CPUNeSy: Controlling Model Writes for Reliable Neuro-Symbolic Reasoning

Large language models are highly effective at recalling statistical patterns, but their accuracy degrades sharply when answers must be derived rather than recalled, especially on deep multi-hop chains. Delegating derivation to deterministic symbolic executors shifts the reliability question to whether model-generated premises are supported by the source. We introduce CPUNeSy (Certified Predicate-Unit Neuro-Symbolic Networks), a serving architecture that controls model writes to symbolic state through a task-defined predicate interface and a certificate gate, and abstains when grounding passes disagree. A component analysis separates deterministic execution from restricted grounding, agreement, and source rechecking. Our experiments show that deterministic execution accounts for most of the accuracy recovery on derivation-heavy tasks, whereas controlled writes primarily improve selective reliability by withholding unsupported or inconsistent answers at the cost of coverage. On controlled multi-hop stress tests in law and formal mathematics, deterministic execution recovers most of the accuracy gap over chain-of-thought and retrieval baselines, with full-pool gains up to 35.0 points. Certification behaves as a selective-serving control rather than an accuracy mechanism: with grounding traces held fixed on ContractNLI, source rechecking removes a quarter of DeepSeek's wrong answers that survive two-vote agreement, at a measurable coverage cost. When abstention is expensive, routing withheld cases to an explicitly uncertified same-model fallback raises full-pool accuracy on MedCalc-Bench Verified by $13.9$ and $4.9$ points for Seed and DeepSeek; these gains do not belong to the certified serving channel. On LeanDojo Benchmark, kernel-restricted pools match BM25 recall@$15$ ($89.3\%$). Gains depend on the grounding model's error regime: bias-dominated grounders benefit less, consistent with the voting bound we state formally. The resulting certificates guarantee derivational validity relative to admitted premises; semantic faithfulness to natural-language sources remains conditional on the source checker, and prospective validation of the deployment protocol is future work.