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REVIEW 4 major objections 5 minor 19 cited by

Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read For a fixed question, accuracy rises with reasoning length up to a point, then falls; models overthink easy problems, underthink hard ones, and length-only preference optimization cuts output by 30–60%.

desk verdict A useful empirical study whose headline fixed-question non-monotonicity claim is not supported by the aggregate curve, but whose length-only preference optimization experiment is solid and deserves a serious referee. read the letter →

arxiv 2505.00127 v1 pith:Q35CKXYE submitted 2025-04-30 cs.CL cs.AI

Jinyan Su , Jennifer Healey , Preslav Nakov , Claire Cardie This is my paper · ORCID
classification cs.CLcs.AI
keywords reasoninglengthoverthinkingunderthinkingpreferenceoptimizationSimPOchain-of-thoughtmathlength-accuracytradeoff
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether more reasoning tokens always make a language model more accurate, and answers no. Across two math benchmarks and two small reasoning models, accuracy first rises as responses get longer, then falls once reasoning becomes excessively long. The authors interpret the rise-and-fall as two failure modes: models overthink easy problems they can solve quickly, and underthink hard problems they cannot solve, apparently misjudging difficulty. They also show that preference-tuning a model to prefer shorter responses—with no correctness labels—reduces generation length by roughly 30–60% while keeping accuracy at an acceptable level. If the findings hold, length itself is a useful control knob for reasoning efficiency.

What carries the argument

The central tool is a length-ranking construction: for each question, ten sampled responses are sorted by token length, and average length and accuracy are computed at each rank, isolating the effect of length from question difficulty. At the question level, the machinery is a cross-model difficulty partition into shared-easy and shared-hard sets plus model-specific advantage sets, compared with t-tests; this separates 'the model sees difficulty and adapts' from 'the model fails to recognize difficulty.' The optimization machinery is SimPO, a reference-free preference optimization algorithm that uses average sequence log-probability as an implicit reward, applied here to preference pairs that prefer shorter responses without checking correctness.

What would settle it

Truncate long responses on solvable questions to the median length of correct responses; if accuracy does not fall, extra reasoning is not the cause of the decline. Conversely, force additional reasoning steps on hard questions that currently get short wrong answers; if accuracy does not rise, those failures are not caused by insufficient thinking.

Watch

Extended reading notes

Core claim

At the sample level, when a single question is answered multiple times, accuracy is non-monotonic in response length: the shortest response is often already correct, accuracy peaks early, and the longest samples are less accurate. At the question level, incorrect answers are on average far longer than correct ones—on the harder benchmark, more than twice as long—and length correlates negatively with accuracy. The authors partition questions into easy, medium, and hard by a model's own consistency, and use cross-model comparisons to show that models detect small difficulty increases on questions they can solve, generating longer responses, but on questions beyond their ability they often produce shorter-than-needed responses, a pattern they call underthinking. Finally, using preference optimization that always prefers the shorter of two unlabeled responses, they cut average generation length by roughly 30–60% with only mild accuracy loss, with most of the reduction coming from incorrect responses.

Load-bearing premise

The interpretation that short incorrect answers are 'underthinking' assumes the model's response length tracks its perceived difficulty of the question, an assumption the paper does not directly test and whose alternative—longer responses themselves introducing errors—it explicitly acknowledges.

