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REVIEW 4 major objections 4 minor 5 cited by

AlphaOne: Reasoning Models Thinking Slow and Fast at Test Time

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

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Pith's one-line read One training-free schedule makes reasoning models think slow, then fast, and solve more problems.

desk verdict AlphaOne's scheduling idea is real and well-ablated, but the paper's universal-dominance claim is contradicted by its own Table 1 and needs correction before publication. read the letter →

arxiv 2505.24863 v1 pith:7OXKREG2 submitted 2025-05-30 cs.CL

Junyu Zhang , Runpei Dong , Han Wang , Xuying Ning , Haoran Geng , Peihao Li , Xialin He , Yutong Bai
show 3 more authors
Jitendra Malik Saurabh Gupta Huan Zhang
This is my paper
classification cs.CL
keywords test-timescalinglargereasoningmodelsprogressmodulationalphamomentslow-to-fastschedulingBernoulliprocesss1ChainofDraft
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

AlphaOne ($\alpha$1) claims that a single scalar controls how much a large reasoning model deliberates before answering, and that the best way to spend that deliberation is to think slowly early and then switch to fast reasoning. The paper introduces the $\alpha$ moment, the point in generation where the thinking phase has been scaled to $\alpha$ times its natural length, and uses a stochastic Bernoulli process to insert “wait” transition tokens before that moment and a deterministic `` insertion after it. Evaluated on six math, code, and science benchmarks with three open reasoning models from 1.5B to 32B parameters, $\alpha$1 reports higher Pass@1 than the vanilla model and than two training-free baselines—s1, which monotonically adds slow thinking, and Chain of Draft, which monotonically removes it—while often using fewer tokens. If the claim holds, test-time scaling of reasoning models becomes a schedule-design problem rather than a search or fine-tuning problem, with a universal knob that unifies existing monotonic scaling strategies.

What carries the argument

The central object is the $\alpha$ moment: the generation timestamp at which the number of generated thinking tokens reaches $\alpha N_{\mathrm{think}}$, where $N_{\mathrm{think}}$ is the model's average natural thinking-token length. Before that moment, $\alpha$1 models slow-thinking activation as $\mathrm{Bernoulli}(p_{\mathrm{wait}})$ with $p_{\mathrm{wait}} = S(t)$ from a user-specified schedule; the paper adopts linear annealing, starting slow and decaying to zero. After the $\alpha$ moment, $\alpha$1 deterministically replaces any “wait” transition token with `</think>`, terminating slow thinking and curbing the “slow thinking inertia” that would otherwise keep the model deliberating. This two-phase mechanism is what allows sparse and dense modulation to be unified: a constant near-zero $p_{\mathrm{wait}}$ with $\alpha > 1$ approximates s1, while $\alpha = 1$ and $p_{\mathrm{wait}} = 0$ recovers vanilla generation.

What would settle it

Run $\alpha$1 on a benchmark split where the 10 calibration questions have unusually short thinking lengths, then evaluate on a held-out split with much longer reasoning chains; if the $\alpha$ moment fires too early and accuracy falls below the vanilla model, the 10-sample estimate is the load-bearing element rather than the schedule itself.

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Extended reading notes

Core claim

The paper's central discovery is that reasoning models solve problems better when slow thinking is front-loaded: a linearly annealed Bernoulli process that frequently appends “wait” after structural delimiters during the first $\alpha$-scaled portion of the thinking phase, followed by replacing every further “wait” with `</think>`, improves accuracy over both the base model and over monotonic slow-thinking increase (s1) and monotonic thinking-budget reduction (Chain of Draft). The authors report an average accuracy boost of +6.15% for the 1.5B model with roughly 14% fewer generated tokens, and claim $\alpha$1's average gains exceed Chain of Draft by +3.12 percentage points and s1 by +4.62 percentage points across all models and benchmarks. They also report that “slow thinking first, then fast thinking” is the better scheduling strategy for LRMs, in contrast to the human pattern of fast-then-slow deliberation.

Load-bearing premise

The load-bearing premise is that the average thinking-phase token length $N_{\mathrm{think}}$, estimated from only 10 randomly sampled test questions per benchmark, is representative enough that the $\alpha$ moment lands correctly on the real questions; if those samples misrepresent the actual questions or the distribution shifts, the schedule misfires and the gains could vanish.

