AI 中文总结
本文针对神经约束推理在分布偏移下易出现约束违反的问题，提出需优先将神经方法与符号方法双向集成，通过多智能体认证推理框架实现计算效率与可证正确性。
AI 中文摘要
约束满足问题的神经求解器已在分布内准确率上取得显著成果，但存在一个根本局限：即使模型报告高置信度，在分布偏移下仍会持续出现约束违反。本文立场文件指出，当存在硬约束且验证成本较低时，神经约束推理必须优先考虑符号集成而非纯学习。我们选择数独作为代表性NP完全测试床来论证这一重点，因为它呈现出易验证与难求解之间的显著不对称性：检查候选解仅需多项式时间O(n²)，而寻找解可能需要指数级搜索。通过对确定性算法、元启发式优化、基于学习的方法及语言条件推理等求解方法的全面调研，我们证明仅神经方法若缺乏实例级认证，无法达到符号方法与神经-符号方法所具备的可证正确性。我们倡导双向集成：神经方法通过学习启发式并将感知转化为符号来增强符号求解器，同时符号方法验证神经输出以确保其可靠性。为将该立场付诸实践，我们提出了多智能体认证推理框架，展示这种集成如何同时实现计算效率与可证正确性。
英文摘要
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 polynomial time $O(n^{2})$, while finding a solution may require exponential search. Through a comprehensive survey of solving methods spanning deterministic algorithms, metaheuristic optimization, learning-based approaches, and language-conditioned reasoning, we demonstrate that neural-only methods without instance-level certification fail to achieve the provable correctness that symbolic and neuro-symbolic approaches provide. We advocate for a bidirectional integration in which neural methods enhance symbolic solvers by learning heuristics and converting percepts into symbols, while symbolic methods verify neural outputs to ensure their reliability. To operationalize this position, we propose a multi-agent certified reasoning framework that demonstrates how this integration can achieve both computational efficiency and provable correctness.
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