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REVIEW 4 major objections 5 minor 3 cited by

Not All Tokens Are What You Need In Thinking

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read By scoring each token in a chain of thought for how much information it carries about the final answer given the question, Conditional Token Selection compresses reasoning training data by up to 76% while keeping accuracy nearly intact…

desk verdict Novel answer-conditioned token pruning for long CoT beats baselines, but the appendix tables are internally inconsistent and the headline numbers need replication before I'd trust them. read the letter →

arxiv 2505.17827 v2 pith:FLMFCF6S submitted 2025-05-23 cs.CL

Hang Yuan , Bin Yu , Haotian Li , Shijun Yang , Christina Dan Wang , Zhou Yu , Xueyin Xu , Weizhen Qi
show 1 more author
Kai Chen
This is my paper
classification cs.CL
keywords chain-of-thoughtcompressionconditionaltokenselectionimportancereasoningefficiencyoverthinkingreferencemodelLLMfine-tuning
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

Large reasoning models generate long chains of thought, and much of that text is redundant: it consumes compute without improving the answer. This paper proposes Conditional Token Selection (CTS), a way to compress chain-of-thought training data by keeping only the tokens that matter for deriving the correct answer, judged relative to the question and the answer itself. Fine-tuning a smaller model on the compressed data maintains or improves accuracy while sharply reducing the number of reasoning tokens produced at inference. On a graduate-level science question benchmark, the method reports a 9.1% accuracy gain with 13.2% fewer reasoning tokens, and at deeper compression a 75.8% token reduction with only a 5% accuracy drop. The intended payoff is cheaper and faster reasoning from the same base models.

What carries the argument

The load-bearing mechanism is the conditional importance score: for each token $y_i$ in the chain, CTS computes $r_i = \mathrm{PPL}(y_i \mid y_{<i}) - \mathrm{PPL}(y_i \mid x_{\mathrm{prob}}, x_{\mathrm{ans}}, y_{<i})$, the drop in predictive surprise when the question and final answer are conditioned on. Tokens with the smallest drop are assumed to carry no extra information about the answer once the surviving tokens are known, an assumption stated as conditional independence $A \perp \bar{y} \mid \tilde{y}$ where $\bar{y}$ is the removed part and $\tilde{y}$ the retained part. The framework also uses a reference model trained on reasoning traces that were themselves compressed by a strong reasoning model to focus on essential symbols and numbers. Iterative segmentation into blocks is used to mitigate violations of the independence assumption.

What would settle it

Take a set of multi-step reasoning problems in which a single critical token (for example, the value of a substitution variable or a key numerical coefficient) appears only deep in the chain, and compress the training data with CTS at a high compression ratio such as $\alpha=0.5$. If the conditional independence assumption fails, accuracy on these problems should drop far more than on problems where the critical information appears early or is recoverable from the question; measuring this gap would directly test the assumption.

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Extended reading notes

Core claim

CTS treats a chain of thought as a sequence of tokens that can be pruned if they are conditionally redundant. A reference model, fine-tuned on curated high-quality reasoning traces, scores each token by the difference between its perplexity given the previous tokens alone and its perplexity given the question, the final answer, and the previous tokens. Tokens whose score is low are removed, segment by segment, at a chosen compression ratio, and the model is then fine-tuned on the compressed data. The paper's central claim is that this procedure preserves the answer-relevant information in the chain, so the trained model reasons both accurately and more tersely. It reports the headline accuracy/token trade-offs on three benchmarks and out-of-domain gains on code generation tasks.

Load-bearing premise

The method assumes that the reasoning tokens it removes carry no information about the answer once the tokens it keeps are known; if that conditional independence fails for a meaningful class of problems, compressed training data will lose tokens that are actually needed to reach the correct answer.

