arXiv:2603.28796v1 Announce Type: cross Abstract: Boolean satisfiability (SAT) problem, the first problem proven to be NP-complete, has become a fundamental challenge in computational complexity, with widespread applications in optimization and verification across many domains. Despite significant algorithmic advances over the past two decades, the performance of SAT solvers has improved at a limited pace. Notably, the 2025 competition winner shows only about a 2X improvement over the 2006 winner in SAT Competition performance after nearly 20 years of effort. This paper introduces GaloisSAT, a novel hybrid GPU-CPU SAT solver that integrates a differentiable SAT solving engine powered by modern machine learning infrastructure on GPUs, followed by a traditional CDCL-based SAT solving stage on CPUs. GaloisSAT is benchmarked against the latest versions of state-of-the-art solvers, Kissat and CaDiCaL, using the SAT Competition 2024 benchmark suite. Results demonstrate substantial improvements in the official SAT Competition metric PAR-2 (penalized average runtime with a timeout of 5,000 seconds and a penalty factor of 2). Specifically, GaloisSAT achieves an 8.41X speedup in the satisfiable category and a 1.29X speedup in the unsatisfiable category compared to the strongest baselines.

arXiv:2602.19027v1 Announce Type: cross Abstract: Inverse lithography (ILT) is critical for modern semiconductor manufacturing but suffers from highly non-convex objectives that often trap optimization in poor local minima. Generative AI has been explored to warm-start ILT, yet most approaches train deterministic image-to-image translators to mimic sub-optimal datasets, providing limited guidance for escaping non-convex traps during refinement. We reformulate mask synthesis as conditional sampling: a generator learns a distribution over masks conditioned on the design and proposes multiple candidates. The generator is first pretrained with WGAN plus a reconstruction loss, then fine-tuned using Group Relative Policy Optimization (GRPO) with an ILT-guided imitation loss. At inference, we sample a small batch of masks, run fast batched ILT refinement, evaluate lithography metrics (e.g., EPE, process window), and select the best candidate. On \texttt{LithoBench} dataset, the proposed hybrid framework reduces EPE violations under a 3\,nm tolerance and roughly doubles throughput versus a strong numerical ILT baseline, while improving final mask quality. We also present over 20\% EPE improvement on \texttt{ICCAD13} contest cases with 3$\times$ speedup over the SOTA numerical ILT solver. By learning to propose ILT-friendly initializations, our approach mitigates non-convexity and advances beyond what traditional solvers or GenAI can achieve.