Neuro-symbolic Learning Yielding Logical Constraints

TL;DR

This paper introduces a novel neuro-symbolic learning framework that integrates neural perception with logical reasoning, enabling end-to-end training through difference-of-convex programming and cardinality constraints, supported by theoretical and empirical validation.

Contribution

It presents a new framework that effectively combines neural networks and logical constraints in an end-to-end learning process using advanced optimization techniques.

Findings

Improved neural-symbolic interaction during training and inference.

Effective relaxation of logical constraints via difference-of-convex programming.

Empirical results demonstrate the framework's robustness and accuracy.

Abstract

Neuro-symbolic systems combine the abilities of neural perception and logical reasoning. However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This paper proposes a natural framework that fuses neural network training, symbol grounding, and logical constraint synthesis into a coherent and efficient end-to-end learning process. The capability of this framework comes from the improved interactions between the neural and the symbolic parts of the system in both the training and inference stages. Technically, to bridge the gap between the continuous neural network and the discrete logical constraint, we introduce a difference-of-convex programming technique to relax the logical constraints while maintaining their precision. We also employ cardinality constraints as the language for logical constraint learning and incorporate a trust region method to avoid the degeneracy of logical constraint in learning. Both theoretical analyses and empirical evaluations substantiate the effectiveness of the proposed framework.