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Statistical Early Stopping for Reasoning Models

ICML 2026 · Large language models › Reasoning and chain of thought · approach: Efficient and adaptive thinking · 0 citations (OpenAlex)

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Proposes two statistically principled early-stopping rules (renewal-process sequential test and maxwise conformal stopping) that monitor uncertainty keyword arrivals in reasoning traces to halt overthinking on ill-posed math queries with FPR control.

Problem

Reasoning models overthink on ill-posed or ambiguous queries, wasting tokens; existing stopping methods (prompting, length, probing, logit entropy) lack false-positive guarantees, are brittle under distribution shift, or require internal activations.

Approach

Treat occurrences of interpretable uncertainty keywords in the reasoning trace as a point process; stop with a renewal-process sequential test (Sidák-corrected) or a conformal maxwise threshold on keyword density, giving FPR control using only calibration traces from well-posed queries and black-box-compatible text.

Key results

• Renewal and Maxwise reach average power of about 70% on GSM-MC, 71-73% on MiP, while keeping FPR at or below about 5% (Renewal FPR 3.75% on GSM-MC, 1.12% on MiP).
• Maxwise saves 63.30% of tokens on GSM-MC and 69.83% on MMLU-style ill-posed queries, versus 32.17% power for length-based stopping on GSM-MC.
• Keyword-based stopping recovers about 82-85% of an oracle classifier's detection power (regression slopes 0.8238 Renewal, 0.8532 Maxwise).

Surprising findings

• Length-based stopping and prompting baselines fail to give meaningful power; some models do not produce longer traces on ill-posed queries.
• Linear probing shows large FPR inflation (up to ~40%) under distribution shift on MiP and MMLU, while a single-component PLS reduces FPR there.

Limitations

• FPR guarantees rely on exchangeability, which is violated in practice; Renewal and Sidák corrections are approximations.
• Power is bounded by how much ill-posedness is expressed in the reasoning trace; UMWP traces often end before the first 250-token check.
• Keyword lexicon was built from four models and GSM8K-derived ill-posed queries, and evaluation uses the bin size B=250 chosen by the authors.

Experimental setup

Datasets: GSM8K AbstentionBench GSM8K subset GSM-MC UMWP MiP MMLU math subsets GPQA HLE

Benchmarks: GSM-MC UMWP MiP MMLU (math subsets) GPQA HLE

Metrics: false positive rate (early stop rate on well-posed) power (early stop rate on ill-posed) token savings accuracy drop

Baselines: Confidence dampening prompt Critical reasoning prompt Length-based stopping DEER Entropy-based stopping Linear probing

Builds on: conformal prediction renewal theory Sidák correction AbstentionBench DEER

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