SymDiag: Explainable Diagnosis for LLM Reasoning via Neuro-Symbolic Verification

2026-08-09

AI Summary

This work addresses the unfaithfulness of reasoning chains in large language models (LLMs), a problem inadequately tackled by existing verification methods that lack interpretable error diagnosis. To this end, the authors propose SymDiag, a novel framework that translates natural language reasoning steps into symbolic constraints and leverages step-level satisfiability and logical entailment analysis to pinpoint errors while generating verifiable diagnostic evidence. SymDiag innovatively reframes reasoning verification as structured fault diagnosis and introduces a Self-Auditor mechanism to distinguish translation artifacts from genuine reasoning flaws. By integrating neuro-symbolic systems, formal verification, and counterexample generation, the approach substantially improves detection of unfaithful reasoning across multiple benchmarks, offering more precise and interpretable feedback than methods relying solely on final answers or LLM-based judgments, thereby enabling effective multi-turn reasoning repair.

Abstract

Large language models (LLMs) increasingly serve as data-driven reasoners, yet their chains-of-thought (CoT) can be unfaithful even when final answers are correct. Most existing ``verification'' signals are not diagnostic: answer matching observes only the outcome, LLM-as-judge provides subjective and non-verifiable critiques, and scalar rewards (e.g., PRMs/RMs) offer little insight into where a multi-step derivation fails.We propose \textbf{SymDiag}, a neuro-symbolic framework that \textbf{reframes reasoning verification as structured failure diagnosis}. SymDiag translates natural-language CoT into symbolic constraints and performs step-level satisfiability/entailment checks to (i) localize failing steps and (ii) produce verifiable diagnostic evidence, including counterexamples, inconsistency witnesses, and missing-premise indicators. A central challenge is that apparent ``logic violations'' can be caused either by genuine reasoning defects or by neural-to-symbolic translation noise. SymDiag therefore incorporates a Self-Auditor that disentangles TranslationError from ReasoningError via dual symbolic encodings consistency checks, enabling robust diagnosis under partial observability. Across diverse mathematical, logical, scientific, and general reasoning benchmarks, SymDiag improves detection of unfaithful reasoning and provides substantially more effective feedback for multi-round reasoning repair than outcome-only verification and LLM-based judging, offering a principled foundation for trustworthy and scalable reasoning diagnosis.

Problem

• unfaithful reasoning
• chain-of-thought verification
• reasoning diagnosis
• neuro-symbolic verification
• failure localization

Innovation

• neuro-symbolic verification
• chain-of-thought diagnosis
• symbolic reasoning
• failure localization
• self-auditor