产生逻辑约束的神经符号学习
Neuro-symbolic Learning Yielding Logical Constraints
AI总结：
针对神经符号系统难以端到端学习的问题，提出融合神经网络训练、符号接地与逻辑约束综合的框架，通过凸差分规划、基数约束和信赖域方法实现精确高效学习。
摘要：
神经符号系统结合了神经感知与逻辑推理的能力。然而，神经符号系统的端到端学习仍是一个尚未解决的挑战。本文提出了一个自然框架，将神经网络训练、符号接地和逻辑约束综合融合为一个连贯且高效的端到端学习过程。该框架的能力源于系统在训练和推理阶段中神经部分与符号部分之间改进的交互。从技术上讲，为弥合连续神经网络与离散逻辑约束之间的鸿沟，我们引入了一种凸差分规划技术来松弛逻辑约束，同时保持其精确性。我们还采用基数约束作为逻辑约束学习的语言，并结合信赖域方法以避免学习过程中逻辑约束的退化。理论分析和实证评估均证实了所提框架的有效性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
