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arXiv · 2309.15458

LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints

Weidi Xu·Jingwei Wang·Lele Xie·Jianshan He·Hongting Zhou·Taifeng Wang·Xiaopei Wan·Jingdong Chen·Chao Qu·Wei Chu
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Abstract

Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP, whose layers perform mean-field variational inference over an MLN. It can be plugged into any off-the-shelf neural network to encode FOLCs while retaining modularity and efficiency. By exploiting the structure and symmetries in MLNs, we theoretically demonstrate that our well-designed, efficient mean-field iterations effectively mitigate the difficulty of MLN inference, reducing the inference from sequential calculation to a series of parallel tensor operations. Empirical results in three kinds of tasks over graphs, images, and text show that LogicMP outperforms advanced competitors in both performance and efficiency.

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Weidi Xu, Jingwei Wang, Lele Xie, Jianshan He, Hongting Zhou, Taifeng Wang, Xiaopei Wan, Jingdong Chen, Chao Qu, Wei Chu. 2023-09-27. LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints. https://arxiv.org/abs/2309.15458

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