Neuro-symbolic PRM: Enhancing Scientific Reasoning via Structured Traces and Symbolic Verification

2026-08-26

AI Summary

论文提出神经符号框架，通过分离符号有效性和语义基础性，利用符号验证器和过程奖励模型解决工具增强大语言模型在STEM任务中的多步推理问题。

Abstract

While tool-augmented Large Language Models have significantly improved multi-step reasoning in quantitative STEM tasks, a critical residual failure mode remains: intermediate reasoning steps that are syntactically well-formed, mathematically executable, and unit-consistent, yet contextually ungrounded. Current approaches either rely on formal verifiers that cannot assess semantic intent, or burden Process Reward Models (PRMs) with the dual task of checking both arithmetic and logic. In this paper, we propose a neuro-symbolic framework that cleanly decouples reasoning into two formal dimensions: Symbolic Validity ($V$) and Semantic Groundedness ($G$). We guarantee $V$ by construction using a deterministic symbolic verifier acting as a hard filter. To assess $G$, we train a PRM conditionally on the verifier-accepted manifold. To train this PRM efficiently, we introduce Counterfactual Symbolic Perturbation (CSP), a novel data synthesis strategy that algorithmically generates constraint-preserving hard negatives (steps that perfectly pass the verifier but are logically flawed). At inference, we deploy a verifier-first constrained search that guarantees execution consistency for verifier-covered operations while relying on the PRM solely to rank semantic grounding. By targeting the exact residual error class of strong tool-using LLMs, our method significantly improves reasoning reliability without the sprawling heuristics of prior frameworks.

Problem

• Large Language Models
• STEM tasks
• multi-step reasoning
• contextual grounding
• Symbolic Verification

Innovation

• neuro-symbolic framework
• symbolic validity
• semantic groundedness
• counterfactual symbolic perturbation
• process reward model