Editorial extensions

If this is right

  • For a fixed question, accuracy peaks at an interior response length, so both minimal and maximal reasoning are risky; a token-budget-aware sampler that avoids the longest chains should match or beat unconstrained sampling.
  • Because over 60% of questions are solved by the shortest sampled response when they are solvable at all, much of the compute spent generating long chains is wasted.
  • Preference optimization with only length preferences, and no ground-truth correctness, reduces generation length by 30–60% while keeping accuracy in an acceptable range; most savings come from shortening incorrect responses, but correct responses also shrink by 10–25%.
  • Length reduction does not require labeled preference pairs, so unlabeled corpora can be used to make reasoning models cheaper at inference time.
  • Incorrect responses are markedly longer than correct ones and correlate negatively with accuracy, making length a usable signal for detecting likely-failed reasoning.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A length-aware self-consistency vote that discards the longest samples could improve accuracy and cut cost; the paper only notes this direction as motivation.
  • The peaked length–accuracy curve implies a model- and dataset-specific optimal length; an unlabeled-data controller that predicts the plateau would be a natural next step beyond the paper's experiments.
  • Because length diverges from perceived difficulty mainly on questions beyond a model's ability, calibration or perplexity outliers might flag when self-correction is unlikely to help—a connection the paper raises but does not test.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper empirically studies how reasoning length relates to answer correctness for two 1.5B reasoning models, DeepSeek-R1-Distill and DeepScaler-R1-Preview, on GSM8K and MATH. For each question it samples N=10 responses, ranks them by length, and analyzes the averaged accuracy at each length rank. The authors claim three main findings: (1) for a fixed question, accuracy is non-monotonic in reasoning length, rising then falling; (2) models overthink easy questions and underthink hard ones, indicating poor calibration of reasoning length to perceived difficulty; and (3) applying SimPO with a length-only preference signal on unlabeled data reduces generation length by roughly 30-60% while maintaining acceptable accuracy. The paper includes sample-level rank statistics, question-level difficulty splits with t-tests, and a preference-optimization intervention.

Significance. If the central claims were fully supported, the paper would make a useful contribution to the growing literature on reasoning-length calibration in LLMs. The strengths include a transparent sampling protocol with stated hyperparameters, rank-based metrics that are easy to reproduce, explicit t-test tables, and an honest acknowledgment in Section 5 that the causal interpretation of length-correctness correlations is ambiguous. The SimPO intervention is a concrete, falsifiable test of whether length-only preferences can reduce cost without large accuracy loss. However, the headline fixed-question non-monotonicity claim is not directly tested by the reported aggregated curves, and the under/overthinking interpretation rests on correlational and between-set comparisons that do not establish the claimed difficulty-miscalibration mechanism. These issues are load-bearing for the paper's main conclusions, so the manuscript needs additional analysis before the claims can be accepted.

major comments (4)
  1. [Section 4.1, Figure 1, and Appendix A.2] The claim that 'for a fixed question, accuracy is non-monotonic in reasoning length' is not established by the reported Acc_r curve. Acc_r is the fraction of questions whose r-th shortest sample is correct, averaged over all questions. This is an aggregate over questions of widely different difficulty, so the curve can be non-monotonic even if every individual question has a monotone or flat length-accuracy relationship. For example, the early rise can be driven by Medium questions whose correct samples are comparatively longer, and the later decline can be driven by Easy questions whose shortest samples are already correct. The final rank is also an extreme order statistic and may be affected by the 8k token cap. To support the fixed-question claim, the authors should condition on within-question outcome variability: for instance, plot Acc_r restricted to Medium questions, compute a per-question measure of whether correctness improves or degrades with length rank, or fit a mixed-effects logistic regression with a question-level random intercept. The existing correlations in Appendix B.2 on Medium questions are related but do not directly replace this analysis.
  2. [Section 4.1, text after Figure 1] The text states that 'a consistent non-monotonic trend' is observed across models and datasets, but the same paragraph reports that R1-Preview on MATH achieves its best accuracy at r*=0 with accuracy declining at higher ranks. That is a monotonically decreasing pattern, not a non-monotonic one. The blanket claim should be qualified to the model-dataset pairs where a rise-then-fall pattern is actually observed, and the single decreasing case should be discussed as an important exception rather than folded into the general statement.
  3. [Section 5.1, Tables 2 and 3] The underthinking/overthinking interpretation is not supported by the t-test comparisons as presented. For hard questions, Table 3 shows several non-significant or directionally inconsistent comparisons, and the conclusion that models 'do not consistently recognize or reflect increased difficulty' is drawn from the absence of a predicted pattern across sets that differ in intrinsic difficulty. Since the sets are defined by N=10 all-correct/all-incorrect outcomes, the split is arbitrary and the 'needed length' for a question is never measured. The paper itself acknowledges in Section 5 that longer responses may make a question appear more difficult than it truly is, which undermines the causal story. I recommend reframing these results as exploratory evidence or hypotheses, and adding a direct within-question test: for Medium questions with at least one correct sample, compare the lengths of correct versus incorrect samples, and check whether the probability of error increases with relative length after controlling for question difficulty.
  4. [Section 6, Figures 4 and 5] The claim that length-only SimPO preference optimization 'significantly reduces' length while maintaining 'acceptable accuracy' is based on a single training run without confidence intervals, multiple seeds, or a precise definition of acceptable accuracy. Figure 4 shows accuracy fluctuating during training, so it is unclear which training step is used for the headline 30-60% reduction and what the corresponding accuracy is. The authors should report exact numbers at a selected checkpoint, include error bars over at least three seeds, and state the accuracy drop relative to the base model. Without this, the practical recommendation that length-only preferences can replace correctness-based preferences is not robustly supported.
minor comments (5)
  1. [Table 1] The 'Mean ± Std' entries, such as 1374.82 ± 92.34, appear to be standard errors rather than standard deviations given the sample sizes; if so, please relabel the column as 'Mean ± SE' or report standard deviations.
  2. [Section 4.1 vs. Appendix B.1] The main text says that for over 60% of questions across all model-dataset combinations the shortest sample is correct, but Appendix B.1 reports over 80% for R1-Preview on both datasets and over 60% for R1-Distill. Please reconcile these numbers.
  3. [Related Work] The citation 'Fu et al. proposes Dynasor-CoT...' is missing a year and is incomplete; please provide the full reference.
  4. [Table 3 caption] The caption contains a typo: 'shared-sard set' should be 'shared-hard set'.
  5. [Section 5.1, Tables 2 and 3] The naming of 'M1-Advantage' and 'M2-Advantage' sets is confusing, especially in the hard-question table where a set that is hard for one model but not the other is labeled as the other model's advantage set. Consider using explicit set definitions such as Q^hard_i \ Q^hard_j in each panel.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's claims are empirical measurements, and the SimPO experiment is an independent intervention rather than a fitted derivation.

