VERGE: Formal Refinement and Guidance Engine for Verifiable LLM Reasoning

TL;DR

VERGE is a neurosymbolic framework that enhances LLM reasoning accuracy by combining formal verification, semantic routing, and iterative refinement to ensure logical correctness in high-stakes applications.

Contribution

It introduces a novel multi-model consensus, semantic routing, and precise error localization techniques to improve the logical reliability of LLM outputs.

Findings

Achieved an 18.7% performance uplift on reasoning benchmarks.

Successfully classifies claims by logical status and refines answers iteratively.

Combines LLMs with SMT solvers for verification-guided reasoning.

Abstract

Despite the syntactic fluency of Large Language Models (LLMs), ensuring their logical correctness in high-stakes domains remains a fundamental challenge. We present a neurosymbolic framework that combines LLMs with SMT solvers to produce verification-guided answers through iterative refinement. Our approach decomposes LLM outputs into atomic claims, autoformalizes them into first-order logic, and verifies their logical consistency using automated theorem proving. We introduce three key innovations: (1) multi-model consensus via formal semantic equivalence checking to ensure logic-level alignment between candidates, eliminating the syntactic bias of surface-form metrics, (2) semantic routing that directs different claim types to appropriate verification strategies: symbolic solvers for logical claims and LLM ensembles for commonsense reasoning, and (3) precise logical error localization via Minimal Correction Subsets (MCS), which pinpoint the exact subset of claims to revise, transforming binary failure signals into actionable feedback. Our framework classifies claims by their logical status and aggregates multiple verification signals into a unified score with variance-based penalty. The system iteratively refines answers using structured feedback until acceptance criteria are met or convergence is achieved. This hybrid approach delivers formal guarantees where possible and consensus verification elsewhere, advancing trustworthy AI. With the GPT-OSS-120B model, VERGE demonstrates an average performance uplift of 18.7% at convergence across a set of reasoning benchmarks compared to single-pass approaches.