DeepAI AI Chat
Log In Sign Up

Homomorphism Autoencoder – Learning Group Structured Representations from Observed Transitions

by   Hamza Keurti, et al.
Max Planck Society
ETH Zurich

How can we acquire world models that veridically represent the outside world both in terms of what is there and in terms of how our actions affect it? Can we acquire such models by interacting with the world, and can we state mathematical desiderata for their relationship with a hypothetical reality existing outside our heads? As machine learning is moving towards representations containing not just observational but also interventional knowledge, we study these problems using tools from representation learning and group theory. Under the assumption that our actuators act upon the world, we propose methods to learn internal representations of not just sensory information but also of actions that modify our sensory representations in a way that is consistent with the actions and transitions in the world. We use an autoencoder equipped with a group representation linearly acting on its latent space, trained on 2-step reconstruction such as to enforce a suitable homomorphism property on the group representation. Compared to existing work, our approach makes fewer assumptions on the group representation and on which transformations the agent can sample from the group. We motivate our method theoretically, and demonstrate empirically that it can learn the correct representation of the groups and the topology of the environment. We also compare its performance in trajectory prediction with previous methods.


page 1

page 2

page 3

page 4


Equivariant Representations for Non-Free Group Actions

We introduce a method for learning representations that are equivariant ...

Representation Learning in Partially Observable Environments using Sensorimotor Prediction

In order to explore and act autonomously in an environment, an agent nee...

Learning Group Structure and Disentangled Representations of Dynamical Environments

Discovering the underlying structure of a dynamical environment involves...

Intelligence, physics and information – the tradeoff between accuracy and simplicity in machine learning

How can we enable machines to make sense of the world, and become better...

Neural Group Actions

We introduce an algorithm for designing Neural Group Actions, collection...

Latent Topology Induction for Understanding Contextualized Representations

In this work, we study the representation space of contextualized embedd...

Understanding Dynamics of Nonlinear Representation Learning and Its Application

Representations of the world environment play a crucial role in machine ...