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REVIEW 4 major objections 4 minor 34 cited by

When More is Less: Understanding Chain-of-Thought Length in LLMs

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

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Pith's one-line read Chain-of-thought accuracy peaks at an intermediate length: longer is not better.

desk verdict Empirical inverted-U is solid and useful; the scaling-law proof is conditional on an unverified linear ansatz, and the general extension does not prove what it claims. read the letter →

arxiv 2502.07266 v3 pith:CB6LK7KV submitted 2025-02-11 cs.AI cs.CLcs.LG

Yuyang Wu , Yifei Wang , Ziyu Ye , Tianqi Du , Stefanie Jegelka , Yisen Wang This is my paper · ORCID
classification cs.AIcs.CLcs.LG
keywords chain-of-thoughtoptimalCoTlengthinvertedU-shapesimplicitybiaserroraccumulationtaskdecompositionreinforcementlearninglength-filteredvoting
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

Task accuracy follows an inverted U-shape as chain-of-thought (CoT) length grows: very short chains under-decompose the problem and very long chains accumulate errors. The paper argues this curve holds across real models and controlled arithmetic tasks, and that the peak location follows a scaling law: harder tasks push the peak to longer chains, while stronger models peak with shorter chains. This 'simplicity bias' also shows up during reinforcement learning, where models converge to the optimal (often shorter) length. If correct, the result turns CoT length from a free parameter into a quantity that should be calibrated per task difficulty and per model.

What carries the argument

The load-bearing object is the per-step success product in Proposition 4.2: each CoT step must both state the right sub-question and answer it correctly, so $N$ steps compound the per-step success probability $(1-\sigma(T))(1-E(N,M,T))$ into $A(N)$. Longer chains make each sub-question easier (lower $E$) but multiply more factors, and they also increase the chance of a sub-question error. The explicit linear forms $\sigma(T)=T/C$ and $E(N,M,T)=T/(NM)$ turn this tradeoff into the closed-form optimum of Theorem 4.3, whose derivative condition is solved by the Lambert W function (the function $w$ with $w e^w = x$).

What would settle it

Take a reasoning task with verification steps that catch earlier errors, so per-step error decays faster than linearly with $N$, and measure accuracy against CoT length over a wide range; if accuracy keeps rising monotonically instead of peaking, the inverted-U claim and its linear error model are falsified. A second check is to measure the optimal length for one fixed difficulty across a fine grid of model sizes; if the optimum does not decrease monotonically with capability, Corollary 4.4 is contradicted.

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Extended reading notes

Core claim

The paper's central claim is formalized as a product decomposition of final accuracy: $A(N) = \alpha [(1-\sigma(T))(1-E(N,M,T))]^N$, where $N$ is the number of reasoning steps, $T$ is task difficulty, $M$ is model capability, $\sigma(T)$ is the error rate of generating a sub-question, and $E(N,M,T)$ is the error rate of answering each sub-question. Under the linear-error model $\sigma(T)=T/C$ and $E(N,M,T)=T/(NM)$, the accuracy function has an interior maximum at $N^*=T Z/(M(Z+1))$ with $Z=W_{-1}(-1-T/(Ce))$; this optimum increases with $T$ and decreases with $M$. Thus the author's intended claim is not merely that long CoTs fail, but that there is a provable, predictable peak length that explains both overthinking and the preference of stronger models for shorter reasoning paths.

Load-bearing premise

The theory assumes the two error rates take the exact linear forms $\sigma(T)=T/C$ and $E(N,M,T)=T/(NM)$, and these forms already build in the inverse dependence on $N$ and $M$ that the optimal-length formula outputs; if the true per-step error rates are not linear in $T/(NM)$ and $T/C$, the explicit formula for $N^*$ and the monotonicity results do not follow. The empirical optimal-length measurements additionally depend on coarse length binning and on excluding questions whose accuracy is near zero or near one.

