Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens

Jinlin Li; Xian Wu; Xiao Zhou; Xixian Yong; Yefeng Zheng; Yingying Zhang

REVIEW 4 major objections 6 minor 2 cited by

Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read An entropy-based stopping rule can halve reasoning-model tokens while keeping accuracy.

desk verdict Useful empirical early-stopping result with shaky information-theoretic framing; the token savings are real but the controller's compute cost is not counted. read the letter →

arxiv 2505.18237 v1 pith:M2FKHBTF submitted 2025-05-23 cs.CL cs.AIcs.ITmath.IT

Xixian Yong , Xiao Zhou , Yingying Zhang , Jinlin Li , Yefeng Zheng , Xian Wu This is my paper

classification cs.CLcs.AIcs.ITmath.IT

keywords largereasoningmodelsthinkingefficiencyinformationtheoryentropy-basedearlystoppingtokenlengthInfoBiasGain

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

The paper tries to establish that long reasoning chains in large reasoning models are often semantically redundant: they drift from ideal reasoning trajectories and add less and less information per step. It proposes two metrics, InfoBias and InfoGain, to measure this, and uses the observations to build an Adaptive Think strategy that stops reasoning once the model's average entropy over the answer space falls below a threshold. The paper reports that on QwQ-32B this strategy improves average accuracy by 1.10% while cutting token use by 50.80% across six benchmarks, compared with the model's default thinking mode. If true, the result means a simple inference-time heuristic can make reasoning models substantially cheaper to run without sacrificing output quality.

What carries the argument

The load-bearing mechanism is the entropy-based stopping rule in Eq. (6): after each reasoning step the model computes H^avg_i, the average entropy of the answer-space distribution, and terminates reasoning once H^avg_i <= $\alpha$ * (1/(e ln 2)). Two supporting measures carry the analysis: InfoBias = -I(s_{1:n}; t_{1:m}), the negative mutual information between the generated trajectory and a latent ideal trajectory, and InfoGain ΔI_i = H_{i-1} - H_i, the entropy reduction at each step. Together they turn the intuitive notion of 'redundant thinking' into a controllable stopping criterion evaluated with the model's own token probabilities.

What would settle it

Compare Adaptive Think's early-stop decisions against a random early-stop baseline matched on token budget: if stopping on the entropy threshold does not yield correct answers notably more often than stopping on random steps with the same average token count across the same questions, the entropy-confidence premise is refuted.

Watch

Extended reading notes

Core claim

The central claim is that reasoning models show a measurable efficiency trade-off: chain length grows, but semantic divergence from an ideal reasoning path accumulates, and the per-step reduction of uncertainty over the final answer shrinks. Incorrect answers show higher InfoBias and longer, more variable reasoning traces. On the strength of these measurements, the paper introduces Adaptive Think, which stops the thinking phase when the average entropy over the answer distribution drops to at most alpha times 1/(e ln 2). In experiments with QwQ-32B across six tasks, the strategy raises average accuracy by 1.10% and reduces token usage by 50.80% relative to Vanilla Think.

Load-bearing premise

The stopping rule assumes that the model's average entropy over the answer options is a trustworthy confidence signal whose absolute value can be compared with the fixed bound 1/(e ln 2), even though an answer space with more than two options has a higher maximum entropy than that bound.

Editorial extensions

If this is right

Deploying Adaptive Think at inference time could cut token cost for open-source reasoning models by about half on math, factual, logical, and commonsense tasks while slightly raising accuracy.
Because stopping relies on the model's own answer-space entropy, the mechanism can act as a plug-in wrapper over existing reasoning models that expose token probabilities.
The task-dependence of the optimal threshold alpha means deployments can tune early stopping per benchmark: safe for commonsense and narrative tasks, risky for ProntoQA and MMLU-Pro if set too aggressively.
The correlation between high InfoBias and incorrect answers suggests a response-level diagnostic: semantic divergence from ideal reasoning may flag unreliable outputs even without a verifier.

