# When to Trust the Cheap Check: Weak and Strong Verification for Reasoning Source: [When to Trust the Cheap Check: Weak and Strong Verification for Reasoning]() Collection index: [llms.txt]() Data updated: 2026-02-21T05:00:09.597Z Authors: Shayan Kiyani, Sima Noorani, George Pappas, Hamed Hassani Published: 2026-02-19T18:47:38.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Sequential puzzle-solving on Sudoku](): Sequential puzzle-solving; Sudoku; Accuracy: 43.1. ## Original sources and implementation [Original paper]() [PDF]()