High-Throughput SAT Sampling

2025-02-12

AI Summary

To address the low throughput and poor parallelizability of Boolean satisfiability (SAT) sampling on GPUs, this work pioneers a differentiable, supervised regression formulation of SAT sampling based on multi-level, multi-output Boolean circuits. Our method leverages CNF reconstruction, logic synthesis, and gradient-driven optimization to enable tensorized, bit-level parallel computation. It supports end-to-end GPU-accelerated training and inference, achieving 33.6×–523.6× speedup over state-of-the-art heuristic samplers across 60 standard benchmarks—significantly breaking traditional SAT sampling throughput bottlenecks. Key contributions include: (1) a circuit-structure-guided differentiable modeling framework; (2) joint optimization of fine-grained bit-level parallelism and solution diversity; and (3) the first efficient, GPU-native solving paradigm specifically designed for SAT sampling.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Hardware-aware ML

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• 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

Abstract

In this work, we present a novel technique for GPU-accelerated Boolean satisfiability (SAT) sampling. Unlike conventional sampling algorithms that directly operate on conjunctive normal form (CNF), our method transforms the logical constraints of SAT problems by factoring their CNF representations into simplified multi-level, multi-output Boolean functions. It then leverages gradient-based optimization to guide the search for a diverse set of valid solutions. Our method operates directly on the circuit structure of refactored SAT instances, reinterpreting the SAT problem as a supervised multi-output regression task. This differentiable technique enables independent bit-wise operations on each tensor element, allowing parallel execution of learning processes. As a result, we achieve GPU-accelerated sampling with significant runtime improvements ranging from $33.6 imes$ to $523.6 imes$ over state-of-the-art heuristic samplers. We demonstrate the superior performance of our sampling method through an extensive evaluation on $60$ instances from a public domain benchmark suite utilized in previous studies.

Problem

• GPU-accelerated SAT sampling
• CNF transformation optimization
• Diverse valid solutions search

Innovation

• GPU-accelerated SAT sampling
• Multi-level Boolean functions transformation
• Gradient-based optimization for diverse solutions