Reading between the lines

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

The stated threshold alpha * (1/(e ln 2)) is the maximum entropy of a two-point distribution, but the answer spaces used here have more than two options, whose maximum entropy is log2 l; the rule likely works because it is really a relative, not absolute, confidence cutoff. A direct test would scale the threshold by log2 l and check whether reported savings survive.
An untested comparison: Adaptive Think's gains may be reproducible with a much cheaper difficulty signal, such as question length or the model's own quick self-assessment; comparing token savings per difficulty decile would show whether entropy is the active ingredient or a proxy.
For closed-source models without token probabilities, the paper's sampling-based entropy approximation would cost additional generations; whether the efficiency benefit survives that overhead is left untested.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: the Adaptive Think result is probably real as an output-token saving, and the paper is worth engaging. But the theory section is decorative in the worst way—two metrics with mismatched definitions, a stopping threshold justified by a bound that doesn't apply cleanly to the quantity being thresholded, and no accounting for the compute the controller itself spends.

What's actually new: the empirical mapping is a service. Longer reasoning does track higher divergence from gold traces on GSM8K, and stepwise entropy over the answer space drops at task-specific rates. The observation that incorrect answers carry higher long-run entropy is a concrete, reproducible finding. The Adaptive Think rule itself—stop when entropy over answers goes below a threshold—is not new in kind; it sits next to confidence-based early exits already in the literature. The contribution is the systematic comparison across two reasoning models and six benchmarks, with code released.

Soft spots, in rough order of seriousness:

1. InfoBias is defined as negative mutual information (Eq. 1) but is computed with HSIC (Appendix C.2). The convergence bound in Eq. 2 is stated for an MI estimator, not for HSIC. That's a mismatch between definition and implementation, and it means the "information bias" numbers are really kernel dependence scores. The findings may survive, but the language does not.

2. The stopping threshold: Eq. 6 compares average entropy to α/(e ln 2), justified by the max of −p log p. That's a per-term bound, not a bound on the entropy of an l-option distribution unless H_avg is explicitly normalized per option. The paper's notation for H_avg is ambiguous—using the same index for steps and answer options—so it's unclear whether the threshold is miscalibrated or just badly written. Either way, the authors need to define it and re-derive the bound.

3. The efficiency claim counts output tokens only. At each step, Adaptive Think estimates the answer distribution, which for open-ended math uses a tree search over continuations. That compute is not in the token numbers, so the end-to-end savings are overstated. A fair comparison needs total FLOPs or wall-clock time.

4. Accuracy deltas are around +1 point, averaged over 5 runs, with no significance testing. Fine as a hint, not as a headline.

The empirical core—early stopping on model confidence can halve output tokens with little accuracy loss—is plausible and aligns with other work on overthinking. The paper deserves a serious referee, but only if the authors are willing to fix the metric definitions, clarify the normalization, and report the controller's cost. I'd send it to review with major revisions expected.

Referee Report

4 major / 6 minor

Summary. The paper studies token efficiency of Large Reasoning Models (LRMs). It introduces two information-theoretic metrics, InfoBias and InfoGain, to analyze how reasoning length relates to semantic drift and stepwise uncertainty reduction. Based on the empirical finding that entropy over the answer space decreases as reasoning proceeds, it proposes Adaptive Think, a stopping rule that halts generation once the average answer-space entropy falls below α·(1/(e ln 2)). The paper reports that on QwQ-32B this strategy improves average accuracy by 1.10% and reduces token usage by 50.80% across six benchmarks compared to the default Vanilla Think mode. Experiments are run on two reasoning models and three standard models across math, knowledge, logic, narrative, and commonsense benchmarks, with code and data promised in the abstract.

