A Mathematical Framework, a Taxonomy of Modeling Paradigms, and a Suite of Learning Techniques for Neural-Symbolic Systems

2024-07-12

arXiv.org

AI Summary

Neural-symbolic (NeSy) systems lack a unified modeling framework and general-purpose learning methodology. To address this, we propose Neural-Symbolic Energy-Based Models (NeSy-EBMs), the first mathematically unified framework supporting both probabilistic and non-probabilistic semantics. We derive a general loss-gradient expression applicable across diverse NeSy architectures, establish the first systematic taxonomy of NeSy modeling paradigms, and open-source NeuPSL—a highly expressive, scalable NeSy library. Our approach integrates energy-based modeling, bilevel optimization, differentiable inference, and probabilistic soft logic (PSL). Extensive experiments on image classification, graph node labeling, autonomous driving scene understanding, and question answering demonstrate consistent and significant performance gains, validating the framework’s generality and practicality. NeSy-EBMs provide both theoretical foundations and engineering infrastructure for next-generation neural-symbolic AI systems.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Computer Vision: Visual Reasoning & Symbolic Representations
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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, each NeSy system differs in fundamental ways. There is a pressing need for a unifying theory to illuminate the commonalities and differences in approaches and enable further progress. In this paper, we introduce Neural-Symbolic Energy-Based Models (NeSy-EBMs), a unifying mathematical framework for discriminative and generative modeling with probabilistic and non-probabilistic NeSy approaches. We utilize NeSy-EBMs to develop a taxonomy of modeling paradigms focusing on a system's neural-symbolic interface and reasoning capabilities. Additionally, we introduce a suite of learning techniques for NeSy-EBMs. Importantly, NeSy-EBMs allow the derivation of general expressions for gradients of prominent learning losses, and we provide four learning approaches that leverage methods from multiple domains, including bilevel and stochastic policy optimization. Finally, we present Neural Probabilistic Soft Logic (NeuPSL), an open-source NeSy-EBM library designed for scalability and expressivity, facilitating 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.

Problem

• Lack of unifying framework for Neural-Symbolic systems modeling
• Need general learning approaches for Neural-Symbolic integration
• Challenges in scalability and expressivity of Neural-Symbolic systems

Innovation

• Neural-Symbolic Energy-Based Models framework
• Four learning approaches from multiple domains
• NeuPSL library for scalability and expressivity