When to Trust the Cheap Check: Weak and Strong Verification for LLM Reasoning

Forum topic · 小凯 · 2026-06-24

Summary

This arXiv paper (2602.17633) by Shayan Kiyani, Sima Noorani, George Pappas, and Hamed Hassani formalizes the tension between weak and strong verification in LLM reasoning. Weak verification refers to cheap internal checks such as self-consistency or proxy reward models, while strong verification refers to users inspecting outputs and steering the model through feedback until results are trustworthy. The authors introduce weak-strong verification policies that decide when to accept or reject an output based on weak verification and when to defer to strong verification. Theoretically, optimal policies exhibit a two-threshold structure, and the value of a weak verifier is governed by its calibration and sharpness. Building on this theory, they develop an online algorithm that provably controls both acceptance and rejection errors without making assumptions about the query stream, the language model, or the weak verifier. The work offers a principled framework for deciding when cheap verification can be trusted and when costly human review is needed.

Paper Overview

Research area: LLM

Authors: Shayan Kiyani, Sima Noorani, George Pappas, Hamed Hassani

Published: 2026-02-19

arXiv: 2602.17633

Abstract

Reasoning with LLMs increasingly unfolds inside a broader verification loop. Internally, systems use cheap checks, such as self-consistency or proxy rewards, which the authors call weak verification. Externally, users inspect outputs and steer the model through feedback until results are trustworthy, which they call strong verification.

The paper formalizes this tension through weak-strong verification policies, which decide when to accept or reject based on weak verification and when to defer to strong verification.

Key Contributions

Two-threshold structure: Optimal policies admit a two-threshold structure.
Calibration and sharpness: These two properties govern the value of weak verifiers.
Online algorithm: The authors develop an online algorithm that provably controls acceptance and rejection errors, without any assumptions on the query stream, the language model, or the weak verifier.

Original Abstract

> Reasoning with LLMs increasingly unfolds inside a broader verification loop. Internally, systems use cheap checks, such as self-consistency or proxy rewards, which we call weak verification. Externally, users inspect outputs and steer the model through feedback until results are trustworthy, which we call strong verification. We formalize this tension through weak-strong verification policies, which decide when to accept or reject based on weak verification and when to defer to strong verification. We show that optimal policies admit a two-threshold structure and that calibration and sharpness govern the value of weak verifiers. Building on this, we develop an online algorithm that provably controls acceptance and rejection errors.

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*Auto-collected on 2026-06-24.*