Softened Symbol Grounding for Neuro-symbolic Systems

TL;DR

This paper introduces a novel softened symbol grounding method for neuro-symbolic systems, effectively bridging neural network training and symbolic reasoning to improve learning efficiency and problem-solving capabilities.

Contribution

It proposes a new framework that models symbol states with a Boltzmann distribution, uses an innovative MCMC sampling technique, and incorporates an annealing mechanism to enhance symbol grounding.

Findings

Successfully solves complex neuro-symbolic tasks beyond existing methods

Improves symbol grounding efficiency and effectiveness

Demonstrates superior performance on three benchmark tasks

Abstract

Neuro-symbolic learning generally consists of two separated worlds, i.e., neural network training and symbolic constraint solving, whose success hinges on symbol grounding, a fundamental problem in AI. This paper presents a novel, softened symbol grounding process, bridging the gap between the two worlds, and resulting in an effective and efficient neuro-symbolic learning framework. Technically, the framework features (1) modeling of symbol solution states as a Boltzmann distribution, which avoids expensive state searching and facilitates mutually beneficial interactions between network training and symbolic reasoning;(2) a new MCMC technique leveraging projection and SMT solvers, which efficiently samples from disconnected symbol solution spaces; (3) an annealing mechanism that can escape from %being trapped into sub-optimal symbol groundings. Experiments with three representative neuro symbolic learning tasks demonstrate that, owining to its superior symbol grounding capability, our framework successfully solves problems well beyond the frontier of the existing proposals.