Title: Learning Geometric Representations of Interactive Objects. Abstract: We address the problem of learning geometric representations from observations perceived by an agent operating within an environment and interacting with an external object. To this end, we propose a representation learning framework that extracts the state of both the agent and the object from unstructured observations of arbitrary nature (e.g., images). Supervision comes from the performed actions alone, while the dynamics of the object is assumed to be unknown. We provide a theoretical foundation and formally prove that an ideal learner is guaranteed to infer an isometric representation, disentangling the agent from the object. Finally, we investigate empirically our framework on a variety of scenarios. Results show that our model reliably infers the correct representation and outperforms vision-based approaches such as a state-of-the-art keypoint extractor.   
