Verify, Repair, Repeat, or Stop? Robust Stopping for Noisy Verify-Repair Loops in LLM Agents

2026-07-20

AI Summary

This work addresses the challenges in the verification–repair loop of large language model (LLM) agents, where noisy verifiers and repairers may corrupt correct solutions and reliable termination mechanisms are lacking. The authors propose the VRR-Stop framework, which employs a four-parameter noise model to distinguish between misjudgments and destructive repairs, integrates belief filtering to estimate the true validity of candidate solutions, and terminates the loop based on the sign of marginal gain. Innovatively framing termination as a sign-identifiable problem, VRR-Stop avoids the need for precise estimation of all noise parameters and incorporates an estimation-free VRR-Guard as a safety fallback. On the GSM8K stress test, VRR-Stop improves true solution validity by 60.6 percentage points over fixed five-round repair while adding only 0.72 rounds on average, with stopping reliability ensured jointly by verifier discriminability and decision margin.

Abstract

Verify-repair loops are a standard means for large language model (LLM) agents to correct faulty plans in code generation, mathematical reasoning, and tool use. When both the verifier and the repairer are noisy, repair can damage already-correct plans, and reported acceptance keeps rising while true validity falls, so existing methods lack a principled basis for deciding when repair should stop. We propose VRR-Stop, a robust stopping framework for noisy verify-repair-repeat (VRR) loops. A four-parameter noise model separates verifier false acceptance and false rejection from the repair and damage behavior of the repairer. Belief filtering turns repeated verification votes into an estimate of committed validity, and the loop commits or repairs according to the sign of the true marginal gain, which requires only sign identifiability rather than accurate recovery of all parameters. When verifier discrimination approaches zero, calibration itself fails and estimation error can flip the stopping sign, so we pair VRR-Stop with VRR-Guard, an estimation-free fallback that replaces the incumbent candidate only under a sufficient verification margin. On a GSM8K stress setting, VRR-Stop improves final true validity by 60.6 percentage points over fixed five-round repair at an average cost of 0.72 repair rounds. Across settings, stopping reliability is governed jointly by verifier discrimination and the decision margin rather than by the absolute size of estimation error.

Problem

• verify-repair loops
• noisy verification
• stopping criterion
• LLM agents
• true validity

Innovation

• verify-repair loop
• robust stopping
• noise modeling
• belief filtering
• marginal gain