Editorial extensions

If this is right

  • Models trained on chains of their own optimal length outperform models trained on uniformly mixed chain lengths, and a smaller model with correctly sized chains can beat a larger model with poorly sized chains.
  • Filtering out very long chains before majority voting (Length-Filtered Vote) improves accuracy over plain majority voting because very short and very long chains contribute noisier votes.
  • Reinforcement learning with outcome rewards converges to the optimal chain length, so the observed shrinking of CoT during RL is the expected consequence of reward optimization, not a separate anomaly.
  • Optimal per-step complexity rises with task difficulty, so forcing every problem into the same step granularity is suboptimal for hard tasks.

Reading between the lines

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

  • If the inverted-U law holds across real tasks, then test-time compute is not monotone: for each question there is a compute budget beyond which extra tokens actively hurt accuracy, so overthinking is a measurable phenomenon rather than just a cost concern.
  • The theory predicts that when two models of different sizes are fine-tuned on the same fixed-length CoT corpus, the larger model will be further from its potential until the chain lengths in the data are re-matched to its capability; this is a direct comparison a user could run.
  • Length-aware filtering could be extended to reward shaping during RL by explicitly penalizing chains far from the estimated optimal length, which may speed convergence to the same peak that outcome-only rewards reach more slowly.
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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 / 4 minor

Summary. This paper studies how chain-of-thought (CoT) length affects LLM accuracy. It argues that accuracy follows an inverted U-shaped curve in CoT length, that the optimal length increases with task difficulty and decreases with model capability (simplicity bias), and that RL training shifts models toward shorter chains. The evidence is threefold: real-world evaluations on Qwen and Llama models over MATH, MMLU, and GPQA; controlled synthetic arithmetic experiments with GPT-2 models of varying depth; and a theoretical model in which total accuracy is A(N)=alpha[(1-E)(1-sigma)]^N. Under the linear ansatz sigma(T)=T/C and E(N,M,T)=T/(NM), Theorem 4.3 gives an explicit optimum N*=T Z/(M(Z+1)), and Corollary 4.4 states the scaling laws. The paper also proposes training with optimal-length CoT data and a length-filtered majority vote. I agree with the reader that the controlled synthetic experiments cleanly demonstrate the inverted U and the scaling trends, but the formal scaling laws are conditional on an unvalidated functional ansatz, the printed Lambert-W formula in Theorem 4.3 is mistyped, and the general extension in Appendix F does not logically establish monotonicity of the maximizer from monotonicity of a lower bound.

Significance. If fully established, the paper would be a useful contribution: it challenges the default assumption that longer CoT is always better, offers a transparent mechanism (the trade-off between task decomposition and error accumulation), and gives practical guidance for adaptive CoT calibration. The controlled synthetic experiments are a genuine strength: they systematically vary task difficulty and model capability, show the inverted U, and demonstrate that RL converges to the optimal length. The theoretical model is simple and the empirical inverted-U does not depend on the theory for its support. The significance is currently limited because the scaling laws are largely derived from assumed functional forms rather than independently confirmed, and the real-world length estimates are noisy. With the theory either validated or explicitly presented as a conditional heuristic, the paper would be a solid empirical and conceptual contribution.

