Learning interpretable representations with variational autoencoders (VAEs) is a major goal of representation learning. The main challenge lies in obtaining disentangled representations, where each latent dimension corresponds to a distinct generative factor. This difficulty is fundamentally tied to the inability to perform nonlinear independent component analysis. Here, we introduce the framework of action-induced representations (AIRs) which models representations of physical systems given experiments (or actions) that can be performed on them. We show that, in this framework, we can provably disentangle degrees of freedom w.r.t. their action dependence. We further introduce a variational AIR architecture (VAIR) that can extract AIRs and therefore achieve provable disentanglement where standard VAEs fail. Beyond state representation, VAIR also captures the action dependence of the underlying generative factors, directly linking experiments to the degrees of freedom they influence.

翻译：利用变分自编码器（VAEs）学习可解释表示是表示学习的重要目标。其主要挑战在于如何获得解耦表示，即每个潜在维度对应一个独立的生成因子。这一困难本质上与非线性的独立成分分析无法实现有关。本文提出了动作诱导表示（AIRs）框架，该框架通过对物理系统施加可执行实验（或动作）来建模其表示。我们证明，在此框架下，能够严格实现自由度相对于其动作依赖性的解耦。进一步，我们提出了一种变分AIR架构（VAIR），该架构能够提取AIRs，从而在标准VAEs失效的场景下实现可证明的解耦。除了状态表示外，VAIR还能捕捉底层生成因子的动作依赖性，直接将实验与其影响的自由度关联起来。