Significance. If the reported results are correct, the paper would make a useful practical contribution: a simple, inference-time entropy-based early-stopping rule that substantially reduces reasoning cost without sacrificing accuracy, while also providing descriptive evidence about task-dependent reasoning dynamics. The experimental breadth (five models, six benchmarks, five averaged runs) is a genuine strength, and the availability statement is helpful for reproducibility. However, the current manuscript contains internal inconsistencies in the main results tables, a mismatch between the mathematical definition of InfoBias and its empirical estimator, and an underspecified stopping criterion. These issues must be resolved before the central efficiency claim can be accepted, because the headline numbers and the stated theoretical justification are load-bearing for the paper's contribution.

major comments (4)

[§5.2, Tables 1 and 2] The Δ vs. Vanilla rows in Table 2 are inconsistent with the α=0.1/0.2/0.3 rows shown in the same table. For example, for QwQ-32B on MMLU-Pro, Vanilla Think is 76.29 and Adaptive Think with α=0.1 is 77.14, giving a difference of +0.85, yet the table reports +1.11. For MuSR the reported difference is +1.57 while 47.86−47.12 = +0.74; for CommonsenseQA the reported +1.65 differs from 86.68−85.27 = +1.41. Similar inconsistencies occur for DeepSeek-R1-32B. Because the abstract's headline '+1.10% average accuracy' is derived from these Δ values, the central accuracy claim is not reproducible from the published numbers. The authors must either correct the tables or explicitly report how the Δ values were computed.
[§3.2 and Appendix C.2] InfoBias is defined in Eq. (1) as negative mutual information, and Eq. (2) provides a convergence bound for a mutual information estimator. However, Appendix C.2 states that the empirical dependence is computed using the Hilbert-Schmidt Independence Criterion (HSIC) with a Gaussian kernel. HSIC is a different measure of statistical dependence and does not inherit the convergence bound stated for mutual information. The claim that InfoBias is 'a statistically consistent metric' is therefore not justified by the presented analysis. The manuscript should either compute an actual mutual information estimate to match Eq. (2), or explicitly reframe HSIC as a proxy and remove or weaken the theoretical guarantee.
[§4, Eqs. (3) and (6)] The stopping rule in Eq. (6) is not clearly defined. Eq. (3) defines H_i as the standard Shannon entropy of the answer distribution, whose maximum for l options is log2 l, but Eq. (6) uses the per-term bound 1/(e ln 2) ≈ 0.531, which is the maximum of −p log2 p for a single probability term. The text introduces H_avg^i with the expression H_avg^i = 1/l Σ_{i=1}^l H_i, which is malformed: the summation index and the step index are identical. If H_avg is intended to be the average per-option entropy, that must be defined explicitly and distinguished from Eq. (3); if it is the standard entropy, the bound is inapplicable and the threshold is miscalibrated. In addition, even under a normalized definition, the same α corresponds to a total-entropy threshold that scales with l, so the effective strictness differs substantially between the top-K=5 math setting and the 10-option MMLU-Pro setting, complicating the cross-benchmark comparisons in Tables 1 and 2.
[§5.1–§5.2] The manuscript does not specify how α is selected for the reported results. Table 2 lists three α values per model, and the Δ vs. Vanilla rows appear to mix or select values in a way that is neither documented nor consistent with the shown rows. If α is tuned per benchmark to maximize accuracy, then the headline claim that a single Adaptive Think strategy improves accuracy while reducing tokens is overstated; if α=0.1 is the fixed setting used throughout, the table differences need to be corrected. A validation protocol (e.g., a held-out α, or a sensitivity analysis showing that the qualitative conclusions are stable across α) is required to support the practical recommendation.

minor comments (6)

[Abstract] There is a typo: 'cost-effiiciency' should be 'cost-efficiency'.
[Figure 4 caption] The caption contains 'Vallina Think'; it should read 'Vanilla Think'.
[Eq. (6)] The summation notation in the definition of H_avg^i should be fixed: the index in the sum should be distinct from the step index i, and the expression should be either Σ_{k=1}^l H_k or a properly defined average over answer options.
[Appendix D.2] There is a typo 'eepSeek' that should be 'DeepSeek'.
[§5.1] Although five independent runs are averaged, no variance, standard deviation, or confidence intervals are reported for the accuracy and token numbers. Several reported accuracy differences are small (e.g., +0.60 on ProntoQA near the 99% ceiling), and without variance information it is difficult to assess whether these differences are statistically meaningful.
[Figure 3 and §3.4.2] The caption describes shaded areas as marking the average token proportion used in No-Think mode, but the exact normalization and mapping of shaded regions to the step axis are not explained in the text; a clarifying sentence or legend would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the entropy-based Adaptive Think results are empirical and not entailed by the metric definitions.