Editorial extensions

If this is right

  • On the paper's evidence, the tested o1-style reasoning models can be improved without training by choosing $\alpha$ and a slow-to-fast schedule, which changes what practitioners can do when test-time compute is limited.
  • Because $\alpha$1 reports higher accuracy with fewer tokens than the monotonic baselines, token budget and reasoning depth are not simply traded off; the right schedule can improve both at once.
  • The existence of an optimal $\alpha$ (around 1.4 in the reported settings) means that blindly scaling thinking time is suboptimal; there is a sweet spot that depends on model and benchmark.
  • The framework unifies s1 and Chain of Draft as special cases, so observations about those methods can be reinterpreted as points on a shared schedule family.

Reading between the lines

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

  • Because the method needs only the average thinking length, not per-question difficulty, a natural extension is to make $\alpha$ or $N_{\mathrm{think}}$ adaptive per query based on confidence or difficulty; the paper does not test this.
  • The dependence on “wait” as the transition token suggests the mechanism might generalize to any model-specific trigger; if it does, replacing “wait” with an arbitrary token should still help, which is a testable prediction.
  • Since $\alpha$1 is training-free and parallel scaling is non-conflicting, combining it with best-of-N or self-consistency could compound gains; the paper lists this as a future direction but does not demonstrate it.
  • The reported contrast with humans (slow-first for LRMs versus fast-first for people) is an observation about current model training rather than an immutable law; future models that learn to self-schedule might make an external $\alpha$ unnecessary.
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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. The paper proposes AlphaOne (α1), a training-free test-time decoding strategy for large reasoning models (LRMs). The method defines an "α moment" at a token budget of α times the average thinking-phase length; before this moment it stochastically inserts the slow-thinking transition token "wait" after "\n\n" according to an annealed Bernoulli schedule, and after this moment it replaces "wait" with "</think>" to force a shift to fast reasoning. Experiments on three LRMs (1.5B, 7B, 32B) across six benchmarks (AIME24, AMC23, Minerva, MATH500, LiveCodeBench, OlympiadBench) compare α1 against the base model, s1, and Chain-of-Draft in terms of Pass@1 and token count. The paper claims that α1 consistently outperforms all baselines on all benchmarks, and distills the insight that "slow thinking first, then fast thinking" is the best schedule for LRMs.

Significance. The core idea of a parameterized, dense slow-to-fast reasoning schedule with a deterministic cutoff is simple, novel, and potentially useful for efficient LRM inference. The paper includes valuable ablations (scheduling functions, α scaling, wait-token frequency, post-α modulation, and transitioning-token choice) and reports per-benchmark N_think values, which aids reproducibility. If the empirical claims survive correction, the method offers a cheap, training-free way to improve reasoning accuracy while reducing token use on many benchmarks. However, the headline dominance claim is contradicted by the paper's own Table 1, and the evaluation protocol uses test-set information to set key parameters and reports no uncertainty quantification. These issues materially weaken the current evidence, although they are fixable within the manuscript's scope.

major comments (4)
  1. [§4.2, Table 1] This is the central empirical claim of the paper, so the overstatement is load-bearing and must be fixed.
  2. [§4.1, Table 3, App. A.2] The concern is not that the framework is circular in a formal sense; rather, the empirical evaluation is not fully out-of-sample.
  3. [§4.2] The absence of uncertainty quantification is particularly problematic for the cells where α1 trails by a small margin, since those margins are comparable to the margins it leads by elsewhere.
  4. [§B.1] This is a presentation issue but it affects reproducibility of the ablation claim.
minor comments (4)
  1. [Eq. (2) and Fig. 6/9] The REP metric's normalization is described only as "dividing the current thinking phase token length by the maximum token length," but the maximum is not specified (presumably 8192). It would help to state the denominator explicitly and to note that REP is sensitive to token counts near zero, which may make the metric less robust for methods with very short thinking phases.
  2. [§3.3] The term "slow thinking inertia" is used as an explanatory concept but is never operationalized; consider defining it more concretely (e.g., by the measured probability of generating "wait" or "</think>" before and after the α moment). The post-α ablation in Table 2 provides empirical support, but a quantitative definition would make the mechanism clearer.
  3. [§4.1] The sentence "We set α as 1.4" appears in the implementations paragraph, but Figure 5 later shows that the optimal α varies by model and benchmark and can be as high as ~5.6. Clarify whether α=1.4 is the value used for all Table 1 results or only the default, and whether any per-benchmark tuning was performed. The current presentation is ambiguous about this key parameter.
  4. [Limitations] The Limitations section honestly acknowledges the need for test questions to estimate N_think, which is good. However, the same limitation is not mentioned in the abstract or §4.2, where the method is presented as universally applicable; please make the conditions of applicability explicit in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: AlphaOne's framework is an empirical construction whose test-set dependence and dominance overclaim are validity issues, not self-referential derivation.

