Differentiable Logic Programming for Distant Supervision
Akihiro Takemura, Katsumi Inoue
TL;DR
This work presents a differentiable logic-programming framework for neural-symbolic AI that enables learning under distant supervision without relying on symbolic solvers. It embeds normal logic programs into matrix form (program matrix $\boldsymbol{Q}$ and head matrix $\boldsymbol{D}$) and evaluates both rules and constraints in a differentiable vector space using a distance-based criterion, facilitating gradient-based learning. The MNIST Addition illustration shows how neural predicates interoperate with logical rules via continuous interpretations and BCE losses, yielding competitive accuracy and significantly faster training in several tasks. The approach integrates loop formulas and stable-model semantics in vector spaces, offering a scalable alternative to solver-based neuro-symbolic methods and highlighting future directions toward fuzzy-valued interpretations and broader NeSy tasks.
Abstract
We introduce a new method for integrating neural networks with logic programming in Neural-Symbolic AI (NeSy), aimed at learning with distant supervision, in which direct labels are unavailable. Unlike prior methods, our approach does not depend on symbolic solvers for reasoning about missing labels. Instead, it evaluates logical implications and constraints in a differentiable manner by embedding both neural network outputs and logic programs into matrices. This method facilitates more efficient learning under distant supervision. We evaluated our approach against existing methods while maintaining a constant volume of training data. The findings indicate that our method not only matches or exceeds the accuracy of other methods across various tasks but also speeds up the learning process. These results highlight the potential of our approach to enhance both accuracy and learning efficiency in NeSy applications.