Symbolic Pregression: Discovering Physical Laws from Distorted Video

Kavli Affiliate: Max Tegmark

| First 5 Authors: Silviu-Marian Udrescu, Max Tegmark, , ,

| Summary:

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.

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