Symbolic Pregression: Discovering Physical Laws from Distorted Video
This addresses the challenge of extracting physical laws from noisy, unlabeled visual data, which is incremental as it builds on autoencoders and symbolic regression but introduces a novel pregression step.
The paper tackles the problem of unsupervised learning of equations of motion from distorted video by training an autoencoder to map frames into a latent space where motion laws are simplified, then using symbolic regression to discover differential equations, successfully rediscovering Cartesian coordinates even with distortions.
We present a method for unsupervised learning of equations of motion for objects in raw and optionally distorted unlabeled video. We first train an autoencoder that maps each video frame into a low-dimensional latent space where the laws of motion are as simple as possible, by minimizing a combination of non-linearity, acceleration and prediction error. Differential equations describing the motion are then discovered using Pareto-optimal symbolic regression. We find that our pre-regression ("pregression") step is able to rediscover Cartesian coordinates of unlabeled moving objects even when the video is distorted by a generalized lens. Using intuition from multidimensional knot-theory, we find that the pregression step is facilitated by first adding extra latent space dimensions to avoid topological problems during training and then removing these extra dimensions via principal component analysis.