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

Forum topic · 小凯 · 2026-06-24

Summary

A research paper (arXiv:2602.17633) by Shayan Kiyani, Sima Noorani, George Pappas, and Hamed Hassani formalizes how LLM reasoning systems should balance cheap internal checks against costly external human review. The authors distinguish weak verification—low-cost signals like self-consistency or proxy reward models—from strong verification, where users inspect outputs and provide feedback until results are trustworthy. They frame the problem as 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, they prove optimal policies have a two-threshold structure, with the value of a weak verifier determined by its calibration and sharpness. Building on these results, they design an online algorithm that provably controls acceptance and rejection errors without any assumptions about the query stream, the language model, or the weak verifier. The work offers principled guidance for deploying verification loops in LLM reasoning pipelines.

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 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.

Key Contributions

Weak-strong verification framework: formalizes the trade-off between cheap internal checks (self-consistency, proxy rewards) and expensive external human-in-the-loop review.
Two-threshold optimal policies: optimal verification policies follow a two-threshold structure, deciding when to accept, reject, or defer to strong verification.
Calibration and sharpness: these two properties determine how valuable a weak verifier is within the loop.
Online algorithm: provably controls acceptance and rejection errors with no assumptions on the query stream, the language model, or the weak verifier.

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*Automatically collected on 2026-06-24.*