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.

翻译：人类学习的许多方面被提出为构建心理程序的过程：从获取符号数字表征到关于世界的直觉理论。与此同时，利用信息处理通过率失真理论（RDT）建模人类认知具有悠久的传统。然而，当心理表征以程序形式存在时，如何应用RDT仍未被充分理解。本研究通过提出速率（描述长度）、失真（误差）和计算成本（搜索预算）三者之间的权衡，对RDT进行适配。我们使用旋律任务的模拟来研究这种权衡的含义，并表明跨任务构建共享程序库可带来全局性收益。但这种收益以对课程顺序的敏感性为代价，这也是人类学习者的典型特征。最后，我们利用部分信息分解方法生成训练课程，以诱导更有效的程序库和更好的泛化能力。