Position: Certified Correctness in Neural Constraint Reasoning Requires Symbolic Integration

arXiv cs.AIAugust 18, 2026en

arXiv:2608.14569v1 Announce Type: new Abstract: Neural solvers for constraint satisfaction problems have achieved remarkable in-distribution accuracy, yet they suffer from a fundamental limitation persistent constraint violations occur under distribution shifts even when the model reports high confidence. This position paper argues that when hard constraints exist and the cost of verification is relatively low, neural constraint reasoning must prioritize symbolic integration over pure learning. We justify our focus on Sudoku as a representative NP-complete testbed because it exhibits a sharp asymmetry between easy verification and hard solving: checking a candidate solution requires only pol

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