Apperception

Abstract

This paper describes a neuro-symbolic system for distilling interpretable logical theories out of streams of raw, unprocessed sensory experience. We combine a binary neural network, that maps raw sensory input to concepts, with an inductive logic programming system, that combines concepts into declarative rules. Both the inductive logic programming system and the binary neural network are encoded as logic programs, so the weights of the neural network and the declarative rules of the theory can be solved jointly as a single SAT problem. This way, we are able to jointly learn how to perceive (mapping raw sensory information to concepts) and apperceive (combining concepts into declarative rules). We apply our system, the Apperception Engine, to the Sokoban domain. Given a sequence of noisy pixel images, the system has to construct objects that persist over time, extract attributes that change over time, and induce rules explaining how the attributes change over time. We compare our system with a neural network baseline, and show that the baseline is significantly outperformed by the Apperception Engine.