Editorial extensions

If this is right

  • If CTS works as reported, small models fine-tuned on compressed chains will use far fewer tokens per answer, lowering inference latency and cost without giving up reasoning accuracy.
  • The reported trade-off implies that a substantial fraction of tokens in state-of-the-art long reasoning traces are redundant, because the trained model learns to skip them naturally.
  • The method generalizes to code generation even when trained only on math data, suggesting that answer-conditional token importance transfers across reasoning domains.
  • Answer-conditioned scoring beats unconditional baselines, which indicates that conditioning on the question and final answer is what preserves answer-critical tokens such as numbers and variables.
  • The reference model's training cost can be amortized in practice, with the paper's break-even calculation at roughly 27,500 inference calls.

Reading between the lines

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

  • If the conditional independence assumption fails on adversarial reasoning traces, accuracy could drop disproportionately at high compression; one could test this on problems where a single removed token in an early segment is required to interpret a later segment.
  • CTS could be applied iteratively to its own compressed outputs: re-scoring with the same reference model might reach higher compression before accuracy degrades, effectively finding a fixed point of the pruning operator.
  • The ablation suggests that conditional scoring without a specially trained reference model retains most of the benefit, so a generic model might transfer the approach to non-math reasoning with little extra work.
  • It is an open question whether the gains come from removing noisy tokens (regularization) or from teaching shorter reasoning paths (a form of curriculum); distinguishing these would predict whether the gains persist at larger scales.
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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 proposes Conditional Token Selection (CTS), a method for compressing long chain-of-thought training data by scoring each reasoning token with a conditional importance metric, defined as the difference between unconditional and answer-conditional perplexity, and by training a reference model on a DeepSeek-R1-curated subset of important tokens. The compressed CoT sequences are then used to fine-tune smaller instruct models (Qwen2.5-7B/14B-Instruct and Llama-3.1-8B-Instruct). Experiments compare CTS with LLMLingua, TokenSkip, and GPT-4o-based compression on MATH500, AIME24, GPQA Diamond, HumanEval, and MBPP. The headline claims are a 9.1% accuracy improvement on GPQA Diamond with 13.2% fewer reasoning tokens and a 75.8% token reduction with only a 5% accuracy drop.

Significance. If the reported results hold, CTS would be a practical and flexible method for reducing the training and inference cost of long CoT distillation, with a plausible mechanism grounded in conditional importance scoring. The idea of training a reference model on a separately curated set of important tokens is interesting, and the comparison against two established compression baselines is valuable. However, the manuscript as printed does not allow the central token-reduction and cross-domain claims to be verified because key tables are internally inconsistent. The contribution is therefore not yet established; with corrected data and proper statistical reporting, the idea could be a useful step toward efficient reasoning-model distillation.

