
characteristic of human learners. Finally, we use methods from partial
information decomposition to generate training curricula that induce more
effective libraries and better generalization.
