A Mathematical Framework and a Suite of Learning Techniques for Neural-Symbolic Systems

TL;DR

This paper introduces Neural-Symbolic Energy-Based Models (NeSy-EBMs), a unifying mathematical framework for neural-symbolic systems that enables diverse learning techniques and demonstrates practical benefits across multiple AI tasks.

Contribution

The paper proposes NeSy-EBMs as a comprehensive framework for neural-symbolic modeling, including new learning methods and an open-source library for scalable real-world applications.

Findings

NeSy-EBMs improve performance in image classification tasks.

The framework enhances graph node labeling accuracy.

NeSy-EBMs demonstrate advantages in autonomous vehicle and question answering tasks.

Abstract

The field of Neural-Symbolic (NeSy) systems is growing rapidly. Proposed approaches show great promise in achieving symbiotic unions of neural and symbolic methods. However, a unifying framework is needed to organize common NeSy modeling patterns and develop general learning approaches. In this paper, we introduce Neural-Symbolic Energy-Based Models (NeSy-EBMs), a unifying mathematical framework for discriminative and generative NeSy modeling. Importantly, NeSy-EBMs allow the derivation of general expressions for gradients of prominent learning losses, and we introduce a suite of four learning approaches that leverage methods from multiple domains, including bilevel and stochastic policy optimization. Finally, we ground the NeSy-EBM framework with Neural Probabilistic Soft Logic (NeuPSL), an open-source NeSy-EBM library designed for scalability and expressivity, facilitating the real-world application of NeSy systems. Through extensive empirical analysis across multiple datasets, we demonstrate the practical advantages of NeSy-EBMs in various tasks, including image classification, graph node labeling, autonomous vehicle situation awareness, and question answering.