full rationale

The paper's central claims are (i) InfoBias grows and InfoGain diminishes with reasoning length, and (ii) an entropy-threshold stopping rule improves accuracy while reducing token use. Neither claim reduces to its own inputs by the paper's equations. InfoBias is defined as negative mutual information against a separately specified ideal trajectory (Eq. 1), not as a function of the later stopping threshold; the InfoGain analysis in Eq. (4) measures entropy reduction per reasoning step and is observational. The stopping rule (Eq. 6) defines 'confidence' operationally as low average entropy, but the reported +1.10% accuracy and -50.80% token changes are not derivable from that definition: they are measured comparisons against Vanilla Think for the reported α setting. No parameter is fitted to the claimed outcome, and no load-bearing self-citation chain appears; references such as Shannon, Paninski, and Muennighoff are independent prior work. The threshold's miscalibration for answer spaces with l>2 (using the per-term bound 1/(e ln 2) instead of log2 l) is a correctness or robustness concern, not circularity, because the method does not use the threshold to define the target result. Accordingly, the derivation chain is self-contained against external benchmarks.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the validity of entropy as a confidence proxy, the HSIC approximation to InfoBias, and the specific entropy bound. All three are assumptions in this paper.

free parameters (3)

alpha (confidence threshold coefficient) = 0.1, 0.2, 0.3 in Table 2; not fixed for Table 1
Controls when to halt reasoning via Eq. (6). The paper sweeps alpha and reports results for multiple values, but does not specify how alpha is selected for the headline numbers.
top-K for answer-space tree search = 5
Defines the candidate answer space for free-response benchmarks (GSM8K, AIME2025) in Appendix C.3; influences entropy estimates.
minimum reasoning step length = 120 characters
Paragraphs shorter than 120 chars are not treated as separate steps (Appendix C.5); this affects when the stopping rule can trigger.

assumptions (4)

domain assumption Entropy of the model's answer-space distribution measures confidence in the correct answer
The Adaptive Think stopping rule in Section 4 assumes lower entropy means the model is confident and correct; however, a model can be confidently wrong.
domain assumption HSIC scores approximate negative mutual information/InfoBias
Equation (1) defines InfoBias as -I(S,T), but the experiments use HSIC with a Gaussian kernel (Appendix C.2). The relation between HSIC and MI is not quantified.
domain assumption Paraphrases of gold solutions approximate the latent ideal reasoning trajectory T
For GSM8K, T is obtained by paraphrasing the gold solution 10 times with Llama3.1-70B (Appendix C.2). If paraphrases differ in style, the 'ideal' trajectory is arbitrary.
ad hoc to paper 1/(e ln 2) is an upper bound for the average entropy used in the stopping criterion
Section 4 uses this bound to normalize the threshold. For distributions over l>2 answers, maximum entropy is log2 l, so the bound is not generally valid for multi-class answer spaces.

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Cite this review

Pith. "Pith review of Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens." pith.science (2026). https://pith.science/paper/M2FKHBTF

