Paper
When to Trust the Cheap Check: Weak and Strong Verification for Reasoning
Authors
Shayan Kiyani, Sima Noorani, George Pappas, Hamed Hassani
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. These signals differ sharply in cost and reliability: strong verification can establish trust but is resource-intensive, while weak verification is fast and scalable but noisy and imperfect. 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 introduce metrics capturing incorrect acceptance, incorrect rejection, and strong-verification frequency. Over population, 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 without assumptions on the query stream, the language model, or the weak verifier.
Metadata
Related papers
Vibe Coding XR: Accelerating AI + XR Prototyping with XR Blocks and Gemini
Ruofei Du, Benjamin Hersh, David Li, Nels Numan, Xun Qian, Yanhe Chen, Zhongy... • 2026-03-25
Comparing Developer and LLM Biases in Code Evaluation
Aditya Mittal, Ryan Shar, Zichu Wu, Shyam Agarwal, Tongshuang Wu, Chris Donah... • 2026-03-25
The Stochastic Gap: A Markovian Framework for Pre-Deployment Reliability and Oversight-Cost Auditing in Agentic Artificial Intelligence
Biplab Pal, Santanu Bhattacharya • 2026-03-25
Retrieval Improvements Do Not Guarantee Better Answers: A Study of RAG for AI Policy QA
Saahil Mathur, Ryan David Rittner, Vedant Ajit Thakur, Daniel Stuart Schiff, ... • 2026-03-25
MARCH: Multi-Agent Reinforced Self-Check for LLM Hallucination
Zhuo Li, Yupeng Zhang, Pengyu Cheng, Jiajun Song, Mengyu Zhou, Hao Li, Shujie... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.17633v1</id>\n <title>When to Trust the Cheap Check: Weak and Strong Verification for Reasoning</title>\n <updated>2026-02-19T18:47:38Z</updated>\n <link href='https://arxiv.org/abs/2602.17633v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.17633v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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. These signals differ sharply in cost and reliability: strong verification can establish trust but is resource-intensive, while weak verification is fast and scalable but noisy and imperfect. 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 introduce metrics capturing incorrect acceptance, incorrect rejection, and strong-verification frequency. Over population, 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 without assumptions on the query stream, the language model, or the weak verifier.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n <category scheme='http://arxiv.org/schemas/atom' term='stat.ML'/>\n <published>2026-02-19T18:47:38Z</published>\n <arxiv:primary_category term='cs.LG'/>\n <author>\n <name>Shayan Kiyani</name>\n </author>\n <author>\n <name>Sima Noorani</name>\n </author>\n <author>\n <name>George Pappas</name>\n </author>\n <author>\n <name>Hamed Hassani</name>\n </author>\n </entry>"
}