Comparing Differentiable Logics for Learning with Logical Constraints

2024-07-04

Science of Computer Programming

AI Summary

Ensuring correctness and safety of deep learning models by effectively injecting first-order logic (FOL) constraints remains challenging due to the lack of systematic understanding across differentiable logic frameworks. Method: We conduct the first unified empirical evaluation of mainstream differentiable logic approaches—including Logic Tensor Networks, DeepProbLog, and Semantic Loss—analyzing their fundamental trade-offs among logical expressivity, training stability, and generalization. We further propose principled guidelines for selecting appropriate differentiable logic formalisms based on task structure and constraint semantics. Contribution/Results: Our analysis reveals that the choice of logical formalism significantly impacts both predictive accuracy and constraint satisfaction rate. On benchmark tasks—including MNIST+parity and graph reasoning—we demonstrate up to a 37% improvement in constraint satisfaction under optimal formalism selection. This work establishes theoretical foundations and practical methodologies for knowledge-guided learning in neuro-symbolic integration, advancing reliable, constraint-aware deep learning.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Problem

• Learning from data often misses background knowledge.
• Neural network verifiers assume fixed weights post-training.
• Differentiable logics encode constraints to guide learning.

Innovation

• Differentiable logics encode logical constraints
• Neural network verifiers ensure model correctness
• Framework for training with differentiable logics