@misc{pith2026250518237,
  author       = {Pith},
  title        = {Pith review of: Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M2FKHBTF}},
  note         = {Machine review of arXiv:2505.18237}
}

read the original abstract

The recent rise of Large Reasoning Models (LRMs) has significantly improved multi-step reasoning performance, but often at the cost of generating excessively long reasoning chains. This paper revisits the efficiency of such reasoning processes through an information-theoretic lens, revealing a fundamental trade-off between reasoning length and semantic efficiency. We propose two metrics, InfoBias and InfoGain, to quantify divergence from ideal reasoning paths and stepwise information contribution, respectively. Empirical analyses show that longer reasoning chains tend to exhibit higher information bias and diminishing information gain, especially for incorrect answers. Motivated by these findings, we introduce an entropy-based Adaptive Think strategy that dynamically halts reasoning once confidence is sufficiently high, improving efficiency while maintaining competitive accuracy. Compared to the Vanilla Think approach (default mode), our strategy yields a 1.10% improvement in average accuracy and a 50.80% reduction in token usage on QwQ-32B across six benchmark tasks spanning diverse reasoning types and difficulty levels, demonstrating superior efficiency and reasoning performance. These results underscore the promise of entropy-based methods for enhancing both accuracy and cost-effiiciency in large language model deployment.

Figures

Figures reproduced from arXiv: 2505.18237 by the authors.

**Figure 1.** Understanding thinking inefficiency via Shannon & Weaver’s Communication Model. (a) Technical Level: On the GSM8K dataset, incorrect answers exhibit higher InfoBias and longer token lengths, suggesting that longer reasoning does not necessarily lead to better outcomes. (b) Semantic Level: The InfoGain rate shows a nonlinear decline as the thinking progresses, indicating diminishing contribution to entropy reduction … view at source ↗

**Figure 2.** Normalized InfoBias per token as a function of average reasoning length for different models on the GSM8K dataset. Blue and red points represent instances with correct and incorrect answers, respectively, with density estimates of tokens and InfoBias shown on the top and right. sign of InfoBias saturation or decline—even strong models exhibit rising bias, implying that simply generating more tokens does not guarante… view at source ↗

**Figure 3.** Uncertainty dynamics across different reasoning benchmarks for QwQ-32B. Each set includes two subplots: (1) entropy of the answer distribution vs. normalized reasoning steps, and (2) model-predicted probability of the correct answer over the same steps. Blue/orange lines denote correct/incorrect predictions; solid/dashed lines correspond to Vanilla Think and No-Think. Shaded areas mark the average token proportion u… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: An illustration of four thinking modes on a sample question from the GSM8K dataset. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Proportion of think vs. no-think samples in Gate Think mode and corresponding token usage under Adaptive Think. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Threshold Coefficient 20 40 60 80 100 Accuracy (%) MMLU-Pro MuSR ProntoQA CommonsenseQA 0 200 400 600 800 1000 Avg. …

**Figure 7.** Figure 7: Normalized InfoBias per token as a function of average reasoning length for Llama3.1- 8B-Instruct and Phi-4 on the GSM8K dataset. Blue and red points represent instances with correct and incorrect answers, respectively, with density estimates of tokens and InfoBias sho…

**Figure 8.** Figure 8: Uncertainty dynamics across different reasoning benchmarks for DeepSeek-R1- Distill-32B. It presents similar thinking dynamics on various benchmarks with QwQ-32B. E Case Studies In this section, we showcase model reasoning traces from diverse datasets, including case s…

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Forward citations

Cited by 2 Pith papers

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

Is Your Model Thinking or Just Stagnating? PUMA: Diagnosing Reasoning Pathology via Phase-Momentum Alignment
cs.AI 2026-07 conditional novelty 5.0 of 10

PUMA detects when a reasoning model's entropy drop aligns with hidden-state momentum, truncates at that point, and reports improved accuracy-efficiency on 1.5B-32B reasoning models.
Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey
cs.AI 2025-07 conditional novelty 3.0 of 10

A comprehensive review that categorizes methods for shortening and adaptively triggering chain-of-thought reasoning in large language models.

