Learning identifiable representations and models from low-level observations is helpful for an intelligent spacecraft to complete downstream tasks reliably. For temporal observations, to ensure that the data generating process is provably inverted, most existing works either assume the noise variables in the dynamic mechanisms are (conditionally) independent or require that the interventions can directly affect each latent variable. However, in practice, the relationship between the exogenous inputs/interventions and the latent variables may follow some complex deterministic mechanisms. In this work, we study the problem of identifiable representation and model learning for latent dynamic systems. The key idea is to use an inductive bias inspired by controllable canonical forms, which are sparse and input-dependent by definition. We prove that, for linear and affine nonlinear latent dynamic systems with sparse input matrices, it is possible to identify the latent variables up to scaling and determine the dynamic models up to some simple transformations. The results have the potential to provide some theoretical guarantees for developing more trustworthy decision-making and control methods for intelligent spacecrafts.

翻译：从低级观测中学习可辨识的表示与模型，有助于智能航天器可靠地完成下游任务。对于时序观测，为确保数据生成过程可被证明是可逆的，现有工作大多假设动态机制中的噪声变量是（条件）独立的，或者要求干预能直接影响每个潜在变量。然而，在实践中，外生输入/干预与潜在变量之间的关系可能遵循某些复杂的确定性机制。本文研究潜在动态系统的可辨识表示与模型学习问题。其核心思想是利用一种受可控规范形式启发的归纳偏置，这类形式本质上是稀疏且依赖于输入的。我们证明，对于具有稀疏输入矩阵的线性及仿射非线性潜在动态系统，能够将潜在变量辨识至尺度变换的程度，并将动态模型确定至某些简单变换的程度。该结果有望为开发更可信赖的智能航天器决策与控制方法提供理论保证。