  All organisms make temporal predictions, and their evolutionary fitness level
depends on the accuracy of these predictions. In the context of visual
perception, the motions of both the observer and objects in the scene structure
the dynamics of sensory signals, allowing for partial prediction of future
signals based on past ones. Here, we propose a self-supervised
representation-learning framework that extracts and exploits the regularities
of natural videos to compute accurate predictions. We motivate the polar
architecture by appealing to the Fourier shift theorem and its group-theoretic
generalization, and we optimize its parameters on next-frame prediction.
Through controlled experiments, we demonstrate that this approach can discover
the representation of simple transformation groups acting in data. When trained
on natural video datasets, our framework achieves better prediction performance
than traditional motion compensation and rivals conventional deep networks,
while maintaining interpretability and speed. Furthermore, the polar
computations can be restructured into components resembling normalized simple
and direction-selective complex cell models of primate V1 neurons. Thus, polar
prediction offers a principled framework for understanding how the visual
system represents sensory inputs in a form that simplifies temporal prediction.
