Neuro-symbolic Learning Yielding Logical Constraints

• URL: http://arxiv.org/abs/2410.20957v1
• Date: Mon, 28 Oct 2024 12:18:25 GMT
• Title: Neuro-symbolic Learning Yielding Logical Constraints
• Authors: Zenan Li, Yunpeng Huang, Zhaoyu Li, Yuan Yao, Jingwei Xu, Taolue Chen, Xiaoxing Ma, Jian Lu,
• Abstract summary: end-to-end learning of neuro-symbolic systems is still an unsolved challenge. We propose a framework that fuses the network, symbol grounding, and logical constraint synthesisto-end learning process.
• Score: 22.649543443988712
• License:
• 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.

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