full rationale

The paper's central machinery is definitional and empirical rather than derived: the α moment is defined as the token position reaching α·N_think (Section 3.1), the pre-α slow-thinking schedule is defined as a Bernoulli process with p_wait := S(t) (Section 3.2), and the post-α behavior is defined as replacing 'wait' with '</think>' (Section 3.3). No equation reduces a reported result to its own inputs by construction. The claim that α1 'unifies and generalizes' s1 and CoD is presented as an explicit design reduction, not as a prediction derived from first principles. The empirical findings (linear anneal is best, post-α modulation helps, slow-then-fast is effective) are comparisons between ablations, not consequences of the definitions. The main validity concerns are not circularity: N_think is estimated from 10 test questions and α is set to 1.4 after observing scaling curves on the same benchmarks, and Section 4.2's statement that α1 'consistently yields a higher problem-solving accuracy than all baseline methods across all models and benchmarks' is contradicted by Table 1 (e.g., QwQ-32B on Minerva, MATH500, and Olympiad; DeepSeek-R1-Distill-7B on Minerva and MATH500). The paper's Limitations section itself acknowledges the test-data dependence: 'This paper obtains it by first running LRMs on 10 random samples, which requires marginal cost. However, in case that no test questions are available, ALPHAONE can only rely on an empirical thinking phase length that may be suboptimal.' This is a leakage and robustness limitation, not an equation-level circularity. Self-citations to co-authored prior work appear only in future-work and multimodal context, and are not load-bearing for the α1 method. Therefore, under the stated criteria, the derivation is self-contained and no circular step can be exhibited.

Assumptions & free parameters 4 free parameters · 3 assumptions · 2 invented entities

The central method rests on two tuned quantities (α and N_think) plus three domain assumptions about how token-level interventions affect the model's reasoning mode. N_think is estimated from test data, which couples the method's success to the evaluation set and weakens the independence of the reported gains.

free parameters (4)
  • alpha = 1.4
    Global scaling factor for the thinking phase budget, chosen by hand. Section 4.1 states 'We set α as 1.4' after the scaling study in Figure 5.
  • N_think (average thinking phase token length) = per-benchmark values in Table 3, e.g., 4130 for AIME24 with 1.5B model
    Measured from 10 random test questions per benchmark. The α moment is defined as the point where generated tokens reach α*N_think, so this estimate directly controls the schedule.
  • scheduling function S(t) = linear annealing: S(t) = -1/T_m * t + 1
    Chosen as the best among four variants in Section 4.3.1. The schedule shape is a modeling choice, not derived from theory.
  • gamma (exponential anneal) = 0.3
    Hyperparameter for the exponential anneal variant in Section 4.3.1; used only in the ablation study, not in the main results.
assumptions (3)
  • domain assumption Assumption 1: The reasoning velocity of slow thinking is smaller than that of fast thinking.
    Stated in Section 2 to justify the reasoning progress model. It is not empirically verified in this paper.
  • domain assumption Appending ' wait' after the structural delimiter '\n\n' activates slow thinking.
    Adopted from Yang et al. (2025c) and used in Section 3.2. The paper provides no independent test of the causal effect of ' wait' tokens.
  • domain assumption Replacing ' wait' with '</think>' after the α moment deterministically terminates slow thinking and switches to fast reasoning.
    Postulated in Section 3.3 to counter 'slow thinking inertia'. Only indirect ablation evidence is provided, not a direct measurement of reasoning mode.
invented entities (2)
  • α moment
    purpose: Threshold in the thinking phase where the generated token count reaches α*N_think; after this point slow thinking is suppressed.
    A definitional construct introduced in Section 3.1. It has no external measurable handle beyond the method's own definitions.
  • Slow thinking inertia
    purpose: Explains why LRMs continue generating slow-thinking tokens after the pre-α phase, motivating the deterministic termination step.
    Inferred from the ablation in Table 2, where removing post-α modulation causes performance to drop. It is not directly measured.

