Neuro-symbolic Learning Yielding Logical Constraints
This work addresses the unsolved problem of end-to-end learning for researchers in neuro-symbolic AI, though it appears incremental as it builds on existing methods with technical improvements.
The paper tackles the challenge of end-to-end learning in neuro-symbolic systems by proposing a framework that integrates neural network training, symbol grounding, and logical constraint synthesis, achieving effectiveness as supported by theoretical and empirical evaluations.
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.