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--> [Submitted on 2 Jun 2026] Title:Position: Certified Correctness in Neural Constraint Reasoning Requires Symbolic Integration View a PDF of the paper titled Position: Certified Correctness in Neural Constraint Reasoning Requires Symbolic Integration, by Shufeng Kong and Xiaochuan Zhang and Caihua Liu View PDF HTML (experimental) 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 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. Comments: Accept by ICML 2026 Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2608.14569 [cs.AI] (or arXiv:2608.14569v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2608.14569 arXiv-issued DOI via DataCite Submission history From: Shufeng Kong [view email] [v1] Tue, 2 Jun 2026 04:06:31 UTC (989 KB) Full-text links: Access Paper: View a PDF of the paper titled Position: Certified Correctness in Neural Constraint Reasoning Requires Symbolic Integration, by Shufeng Kong and Xiaochuan Zhang and Caihua Liu View PDF HTML (experimental) TeX Source view license Current browse context: cs.AI new | recent | 2026-08 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)