Many complex tasks and environments can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to expedite adaptation and enable compositional generalization. Despite progress, our most powerful systems struggle to compose flexibly. While most of these systems are monolithic, modularity promises to allow capturing the compositional nature of many tasks. However, it is unclear under which circumstances modular systems discover this hidden compositional structure. To shed light on this question, we study a teacher-student setting with a modular teacher where we have full control over the composition of ground truth modules. This allows us to relate the problem of compositional generalization to that of identification of the underlying modules. We show theoretically that identification up to linear transformation purely from demonstrations is possible in hypernetworks without having to learn an exponential number of module combinations. While our theory assumes the infinite data limit, in an extensive empirical study we demonstrate how meta-learning from finite data can discover modular solutions that generalize compositionally in modular but not monolithic architectures. We further show that our insights translate outside the teacher-student setting and demonstrate that in tasks with compositional preferences and tasks with compositional goals hypernetworks can discover modular policies that compositionally generalize.

翻译：许多复杂任务和环境可分解为更简单、独立的组成部分。发现这种潜在的组合结构有望加速适应性并实现组合泛化。尽管取得了进展，但我们最强大的系统在灵活组合方面仍面临挑战。尽管这些系统大多采用单体结构，但模块化有望捕获许多任务的组合性质。然而，目前尚不清楚模块化系统在何种条件下能够发现这种隐藏的组合结构。为阐明这一问题，我们研究了一种带有模块化教师网络的教师-学生设定，其中我们完全控制真实模块的组合方式。这使我们能够将组合泛化问题与底层模块的识别问题联系起来。我们从理论上证明，在超网络中，仅通过演示即可实现线性变换下的模块识别，而无需学习指数数量的模块组合。虽然我们的理论假设数据无限极限，但在广泛的实证研究中，我们展示了如何通过有限数据的元学习在模块化（而非单体）架构中发现能够实现组合泛化的模块化解。我们进一步表明，这些见解可推广至教师-学生设定之外，并在具有组合偏好和组合目标的任务中证明，超网络能够发现实现组合泛化的模块化策略。