LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints
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arXiv
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| Main Authors: | , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911198776131584 |
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| author | Xu, Weidi Wang, Jingwei Xie, Lele He, Jianshan Zhou, Hongting Wang, Taifeng Wan, Xiaopei Chen, Jingdong Qu, Chao Chu, Wei |
| author_facet | Xu, Weidi Wang, Jingwei Xie, Lele He, Jianshan Zhou, Hongting Wang, Taifeng Wan, Xiaopei Chen, Jingdong Qu, Chao Chu, Wei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15458 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints Xu, Weidi Wang, Jingwei Xie, Lele He, Jianshan Zhou, Hongting Wang, Taifeng Wan, Xiaopei Chen, Jingdong Qu, Chao Chu, Wei Artificial Intelligence Symbolic Computation 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. |
| title | LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints |
| topic | Artificial Intelligence Symbolic Computation |
| url | https://arxiv.org/abs/2309.15458 |