While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learnt representations meaningful. For this the typical approach is to regularize the learned representation through prior probability distributions. However such priors are usually unavailable or ad hoc. To deal with this, we propose a dynamics-constrained representation learning framework. Instead of using predefined probabilities, we restrict the latent representation to follow specific dynamics, which is a more natural constraint for representation learning in dynamical systems. Our belief stems from a fundamental observation in physics that though different systems can have different marginalized probability distributions, they typically obey the same dynamics, such as Newton's and Schrodinger's equations. We validate our framework for different systems including a real-world fluorescent DNA movie dataset. We show that our algorithm can uniquely identify an uncorrelated, isometric and meaningful latent representation.

翻译：虽然表征学习已成为机器学习和人工智能发展的核心，但如何使学习到的表征具有意义仍是一个关键问题。为此，典型方法是通过先验概率分布对学习到的表征进行正则化。然而，这类先验通常难以获取或具有临时性。为解决这一问题，我们提出了一种动力学约束的表征学习框架。不同于使用预定义概率分布，我们将潜在表征限制为遵循特定的动力学规律——这对于动力系统中的表征学习而言是更自然的约束条件。我们的信念源于物理学的基本观察：尽管不同系统可能具有不同的边际概率分布，但它们通常遵循相同的动力学规律，例如牛顿方程和薛定谔方程。我们通过包括真实荧光DNA影片数据集在内的不同系统验证了该框架。结果表明，我们的算法能够唯一地识别出无相关性、等距且具有意义的潜在表征。