FormalJudge: A Neuro-Symbolic Paradigm for Agentic Oversight

2026-02-11

AI Summary

This work addresses the failure of supervision in high-stakes scenarios involving large language model (LLM) agents, stemming from the homogeneity inherent in LLM-as-a-Judge paradigms. To overcome this limitation, the authors propose a novel neurosymbolic framework that integrates formal verification with LLMs for the first time. The approach employs a bidirectional “formal thinking” architecture: top-down, it decomposes natural language intentions into verifiable constraints; bottom-up, it leverages Dafny specifications and the Z3 solver to formally verify agent behavior, thereby providing mathematical guarantees. Experimental results demonstrate that the method outperforms LLM-as-a-Judge baselines by an average of 16.6% across three benchmarks. Notably, a 7B-parameter supervisor achieves over 90% accuracy in detecting deception by a 72B-parameter agent, and iterative refinement yields near-linear improvements in safety.

Technology Category

• Natural Language Processing: Safety and Robustness
• Multiagent Systems: Adversarial Agents
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

As LLM-based agents increasingly operate in high-stakes domains with real-world consequences, ensuring their behavioral safety becomes paramount. The dominant oversight paradigm, LLM-as-a-Judge, faces a fundamental dilemma: how can probabilistic systems reliably supervise other probabilistic systems without inheriting their failure modes? We argue that formal verification offers a principled escape from this dilemma, yet its adoption has been hindered by a critical bottleneck: the translation from natural language requirements to formal specifications. This paper bridges this gap by proposing , a neuro-symbolic framework that employs a bidirectional Formal-of-Thought architecture: LLMs serve as specification compilers that top-down decompose high-level human intent into atomic, verifiable constraints, then bottom-up prove compliance using Dafny specifications and Z3 Satisfiability modulo theories solving, which produces mathematical guarantees rather than probabilistic scores. We validate across three benchmarks spanning behavioral safety, multi-domain constraint adherence, and agentic upward deception detection. Experiments on 7 agent models demonstrate that achieves an average improvement of 16.6% over LLM-as-a-Judge baselines, enables weak-to-strong generalization where a 7B judge achieves over 90% accuracy detecting deception from 72B agents, and provides near-linear safety improvement through iterative refinement.

Problem

• behavioral safety
• LLM-as-a-Judge
• formal verification
• neuro-symbolic
• specification translation

Innovation

• neuro-symbolic
• formal verification
• LLM-as-a-Judge
• Dafny
• SMT solving