major comments (4)
  1. [Table 1 vs. Table 4] Table 1 reports CTS at α=0.9 on MATH500 with 4703 inference tokens and 91.6% accuracy, while Table 4 (the ablation token counts for the same model and dataset) reports the Proposed condition at α=0.9 with 5012 tokens and at α=0.8 with 4703 tokens. The α=0.8 value in Table 4 equals the α=0.9 value in Table 1, and the α=0.9 value equals the Original row of Table 1. This shifted-row pattern makes the headline token-reduction claims unverifiable from the printed paper.
  2. [Appendix Table 5(b)] Table 5(b), labeled MBPP, is numerically identical to Table 5(a), labeled HumanEval, in every reported accuracy and token count (e.g., 7B Original 51.2/10153; CTS/TokenSkip 0.87/59.8/8205), differing only in the method label. As printed, the MBPP results are a duplicate of the HumanEval results, so the cross-domain generalization claim on MBPP is not supported by any distinct data.
  3. [Experimental Setup / Main Results] All reported results are single runs without error bars, variance estimates, or significance tests. Given that AIME24 contains only 30 problems (so accuracy moves in 3.3-point steps) and the central GPQA claim is a 9.1-point accuracy improvement, the absence of repeated seeds or significance testing is a serious gap that prevents assessing whether the observed improvements are stable.
  4. [Eq. (7) and ablation statement] The token-removal strategy rests on the conditional independence assumption A ⊥ ¯y | ˜y in Eq. (7), which the paper acknowledges is approximate. More concerning, the text states that 'Table 2 in appendix demonstrates that reasoning tokens do not differ substantially across variants,' but the actual token-count table (Table 4) shows counts ranging from 1787 to 5597 across variants and α values, so the statement is contradicted by the paper's own data. Because the efficiency claim depends on these token counts, this needs a corrected and consistent analysis.
minor comments (5)
  1. [Equation (5) and Algorithm 1] Eq. (5) defines the CTS objective with a sparsity penalty, but the algorithm actually selects tokens via a quantile threshold in Algorithm 1; the connection between the optimization objective and the implemented selection rule should be clarified.
  2. [Wording and typos] There are several typos, including 'an standard RM' in the ablation section, 'Where y = ...' capitalized mid-sentence after Eq. (4), and 'Equation 1 (Jiang et al. 2024)' which appears to refer to the wrong equation and possibly the wrong reference.
  3. [Table 1 and Table 7 formatting] In Table 1, the CTS α=0.6 GPQA accuracy '48' is missing a decimal point; in Table 7, '0.033' and '0.363' are inconsistent with the percentages shown elsewhere and should be '3.3' and '36.3' if the other rows are percentages.
  4. [Ablation table reference] The sentence 'Table 2 in appendix demonstrates...' should refer to Table 4, not Table 2; Table 2 is the variant definition table.
  5. [Reference model cost analysis] The RM training cost and break-even analysis is a useful addition, but it should state explicitly whether the 11.44 A800 GPU hours cover the full RM training and whether the break-even calculation amortizes the RM cost across all downstream models tested or only Qwen-7B.

Circularity Check

0 steps flagged · score 2.0 of 10

No meaningful circularity: the CTS pipeline is self-contained and evaluated on external benchmarks; the only self-citation is a non-load-bearing related-work mention.

full rationale

The paper's derivation chain does not reduce to its inputs. The reference model is trained on a separately curated 8M-token subset selected by DeepSeek-R1, explicitly stated to differ from the distilled data being compressed ('It is worth noting that this portion of CoT data differs from the distilled data requiring compression in our method'). The compression of the second 9.3K MATH subset is then used to fine-tune student models, which are evaluated on external benchmarks (MATH500, AIME24, GPQA Diamond, HumanEval, MBPP). No parameter is fitted to those benchmark accuracies, and no equation makes the reported accuracy gains equal to the token-selection scores by construction. Equation (7), A ⊥ ¯y | ˜y, is stated as an assumption, not as a derived theorem, and the paper explicitly acknowledges it is approximate and uses iterative segmentation to mitigate violations; this is a limitation, not circularity. The conditional importance score ri is a defined heuristic, but the claimed downstream improvements are empirical rather than definitional. The sole self-citation (Yu et al. 2025, by several of the present authors) appears only in Related Work describing variable-length CoT training and carries none of the paper's load-bearing argument. The internal inconsistencies in Tables 1/4 and Table 5 are serious verifiability and correctness concerns, but they are not instances of circular reasoning. Overall, the central method and evaluation are independent of the target results, so the circularity score is low.

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

The central statistical assumption is conditional independence. The method also assumes perplexity scores capture answer-relevant importance and that the RM trained on one model's selected tokens transfers to other models.

