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.

我们通过在多个任务之间构建共享的程序库，提出了一种折中方法，其中在描述长度、误差和计算成本之间进行三向权衡，从而适应了心理表示采用编程形式的情况，该方法在仿真的旋律任务中表明共享程序库提供了全局权益，但这是以对教材敏感的代价为代价，这也是人类学习者的特点。最后，我们使用部分信息分解的方法生成能够引起更有效的程序库和更好泛化的训练教材。