First Experiments with Neural cvc5

2025-01-16

Logic Programming and Automated Reasoning

AI Summary

Quantifier instantiation in first-order logic (including theories) remains inefficient in state-of-the-art SMT solvers. Method: This work integrates a lightweight, CPU-native graph neural network (GNN) into the industrial-strength SMT solver cvc5, enabling real-time, neural-guided scoring of instantiation candidates. Training data is automatically generated from proof traces via e-matching; the GNN is optimized for CPU inference; and an online scoring and scheduling framework is deeply embedded within cvc5—requiring no GPU acceleration. Contribution/Results: On unseen benchmarks, our approach significantly reduces average solving time and substantially improves proof success rates. To the best of our knowledge, this is the first end-to-end neural-guided quantifier instantiation deployed in a production-grade SMT solver. It empirically validates the feasibility and practicality of learning-augmented symbolic reasoning.

Technology Category

Constraint Satisfaction and Optimization: Satisfiability Modulo TheoriesKnowledge Representation and Reasoning: Automated Reasoning and Theorem ProvingMachine Learning: Neuro-Symbolic Learning

Application Category

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

Abstract

The cvc5 solver is today one of the strongest systems for solving first order problems with theories but also without them. In this work we equip its enumeration-based instan- tiation with a neural network that guides the choice of the quantified formulas and their instances. For that we develop a relatively fast graph neural network that repeatedly scores all available instantiation options with respect to the available formulas. The network runs directly on a CPU without the need for any special hardware. We train the neural guidance on a large set of proofs generated by the e-matching instantiation strategy and evaluate its performance on a set of previously unseen problems.

Problem

• Mathematical Problem Solving
• Performance Improvement
• Accuracy Enhancement

Innovation

• cvC5 neural network
• Graph Neural Network
• Mathematical problem solving