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Cite this review

Pith. "Pith review of AlphaOne: Reasoning Models Thinking Slow and Fast at Test Time." pith.science (2026). https://pith.science/paper/7OXKREG2

@misc{pith2026250524863,
  author       = {Pith},
  title        = {Pith review of: AlphaOne: Reasoning Models Thinking Slow and Fast at Test Time},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7OXKREG2}},
  note         = {Machine review of arXiv:2505.24863}
}
abstract

This paper presents AlphaOne ($\alpha$1), a universal framework for modulating reasoning progress in large reasoning models (LRMs) at test time. $\alpha$1 first introduces $\alpha$ moment, which represents the scaled thinking phase with a universal parameter $\alpha$. Within this scaled pre-$\alpha$ moment phase, it dynamically schedules slow thinking transitions by modeling the insertion of reasoning transition tokens as a Bernoulli stochastic process. After the $\alpha$ moment, $\alpha$1 deterministically terminates slow thinking with the end-of-thinking token, thereby fostering fast reasoning and efficient answer generation. This approach unifies and generalizes existing monotonic scaling methods by enabling flexible and dense slow-to-fast reasoning modulation. Extensive empirical studies on various challenging benchmarks across mathematical, coding, and scientific domains demonstrate $\alpha$1's superior reasoning capability and efficiency. Project page: https://alphaone-project.github.io/

Figures

Figures reproduced from arXiv: 2505.24863 by the authors.

Figure 1
Figure 1. Conceptual illustration of reasoning modu￾lation strategies. Our α1 employs a slow-to-fast rea￾soning schedule controlled by α. α1 scales more efficiently than monotonously increasing method s1 (yellow) and generally outperforms monotonously de￾creasing (purple) approaches. to slow down reasoning progress automatically. Is such automatic slowing down of reasoning progress determined by LRMs sufficiently reliable? Ac… view at source ↗
Figure 2
Figure 2. Overview of ALPHAONE (α1). Here represents α moment (Section 3.1). α1 applies dense reasoning modulation via a user-defined slow thinking scheduling in pre-α moment. In addition, α1 utilizes a post-α moment modulation by replacing slow thinking transitioning tokens “wait” to “</think>”, which fosters fast thinking. Specifically, α determines when the slow-to-fast reasoning transition occurs. For example, reducing α … view at source ↗
Figure 3
Figure 3. Visualization of different scheduling strategies. We detail the functions in Section 4.3.1. Here represents α moment, which we elaborate in Section 3.1, and denotes the end of the thinking phase. Vanilla s1 Constant Linear Increase Exponential Anneal Linear Anneal 30 32 34 36 38 40 42 44 46 46 48 50 52 54 56 +5.3% Pass @1 (%) (c) DeepSeek-R1-Distill￾Qwen-1.5B (d) DeepSeek-R1-Distill￾Qwen-7B Pass @1 (%) +6.7% Olympia… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Ablation study of different scheduling strategies on (a-b) AMC23 and (c-d) OlympaidBench. 4.3 Analytic Results In this section, we analyze α1 by systematically addressing the following five questions: 4.3.1 What scheduling strategy is better? As shown in [PITH_FULL_IM…
Figure 5
Figure 5. Figure 5: Scaling property of α. We scale α from 0 to the maximum value restricted by the maximum token length, and plot the corresponding reasoning Pass@1 and average thinking phase token length on AMC23 and MATH500. 𝛼1 (Ours) CoD s1 -0.58 -2.73 -2.49 -9.98 -0.86 +11.1 +4.48 +1…
Figure 6
Figure 6. Figure 6: Scaling efficiency analysis with REP us￾ing Deepseek-R1-distill-Qwen-1.5B. The REP metric is introduced in Eq. (2). racy. This indicates that monotonously increasing the thinking phase budget does not consistently bring better reasoning performance, and it is criti￾cal…
Figure 7
Figure 7. Figure 7: Scaling property of “wait” frequency under constant scheduling on AMC23 and OlympiadBench. Increasing pconstant leads to a higher frequency of yielding “wait” in the Bernoulli process Bernoulli(pwait) [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Ablation study of different scheduling strategies on AIME24. B Additional Ablation Study B.1 Scheduling Strategy In addition to the results in [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

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Pith tools

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