major comments (4)
  1. [Section 4.1, Theorem 4.3, Corollary 4.4] The central scaling laws are largely a restatement of the linear ansatz. With sigma(T)=T/C and E(N,M,T)=T/(NM), the maximizer of Eq. (1) is N*=T Z/(M(Z+1)) with Z independent of M, so N* is proportional to 1/M by construction and the T-dependence is inserted through the numerator T and through Z. Corollary 4.4 therefore derives dependencies that are already encoded in the assumptions; no independent evidence is provided for the specific linear forms. Appendix E.2, the only empirical support cited for the model, reports training-loss ratios rather than estimating E or sigma, and its statement that the subtask error rate is taken constant with t is in tension with E=T/(NM), which varies with the per-step size t=T/N. The formal claims should be reframed as conditional on the ansatz, or the ansatz should be validated.
  2. [Theorem 4.3] The theorem statement defines Z=W_{-1}(-1-T/(Ce)), but for 0<T/C<0.9 this argument is less than -1, which is outside the real domain of the Lambert W function. The proof in Appendix G.2 correctly uses W_{-1}(-(1-T/C)/e). The theorem statement must be corrected; as printed, the formula in Eq. (2) is not meaningful for the stated regime.
  3. [Appendix F, Corollaries F.4 and F.5] Theorem F.3 establishes only a lower bound NLB(M,T) on any interior maximizer N*; it does not establish that A(N) has a maximum at all, nor that the maximizer is unique. Corollaries F.4 and F.5 infer monotonicity of N* from monotonicity of the lower bound, which is not logically valid: a lower bound can move monotonically while the maximizer itself moves in the opposite direction or ceases to exist. The claimed qualitative scaling laws under general error functions therefore remain unproved. Additionally, Eq. (19) in the proof of Theorem F.3 misprints the derivative: it should be ln((1-sigma)(1-E(x))) - xE'(x)/(1-E(x)), not ln(1-sigma(1-E(x))) - xE'(x)/(1-E(x)); the printed inequality does not follow from the written expression.
  4. [Section 2.1 and Appendix C.1] The real-world estimate of optimal CoT length is fragile. For each question, the optimal length is the best length bin among 60 sampled solutions, which is a noisy quantity, and the analysis uses coarse bin widths (5 in the cross-model comparison, 2 in the difficulty analysis) and excludes questions with accuracy below 0.01 or above 0.99 after the fact. No error bars or confidence intervals are provided for the estimated optimal lengths themselves, only for the regression line in Figure 2b. Figure 2a uses only four model sizes without repeated seeds. This weakens the real-world evidence for the scaling laws, although the controlled synthetic experiments stand independently.
minor comments (4)
  1. [Section 3.2 heading] The heading contains a duplicated word: 'Scaling Laws of the Optimal CoT Length and and Practical Insights'. It should be 'and Practical Insights'.
  2. [Abstract and Section 5.2] There are typographical artifacts in the text, including 'Length-aware Voteto' in the abstract and 'Length-Filtered V ote' in Section 5.2 and Figure 4c; these should be cleaned up.
  3. [Appendix E.2] The sentence 'the loss of subtask generation tokens for the easiest subtask (t=1) is about 3 times larger than the hardest subtask (t=12)' appears to contradict the intended claim that harder subtasks have larger loss; please clarify whether this is a ratio reversal or a typo.
  4. [Appendix H, Algorithm 1] In Length-Filtered Vote, if a length bin L_j is empty, the computation of p_j[a] divides by |L_j|=0; the algorithm should specify how empty bins are handled.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: theoretical results are conditional on explicitly stated error-rate assumptions; empirical inverted-U and scaling claims are independently measured.

full rationale

The paper's formal results are conditional derivations from explicitly stated assumptions rather than disguised restatements of the target conclusions. Proposition 4.2 defines a product-form accuracy model, and the linear ansatz E(N,M,T)=T/(NM) with σ(T)=T/C in Section 4.1 is introduced as a 'simple case' and motivated by subtask-loss measurements in Appendix E.2, not fitted to the optimal-length data. Theorem 4.3 and Corollary 4.4 are algebraic consequences of that ansatz; they do not feed the empirical inverted-U observations back into the theory as inputs. The empirical scaling laws and inverted-U curves in Sections 2 and 3 come from controlled measurements independent of the theoretical model, and the RL convergence result (Corollary 4.5) is a standard policy-gradient/replicator-dynamics fact proved for arbitrary reward A(N). The only author self-citation, [41], appears in Related Work and is not load-bearing. The logically invalid inference from a lower bound to monotonicity of the maximizer in Corollaries F.4 and F.5 is a correctness flaw, not a circularity, because it does not assume the conclusion it purports to prove. No step in the derivation chain reduces by construction to its own inputs.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The two free conceptual parameters C and M and the two assumed error forms carry most of the theoretical burden. The empirical results are more independent: the controlled arithmetic experiments directly show the inverted U and the scaling trends, and the real-world scans are consistent. No new entities such as particles or mediators are introduced.

