VERGE: Formal Refinement and Guidance Engine for Verifiable LLM Reasoning
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.
697baf7ea67238fac88cbf0d
Vikash Singh
claimed_verified
2026-01-29T21:15:21.775Z
6702352c547acbd64cddf31e
https://cdn-avatars.huggingface.co/v1/production/uploads/6702352c547acbd64cddf31e/elkGeA8piG-K-mXspBOhi.png
Vikash Singh
optimusPrimeBee
user
optimusPrimeBee
697baf7ea67238fac88cbf0e
Darion Cassel
697baf7ea67238fac88cbf0f
Nathaniel Weir
697baf7ea67238fac88cbf10
Nick Feng
697baf7ea67238fac88cbf11
Sam Bayless
VERGE: Formal Refinement and Guidance Engine for Verifiable LLM Reasoning
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.
A neurosymbolic framework integrates large language models with SMT solvers to enhance logical correctness through verification-guided iterative refinement, utilizing formal semantic equivalence checking, semantic routing, and minimal correction subsets for precise error localization and consensus verification.
Large Language Models SMT solvers verification-guided answers iterative refinement atomic claims first-order logic automated theorem proving formal semantic equivalence checking semantic routing symbolic solvers LLM ensembles commonsense reasoning Minimal Correction Subsets logical error localization structured feedback convergence formal guarantees consensus verification