Neural-Symbolic Integration: A Compositional Perspective

TL;DR

This paper presents a modular approach to neural-symbolic integration, allowing flexible combination of black-box neural and symbolic systems that enhances training efficiency and performance.

Contribution

It introduces a compositional framework for integrating neural and symbolic modules as black boxes, without assumptions on internal structures, improving training and performance.

Findings

Effective integration of neural and symbolic modules as black boxes.

Enhanced training efficiency for neural modules.

Empirical performance surpassing previous methods.

Abstract

Despite significant progress in the development of neural-symbolic frameworks, the question of how to integrate a neural and a symbolic system in a \emph{compositional} manner remains open. Our work seeks to fill this gap by treating these two systems as black boxes to be integrated as modules into a single architecture, without making assumptions on their internal structure and semantics. Instead, we expect only that each module exposes certain methods for accessing the functions that the module implements: the symbolic module exposes a deduction method for computing the function's output on a given input, and an abduction method for computing the function's inputs for a given output; the neural module exposes a deduction method for computing the function's output on a given input, and an induction method for updating the function given input-output training instances. We are, then, able to show that a symbolic module -- with any choice for syntax and semantics, as long as the deduction and abduction methods are exposed -- can be cleanly integrated with a neural module, and facilitate the latter's efficient training, achieving empirical performance that exceeds that of previous work.