free parameters (2)
  • C
    Maximum task difficulty scale in sigma(T)=T/C; introduced ad hoc to ensure 0<sigma<1 for tasks in the model's training regime.
  • M
    Model capability boundary in E=T/(NM); adopted from cited reasoning-boundary work, not measured or estimated here.
assumptions (4)
  • domain assumption CoT step errors are independent and multiply: the final accuracy is the product of per-step success probabilities (Definition 4.1, Proposition 4.2).
    This ignores error recovery, dependencies between steps, and behaviors like backtracking; the paper notes these can be viewed as part of task decomposition, but the formal product form is an assumption.
  • ad hoc to paper Sub-question error per token is a constant sigma(T) independent of model capability and step granularity, with linear form sigma(T)=T/C.
    The linear form is chosen for tractability and to keep sigma<1; Appendix E.2 offers indirect loss evidence, but the form is not derived and directly affects the optimum.
  • ad hoc to paper Sub-answer error rate has the exact linear form E(N,M,T)=T/(NM), decreasing linearly in N and M.
    This functional form is what makes the accuracy curve unimodal and makes N* increase with T and decrease with M; the scaling laws are consequences of this assumption.
  • domain assumption RL training is modeled as a stateless multi-armed bandit with binary outcome rewards and a softmax policy.
    Corollary 4.5's replicator-dynamics proof assumes a stationary reward for each fixed length, which omits credit assignment, nonstationarity, and representation learning present in real RL runs.

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Cite this review

Pith. "Pith review of When More is Less: Understanding Chain-of-Thought Length in LLMs." pith.science (2026). https://pith.science/paper/CB6LK7KV

@misc{pith2026250207266,
  author       = {Pith},
  title        = {Pith review of: When More is Less: Understanding Chain-of-Thought Length in LLMs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CB6LK7KV}},
  note         = {Machine review of arXiv:2502.07266}
}
read the original abstract

Large Language Models (LLMs) employ Chain-of-Thought (CoT) reasoning to deconstruct complex problems. While longer CoTs are often presumed superior, this paper challenges that notion, arguing that longer is not always better. Drawing on combined evidence from real-world observations, controlled experiments, and theoretical analysis, we demonstrate that task accuracy typically follows an inverted U-shaped curve with CoT length, where performance initially improves but eventually decreases as the number of CoT steps increases. With controlled experiments, we further uncover the scaling behaviors of the optimal CoT length: it increases with task difficulty but decreases with model capability, exposing an inherent simplicity bias where more capable models favor shorter, more efficient CoT reasoning. This bias is also evident in Reinforcement Learning (RL) training, where models gravitate towards shorter CoTs as their accuracy improves. To have a deep understanding of these dynamics, we establish a simple theoretical model that formally proves these phenomena, including the optimal length's scaling laws and the emergence of simplicity bias during RL. Guided by this framework, we demonstrate significant practical benefits from training with optimally-lengthed CoTs and employing length-aware filtering at inference. These findings offer both a principled understanding of the "overthinking" phenomenon and multiple practical guidelines for CoT calibration, enabling LLMs to achieve optimal reasoning performance with adaptive CoTs tailored to task complexity and model capability.

Figures

Figures reproduced from arXiv: 2502.07266 by the authors.

Figure 1
Figure 1. (a) The performance of a 6-layer GPT2 model (Section 3) follows inverted U-shaped [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Real-world CoT length observations. (a) Larger models tend to achieve optimal performance [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. CoT Behaviors in Synthetic Experiments: (a) Each curve corresponds to a specific CoT strategy with fixed per-step difficulty. The color of the bar beneath each curve represents the optimal per-step difficulty (t) at each task difficulty. The progressively darker gradient colors indicates that harder tasks consistently favor higher per-step difficulty. (b) Change of the optimal CoT length with increasing model size a… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: (a) and (b) compare model performance under different pretraining data distributions: [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Computation tree of arithmetic expres￾sion 5 + (4 + ((2 + 1) + 3)). To begin, we aim to empirically investigate the relationship between reasoning performance and CoT length. Therefore, we need to con￾trol a given model to generate reasoning chains of varying lengths f…
Figure 6
Figure 6. Figure 6: Evaluation between task difficulties and optimal CoT lengths on MATH datasets with [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Evaluation between task difficulties and optimal CoT lengths on MATH datasets with [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: Real-world CoT length observations. (a) Larger models tend to achieve optimal performance [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: Evaluation between task difficulties and optimal CoT lengths on MMLU STEM datasets [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.