Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions

TL;DR

This paper introduces a novel autoencoder-based method that learns group-structured internal representations of environmental interactions, enabling agents to predict action effects without prior group knowledge.

Contribution

It presents a group-equivariant autoencoder that learns internal representations of actions and environment transformations without requiring prior group information.

Findings

Successfully learns group representations of actions

Improves prediction accuracy of future environmental states

Does not require prior knowledge of the group structure

Abstract

How can agents learn internal models that veridically represent interactions with the real world is a largely open question. As machine learning is moving towards representations containing not just observational but also interventional knowledge, we study this problem using tools from representation learning and group theory. We propose methods enabling an agent acting upon the world to learn internal representations of sensory information that are consistent with actions that modify it. We use an autoencoder equipped with a group representation acting on its latent space, trained using an equivariance-derived loss in order to enforce a suitable homomorphism property on the group representation. In contrast to existing work, our approach does not require prior knowledge of the group and does not restrict the set of actions the agent can perform. We motivate our method theoretically, and show empirically that it can learn a group representation of the actions, thereby capturing the structure of the set of transformations applied to the environment. We further show that this allows agents to predict the effect of sequences of future actions with improved accuracy.