full rationale

The paper does not derive its headline findings from fitted parameters or from definitions that presuppose them. Section 4 defines L_r and Acc_r as averages over length-ranked samples and reports an observed non-monotonic pattern; sorting responses by length makes L_r increasing by construction, but it does not force Acc_r to rise and then fall, so the empirical claim has independent content. The difficulty tiers (Easy/Medium/Hard) are defined by the model's own correctness over N=10 samples, and the cross-model length comparisons in Section 5 are separate measurements used interpretively; the paper itself flags the causal ambiguity ('it remains unclear whether the increased length reflects the model's ability to recognize the intrinsic complexity of the question... or whether the longer responses themselves introduce additional errors', Section 5), so the over/underthinking labels are presented as interpretations rather than as consequences of the definitions. The SimPO length-reduction experiment (Section 6) is an intervention that optimizes only for shorter responses and then measures accuracy and length on test data; its success is not assumed by the earlier analysis. There are no load-bearing self-citations and no fitted parameter is relabeled as a prediction. Potential concerns about the aggregate Acc_r curve mixing question difficulties are validity or correctness issues about whether the data support the 'fixed question' claim, not circularity in the derivation chain.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper relies on two design choices (N=10 samples, generation temperature) and a set of domain assumptions about the benchmarks and models. No new theoretical entities are introduced. The central claims are empirical, so the main burden is on the representativeness of the models and datasets and the adequacy of the sample size.