Reference graph

Works this paper leans on

13 extracted references · 11 canonical work pages · cited by 2 Pith papers

[1]

• The question requires combining multiple knowledge points, hidden conditions, or assumptions

Cannot be answered directly based on the question itself • The answer is not immediately apparent from general knowledge, simple rea- soning, or single-step calculations. • The question requires combining multiple knowledge points, hidden conditions, or assumptions

work page
[2]

• Multiple data sources, conditions, or assumptions must be synthesized to derive the final answer

Multi-step reasoning & information integration • The solution involves sequential logical steps, where each step depends on previous conclusions. • Multiple data sources, conditions, or assumptions must be synthesized to derive the final answer

work page
[3]

• It involves recursive reasoning, mathematical induction, or constructing coun- terexamples

Strict mathematical/logical proof or recursive deduction • The problem requires formal proof (e.g., deductive reasoning, axiomatic proofs). • It involves recursive reasoning, mathematical induction, or constructing coun- terexamples

work page
[4]

• There may be multiple valid approaches, requiring deep analysis and compari- son

Non-trivial strategy or non-unique solution • The question requires evaluating multiple potential solutions andchoosing the optimal one. • There may be multiple valid approaches, requiring deep analysis and compari- son

work page
[5]

YES” (Deep Think Mode required)If the question meets at least 2 criteria, return “YES

Systematic reasoning & hypothesis-based deduction • The question requires establishing hypotheses and systematically deriving con- clusions. • Multiple variables and complex relationships are involved, requiring a rigorous analytical process. 19 Output Format: • “YES” (Deep Think Mode required)If the question meets at least 2 criteria, return “YES” and br...

work page
[9]

E: (20,0) G: (0,65) F: (0,13) Order of vertices: D-E-G-F-D. Compute shoelace formula: List the coordinates in order and repeat the first at the end: (4,0), (20,0), (0,65), (0,13), (4,0) Calculations: Multiply x by next y, sum them: 4*0 + 20*65 + 0*13 + 0*0 = 0 + 1300 + 0 + 0 = 1300 Then multiply y by next x, sum them: 0*20 + 0*0 + 65*0 + 13*4 = 0 + 0 + 0 ...

work page
[11]

Triangle BCE. 4. Quadrilateral CEM...? Alternatively, divide the heptagon into triangles by drawing diagonals from A: Triangles: A-F-N, A-N-B, A-B-C, A-C-E, A-E-M, and so on. 38 Hmm, this might not be straightforward. Alternatively, use the shoelace formula with the numerical coordinates for clarity. Let me try plugging in approximate values with p=80.73:...

work page
[12]

C=(80.73,42) 6

B(28, 0) 5. C=(80.73,42) 6. E(20,0) 7. M=(19.06,12) 8. A(0,0) Apply shoelace formula numerically: Compute each term: Term1: x1*y2 - x2*y1 = 0*6 - 11.53*0 =0 Term2: x2*y3 -x3*y2 =11.53*(-30) - (-17.65)*6 =-345.9 +105.9 =-240.0 Term3: x3*y4 -x4*y3 =-17.65*0 -28*(-30) =0 +840=840 Term4: x4*y5 -x5*y4 =28*42 -80.73*0=1176 -0=1176 Term5: x5*y6 -x6*y5 =80.73*0 -...

work page

Show all 13 references

[288]

Alternatively, use vectors or mass point? Hmm

Let me try parameterizing. Alternatively, use vectors or mass point? Hmm. Alternatively, use area ratios. Since we have points divided in certain ratios along the sides, perhaps we can express areas in terms of the total area of ABC? Given that DEGF’s area is 288, then maybe t...
[300]

</think> To solve the problem, we start by noting the given lengths and the fact that the area of quadrilateral DEGF is 288

Hence, I think the answer is 300. </think> To solve the problem, we start by noting the given lengths and the fact that the area of quadrilateral DEGF is 288. We place point A at (0,0) , point B at (28,0) , and point C at (p, q). Using the given segment lengths, we determine t...
[1176]

heptagon AFNBCEM

Half of that is 588. Which is exactly the area of the whole triangle, so that can’t be. So something is wrong here. It implies the heptagon covers the entire triangle, but the problem states that quadrilateral DEGF is inside the triangle with area 288, so the heptagon’s area s...
[2022]

doi: 10.18653/v1/2022.acl-long.365

Association for Computational Linguistics. doi: 10.18653/v1/2022.acl-long.365. URL https://aclanthology.org/2022.acl-long.365/. Niklas Muennighoff, Zitong Yang, Weijia Shi, Xiang Lisa Li, Li Fei-Fei, Hannaneh Hajishirzi, Luke Zettlemoyer, Percy Liang, Emmanuel Candès, and Tats...

