Learning with Logical Constraints but without Shortcut Satisfaction
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911787138416640 |
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| author | Li, Zenan Liu, Zehua Yao, Yuan Xu, Jingwei Chen, Taolue Ma, Xiaoxing Lü, Jian |
| author_facet | Li, Zenan Liu, Zehua Yao, Yuan Xu, Jingwei Chen, Taolue Ma, Xiaoxing Lü, Jian |
| contents | Recent studies in neuro-symbolic learning have explored the integration of logical knowledge into deep learning via encoding logical constraints as an additional loss function. However, existing approaches tend to vacuously satisfy logical constraints through shortcuts, failing to fully exploit the knowledge. In this paper, we present a new framework for learning with logical constraints. Specifically, we address the shortcut satisfaction issue by introducing dual variables for logical connectives, encoding how the constraint is satisfied. We further propose a variational framework where the encoded logical constraint is expressed as a distributional loss that is compatible with the model's original training loss. The theoretical analysis shows that the proposed approach bears salient properties, and the experimental evaluations demonstrate its superior performance in both model generalizability and constraint satisfaction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning with Logical Constraints but without Shortcut Satisfaction Li, Zenan Liu, Zehua Yao, Yuan Xu, Jingwei Chen, Taolue Ma, Xiaoxing Lü, Jian Artificial Intelligence Machine Learning Recent studies in neuro-symbolic learning have explored the integration of logical knowledge into deep learning via encoding logical constraints as an additional loss function. However, existing approaches tend to vacuously satisfy logical constraints through shortcuts, failing to fully exploit the knowledge. In this paper, we present a new framework for learning with logical constraints. Specifically, we address the shortcut satisfaction issue by introducing dual variables for logical connectives, encoding how the constraint is satisfied. We further propose a variational framework where the encoded logical constraint is expressed as a distributional loss that is compatible with the model's original training loss. The theoretical analysis shows that the proposed approach bears salient properties, and the experimental evaluations demonstrate its superior performance in both model generalizability and constraint satisfaction. |
| title | Learning with Logical Constraints but without Shortcut Satisfaction |
| topic | Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2403.00329 |