Advancing Weighted Partial MaxSAT Solving via Differentiable GPU Guidance

arXiv:2611.15091v1 Announce Type: new Abstract: We present a GPU-CPU hybrid framework for Weighted Partial MaxSAT (WPMAX-SAT) that complements state-of-the-art CPU solvers with differentiable GPU optimization. The GPU stage directly optimizes instance-specific categorical decision parameters without a training dataset or a pretrained predictive model. The central challenge in extending differentiable optimization to WPMAX-SAT is the hard/soft clause asymmetry: hard clauses represent inviolable feasibility constraints while soft clauses carry weights. We introduce a hierarchical differentiable loss that prioritizes hard clause satisfaction before optimizing the weighted soft objective, ensuring that GPU gradient descent leans towards the constraint structure of WPMAX-SAT.