Deciphering Raw Data in Neuro-Symbolic Learning with Provable Guarantees

TL;DR

This paper introduces a theoretical framework for understanding when neuro-symbolic systems can successfully learn perception models by analyzing the knowledge base's efficacy, supported by experiments on benchmark tasks.

Contribution

It provides the first criterion to evaluate the effectiveness of symbolic knowledge bases in neuro-symbolic learning, enhancing understanding of their learnability.

Findings

Many knowledge bases meet the efficacy criterion, enabling successful learning.

Some knowledge bases fail the criterion, indicating potential learning failures.

Experimental results validate the usefulness of the proposed criterion.

Abstract

Neuro-symbolic hybrid systems are promising for integrating machine learning and symbolic reasoning, where perception models are facilitated with information inferred from a symbolic knowledge base through logical reasoning. Despite empirical evidence showing the ability of hybrid systems to learn accurate perception models, the theoretical understanding of learnability is still lacking. Hence, it remains unclear why a hybrid system succeeds for a specific task and when it may fail given a different knowledge base. In this paper, we introduce a novel way of characterising supervision signals from a knowledge base, and establish a criterion for determining the knowledge's efficacy in facilitating successful learning. This, for the first time, allows us to address the two questions above by inspecting the knowledge base under investigation. Our analysis suggests that many knowledge bases satisfy the criterion, thus enabling effective learning, while some fail to satisfy it, indicating potential failures. Comprehensive experiments confirm the utility of our criterion on benchmark tasks.