A Bayesian-Symbolic Approach to Learning and Reasoning for Intuitive Physics

Kai Xu, Akash Srivastava, Dan Gutfreund, Felix Sosa, Tomer Ullman, Joshua B. Tenenbaum, Charles Sutton

Keywords: physics learning, symbolic regression, intuitive physics

Abstract: Humans are capable of reasoning about physical phenomena by inferring laws of physics from a very limited set of observations. The inferred laws can potentially depend on unobserved properties, such as mass, texture, charge, etc. This sample-efficient physical reasoning is considered a core domain of human common-sense knowledge and hints at the existence of a physics engine in the head. In this paper, we propose a Bayesian symbolic framework for learning sample-efficient models of physical reasoning and prediction, which are of special interests in the field of intuitive physics. In our framework, the environment is represented by a top-down generative model with a collection of entities with some known and unknown properties as latent variables to capture uncertainty. The physics engine depends on physical laws which are modeled as interpretable symbolic expressions and are assumed to be functions of the latent properties of the entities interacting under simple Newtonian physics. As such, learning the laws is then reduced to symbolic regression and Bayesian inference methods are used to obtain the distribution of unobserved properties. These inference and regression steps are performed in an iterative manner following the expectation–maximization algorithm to infer the unknown properties and use them to learn the laws from a very small set of observations. We demonstrate that on three physics learning tasks that compared to the existing methods of learning physics, our proposed framework is more data-efficient, accurate and makes joint reasoning and learning possible.

One-sentence Summary: A novel computational framework to perform joint learning-reasoning of physics by combining symbolic regression and Bayesian inference.

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