free parameters (3)
  • Number of samples per question N = 10
    Chosen for computational efficiency. Determines the Easy/Medium/Hard categorization and the rank-based metrics. The paper acknowledges in Limitations that larger N would improve statistical reliability.
  • Sampling temperature T and top-p = 1.0, 1.0
    Used to generate diverse reasoning paths for the sample-level analysis. These settings are standard for exploration but affect the length distribution.
  • SimPO hyperparameters (learning rate, beta, gamma) = 5e-7, 2, 1
    Standard preference optimization hyperparameters, reported in Appendix E. The length-reduction results could change with different values.
assumptions (5)
  • domain assumption Ground-truth labels in GSM8K and MATH are correct and answer matching is a valid correctness measure.
    The paper evaluates correctness by comparing to the provided answers; if labels were noisy or matching was flawed, the length-accuracy relationships would be distorted.
  • domain assumption The two models, DeepSeek-1.5B-Distill and DeepScaler-1.5B-Preview, are representative of reasoning LLMs.
    The conclusions are drawn from these two models only; generality to other scales and training strategies is asserted in the Limitations as future work.
  • domain assumption Temperature sampling with T=1.0 produces diverse, independent reasoning paths for a fixed question.
    The sample-level analysis treats the N=10 samples as exchangeable draws; if the samples are correlated or the diversity is limited, the rank-based metrics may not reflect the true length-accuracy curve.
  • domain assumption Shared-easy and shared-hard question sets are comparable in intrinsic difficulty across the two models.
    The cross-model analysis in Section 5.1 interprets length differences on advantage sets as evidence of difficulty perception; this assumes the shared sets are equal anchors for both models.
  • domain assumption Response length in tokens is a meaningful proxy for the amount of reasoning.
    The entire study operationalizes 'overthinking' and 'underthinking' through token counts; if length does not track reasoning effort, the behavioral labels lose meaning.

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Cite this review

Pith. "Pith review of Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs." pith.science (2026). https://pith.science/paper/Q35CKXYE

@misc{pith2026250500127,
  author       = {Pith},
  title        = {Pith review of: Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q35CKXYE}},
  note         = {Machine review of arXiv:2505.00127}
}
read the original abstract

Large language models (LLMs) are increasingly optimized for long reasoning, under the assumption that more reasoning leads to better performance. However, emerging evidence suggests that longer responses can sometimes degrade accuracy rather than improve it. In this paper, we conduct a systematic empirical study of the relationship between reasoning length and answer correctness. We find that LLMs tend to overthink simple problems, generating unnecessarily long outputs, and underthink harder ones, failing to extend their reasoning when it is most needed. This indicates that models might misjudge problem difficulty and fail to calibrate their response length appropriately. Furthermore, we investigate the effects of length reduction with a preference optimization algorithm when simply preferring the shorter responses regardless of answer correctness. Experiments show that the generation length can be significantly reduced while maintaining acceptable accuracy. Our findings highlight generation length as a meaningful signal for reasoning behavior and motivate further exploration into LLMs' self-awareness in reasoning length adaptation.

Figures

Figures reproduced from arXiv: 2505.00127 by the authors.

Figure 1
Figure 1. Reasoning length Lr of the r-th shortest response v.s. accuracy Accr (N = 10). The red marker r ∗ denotes the rank of responses with the highest accuracy. Results for R1-Distill and R1-Preview on the GSM8K and MATH datasets suggest that both overly short and excessively long reasoning can degrade performance. Shortest Correct Response [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Percentage of questions for which the shortest correct response occurs at rank [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Average token length and perplexity of model responses across questions with different [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Testing accuracy and average token length when applying the preference optimization [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Average token length for correct and incorrect responses across different training steps. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: The prompt template used to generate responses [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Distribution of the extreme rank indices [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: Cumulative distribution the extreme rank indices [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 9
Figure 9. Figure 9: Spearman correlation of answering length and correctness. [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]
Figure 10
Figure 10. Figure 10: Pearson correlation of answering length and correctness. [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]
Figure 11
Figure 11. Figure 11: Average token length of responses in model-dataset specific difficulty level. [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: Heatmap of token length for questions categorized by accuracy. Density is normalized [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]
Figure 13
Figure 13. Figure 13: Heatmap of perplexities for questions categorized by accuracy. Density is normalized [PITH_FULL_IMAGE:figures/full_fig_p019_13.png]
Figure 14
Figure 14. Figure 14: Heatmap of perplexity and token length, the density in the heatmap is normalized on all [PITH_FULL_IMAGE:figures/full_fig_p020_14.png]
Figure 15
Figure 15. Figure 15: Accuracy and token length trade-offs during SimPO training steps [PITH_FULL_IMAGE:figures/full_fig_p021_15.png]
Figure 16
Figure 16. Figure 16: Token length reduction rate for correct and incorrect responses when using SimPO. [PITH_FULL_IMAGE:figures/full_fig_p021_16.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.