AFSAT GPU solver achieves near-linear throughput using JAX and DFT

Researchers have unveiled Accelerated Fourier SAT (AFSAT), a fully-engineered GPU-accelerated solver for pseudo-Boolean satisfiability problems. Building on the proof-of-concept FastFourierSAT, AFSAT uses continuous local search (CLS) and the JAX compiler to massively parallelize the search across batches of candidate assignments. The solver supports heterogeneous mixtures of symmetric constraint types and lengths within a single instance, a significant leap in flexibility. By exploiting JAX's pure function composition, automatic vectorization, automatic differentiation, and just-in-time (JIT) compilation, AFSAT achieves substantial improvements in runtime performance and memory efficiency compared to earlier implementations.

Key technical challenges addressed include memory latency and floating-point representation limitations. The team implemented a tailored discrete Fourier transform (DFT) to partially overcome these issues, enhancing numerical stability. AFSAT also leverages automatic parallelization and compact representations to reduce overhead. When scaling to multiple accelerators, the solver demonstrates near-linear throughput using JAX array sharding, making it viable for large-scale SAT problems. The paper (arXiv:2606.06641) is co-authored by Cody J Christopher and Charles Gretton, and published under cs.AI. This work could accelerate research in areas like circuit design, automated reasoning, and combinatorial optimization where SAT solving is critical.