free parameters (3)
  • compression ratio α = 0.5, 0.6, 0.7, 0.8, 0.9 (varied)
    The user-selected ratio controls token retention; the paper reports trade-offs across this range and suggests an optimal around 0.7-0.8. It is not fitted to data, but is a hand-chosen knob that determines the operating point.
  • number of segments m in iterative compression = not specified
    Algorithm 1 requires setting m but no value is given; likely fixed heuristically from Jiang et al. (2023). This affects compression granularity.
  • reference model training hyperparameters = 3 epochs, seq len 4096, LR/batch not specified
    The RM is fine-tuned with 8M tokens over 3 epochs, but learning rate, batch size, and other settings are omitted, making exact reproduction difficult.
assumptions (3)
  • domain assumption Conditional independence A ⊥ ¯y | ˜y (Eq. 7)
    Assumes removed tokens carry no extra information about the answer given the kept tokens; justifies compression. The paper acknowledges it is approximate.
  • domain assumption Perplexity difference is a valid token importance proxy
    The score r_i = PPL(y_i|y_<i) - PPL(y_i|x_prob,x_ans,y_<i) is assumed to rank how much token i matters for deriving the answer; this is inherited from prior prompt-compression work.
  • domain assumption The trained reference model's notion of importance transfers from DeepSeek-R1-curated tokens to the distilled target models
    The RM is fine-tuned on tokens selected by DeepSeek-R1, then used to score tokens in independently generated CoT data; the paper provides no theoretical guarantee of transfer.

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Cite this review

Pith. "Pith review of Not All Tokens Are What You Need In Thinking." pith.science (2026). https://pith.science/paper/FLMFCF6S

@misc{pith2026250517827,
  author       = {Pith},
  title        = {Pith review of: Not All Tokens Are What You Need In Thinking},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FLMFCF6S}},
  note         = {Machine review of arXiv:2505.17827}
}
read the original abstract

Modern reasoning models, such as OpenAI's o1 and DeepSeek-R1, exhibit impressive problem-solving capabilities but suffer from critical inefficiencies: high inference latency, excessive computational resource consumption, and a tendency toward overthinking -- generating verbose chains of thought (CoT) laden with redundant tokens that contribute minimally to the final answer. To address these issues, we propose Conditional Token Selection (CTS), a token-level compression framework with a flexible and variable compression ratio that identifies and preserves only the most essential tokens in CoT. CTS evaluates each token's contribution to deriving correct answers using conditional importance scoring, then trains models on compressed CoT. Extensive experiments demonstrate that CTS effectively compresses long CoT while maintaining strong reasoning performance. Notably, on the GPQA benchmark, Qwen2.5-14B-Instruct trained with CTS achieves a 9.1% accuracy improvement with 13.2% fewer reasoning tokens (13% training token reduction). Further reducing training tokens by 42% incurs only a marginal 5% accuracy drop while yielding a 75.8% reduction in reasoning tokens, highlighting the prevalence of redundancy in existing CoT.

Figures

Figures reproduced from arXiv: 2505.17827 by the authors.

Figure 1
Figure 1. Comparison of accuracy across different compres [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Illustration of Conditional Token Selection. For long CoT datasets, CTS leverages a well-trained reference model [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. An example of CoT compression using CTS, [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: Performance metrics (Reasoning Token Reduction [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 7
Figure 7. Figure 7: Ablation experiments of the Qwen2.5-14B [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Inference token length distribution of Qwen2.5- [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: Inference token length distribution of Qwen2.5- [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: Inference token length distribution of Qwen2.5- [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Reasoning Denoiser: Denoising Reasoning Traces for Hallucination Detection in Large Reasoning Models

    cs.AI 2026-07 conditional novelty 6.0 of 10

    REDE removes irrelevant and repetitive reasoning steps using final-answer attention as supervision, improving hallucination detection AUROC by up to ~19 points over unfiltered traces.

  2. Towards Efficient Large Language Reasoning Models via Extreme-Ratio Chain-of-Thought Compression

    cs.LG 2026-02 unverdicted novelty 6.0 of 10

    Extra-CoT trains a semantic compressor on math CoT data, applies mixed-ratio SFT, and uses CHRPO reinforcement learning to achieve over 73% token reduction on MATH-500 with 0.6% accuracy gain on Qwen3-1.7B.

  3. LISA: Linear-Indexed Sparse Attention for Efficient Long-Context Reasoning

    cs.AI 2026-05 reject novelty 5.0 of 10

    LISA replaces standard attention with linear attention plus indexer-selected sparse attention, claiming O(nM) inference cost and accuracy gains, but the complexity analysis ignores the indexer's full-context scoring.

Reference graph

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