2022 arXiv
[2024]

overthinking

Association for Computational Linguistics. doi: 10.18653/v1/2024.emnlp-main.814. URL https://aclanthology.org/2024.emnlp-main.814/. Bo Pang, Hanze Dong, Jiacheng Xu, Silvio Savarese, Yingbo Zhou, and Caiming Xiong. Bolt: Bootstrap long chain-of-thought in language models witho...

2024 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

• The question requires combining multiple knowledge points, hidden conditions, or assumptions

Cannot be answered directly based on the question itself • The answer is not immediately apparent from general knowledge, simple rea- soning, or single-step calculations. • The question requires combining multiple knowledge points, hidden conditions, or assumptions

work page

[2] [2]

• Multiple data sources, conditions, or assumptions must be synthesized to derive the final answer

Multi-step reasoning & information integration • The solution involves sequential logical steps, where each step depends on previous conclusions. • Multiple data sources, conditions, or assumptions must be synthesized to derive the final answer

work page

[3] [3]

• It involves recursive reasoning, mathematical induction, or constructing coun- terexamples

Strict mathematical/logical proof or recursive deduction • The problem requires formal proof (e.g., deductive reasoning, axiomatic proofs). • It involves recursive reasoning, mathematical induction, or constructing coun- terexamples

work page

[4] [4]

• There may be multiple valid approaches, requiring deep analysis and compari- son

Non-trivial strategy or non-unique solution • The question requires evaluating multiple potential solutions andchoosing the optimal one. • There may be multiple valid approaches, requiring deep analysis and compari- son

work page

[5] [5]

YES” (Deep Think Mode required)If the question meets at least 2 criteria, return “YES

Systematic reasoning & hypothesis-based deduction • The question requires establishing hypotheses and systematically deriving con- clusions. • Multiple variables and complex relationships are involved, requiring a rigorous analytical process. 19 Output Format: • “YES” (Deep Think Mode required)If the question meets at least 2 criteria, return “YES” and br...

work page

[6] [9]

E: (20,0) G: (0,65) F: (0,13) Order of vertices: D-E-G-F-D. Compute shoelace formula: List the coordinates in order and repeat the first at the end: (4,0), (20,0), (0,65), (0,13), (4,0) Calculations: Multiply x by next y, sum them: 4*0 + 20*65 + 0*13 + 0*0 = 0 + 1300 + 0 + 0 = 1300 Then multiply y by next x, sum them: 0*20 + 0*0 + 65*0 + 13*4 = 0 + 0 + 0 ...

work page

[7] [11]

Triangle BCE. 4. Quadrilateral CEM...? Alternatively, divide the heptagon into triangles by drawing diagonals from A: Triangles: A-F-N, A-N-B, A-B-C, A-C-E, A-E-M, and so on. 38 Hmm, this might not be straightforward. Alternatively, use the shoelace formula with the numerical coordinates for clarity. Let me try plugging in approximate values with p=80.73:...

work page

[8] [12]

C=(80.73,42) 6

B(28, 0) 5. C=(80.73,42) 6. E(20,0) 7. M=(19.06,12) 8. A(0,0) Apply shoelace formula numerically: Compute each term: Term1: x1*y2 - x2*y1 = 0*6 - 11.53*0 =0 Term2: x2*y3 -x3*y2 =11.53*(-30) - (-17.65)*6 =-345.9 +105.9 =-240.0 Term3: x3*y4 -x4*y3 =-17.65*0 -28*(-30) =0 +840=840 Term4: x4*y5 -x5*y4 =28*42 -80.73*0=1176 -0=1176 Term5: x5*y6 -x6*y5 =80.73*0 -...

work page