Beyond the Opening: Tracing the First Token's Persistent Influence on Reasoning Length

Introduction

Recent reasoning models, such as DeepSeek-R1 [1], have demonstrated strong performance on complex tasks including mathematics and programming. These models solve problems by generating explicit chains of thought (CoTs) before producing final answers [6]. However, the length of these reasoning traces can vary substantially across problems and even across different generations of the same problem [2, 3], resulting in large differences in inference cost and potentially task performance [7, 8, 9, 18]. Understanding how reasoning length is determined during autoregressive generation is therefore important for characterizing the behavior of reasoning models and developing more effective ways to control their reasoning processes [19].

Reasoning length is a property of the entire generated sequence, whereas generation proceeds through individual token choices. Understanding how these choices affect overall length is therefore an important aspect of understanding what determines reasoning length. Previous studies show that local token choices can substantially affect reasoning length [8, 21]. In particular, studies of the first reasoning token (hereafter, the first token) show that its distribution is concentrated on a few candidate tokens associated with markedly different reasoning lengths, and that changing this token can alter subsequent reasoning length [2, 3]. However, the mechanisms through which local token choices affect subsequent token predictions and lead to differences in reasoning length remain insufficiently understood. The few prevalent first-token candidates and their substantial length effects offer a tractable setting for studying how this choice affects reasoning length through subsequent generation.

Intuitively, the first token may affect subsequent reasoning length by changing the early text generated after it. To test whether its length effect depends entirely on differences in this early text, we take a prefix from an existing reasoning trace and replace only its first token, keeping remaining prefix tokens unchanged. We then allow the model to continue from the modified prefix. Even with the remaining prefix tokens held fixed, substituting a first token typically associated with longer reasoning significantly increases the remaining reasoning length, whereas substituting one associated with shorter reasoning reduces it. These results show that early textual differences do not fully explain the first-token length effect, as the first token can still influence subsequent reasoning length when the intervening prefix text is held fixed.

To trace this persistent influence, we compare next-token distributions under different first-token conditions while holding all other prefix tokens fixed, examining sensitivity to the first token at each generation position. We find that these differences in next-token distributions are highly concentrated at a small set of positions, which also exhibit stronger attention to the first token. We perform two interventions to test whether these positions contribute to the length effect. Blocking their attention to the first token substantially reduces the reasoning-length gap between first-token conditions. Using next-token distributions from a different first-token condition at these positions substantially changes subsequent reasoning length, even when the original first token is retained. Together, these results suggest that attention to the first token at a few sensitive positions helps sustain its influence on subsequent predictions and reasoning length. More broadly, this study links a local token choice to overall reasoning length through its persistent influence on subsequent token predictions. Our key findings are threefold.

• The first-token length effect persists beyond the intervening reasoning text. Even when the subsequent reasoning prefix is held fixed, changing the first token substantially alters the remaining reasoning length.

• The first token’s persistent influence on subsequent predictions is concentrated at a small set of generation positions, which also exhibit stronger attention to the first token.

• Sensitive positions contribute to sustaining the first-token length effect. Blocking their attention to the first token reduces the length gap, while replacing their next-token distributions redirects reasoning length in both directions.

Related Work

Local token choices and reasoning length.

Interventions on token choices during generation can substantially change reasoning length. [8] extend reasoning through budget forcing, suppressing termination and appending Wait when the model attempts to stop. Conversely, [21] shorten reasoning by suppressing reflection-related tokens such as Wait and Hmm during decoding. At the start of reasoning, [2] identify first tokens associated with fast and slow thinking and show that forcing a short-associated first token reduces reasoning length. [3] further connect initial token choices to linear and backtracking reasoning modes with different lengths and accuracies. These studies demonstrate that local token choices can alter reasoning length. We build on this work by examining how the first token’s influence on length is carried through subsequent generation.

Internal representations and control of reasoning length.

Reasoning length can be controlled through budget forcing [8], reinforcement learning with length constraints [9], and training on compressed reasoning traces [10]. Complementary work studies internal representations. [4] predict reasoning length from question activations and identify a direction that modulates reasoning strength. Activation steering controls thinking speed [2] and behaviors such as backtracking and uncertainty [11]. ThinkEdit edits attention-head output projections to mitigate overly short reasoning [5], while FlowSteer learns a nonlinear transformation from verbose to concise reasoning representations [12]. These approaches demonstrate ways to regulate reasoning length.

Preliminaries

Problem Formulation

Given a problem $x$, a reasoning model generates a chain of thought $r=(r_1,\ldots,r_L)$ followed by a final answer. We define reasoning length as $L=|r|$, excluding reasoning delimiters and the final answer, and denote the first reasoning token by $z=r_1$. Our goal is to understand how the influence of $z$ on reasoning length persists as generation unfolds, and through which later generation states it operates.

First-Token Effects on Reasoning Length

We illustrate the first-token effect on reasoning length using GSM8K. Under natural sampling, the first reasoning token is concentrated in a small set of first tokens, primarily Okay, Alright, To, and First (Figure 1a). Reasoning traces beginning with Okay or Alright are substantially longer on average than those beginning with To or First (Figure 1b). This length contrast persists when we force the reasoning trace for each question to begin with each of the four tokens, indicating that the first token can shape subsequent reasoning length rather than merely correlate with it (Figure 1c). Further experimental details and numerical results are provided in Appendix § 9. These observations motivate our central question: how does the first token influence reasoning length as reasoning unfolds?

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Experimental Setup

Models and tasks.

We study three DeepSeek-R1 distilled models [1]: Distill-Qwen-1.5B, Distill-Qwen-7B, and Distill-Llama-8B, abbreviated as Qwen-1.5B, Qwen-7B, and Llama-8B. We use all 500 MATH-500 test questions [14, 15] and a fixed random sample of 500 GSM8K training questions [13], with the same question sets across models and conditions. HumanEval [16] and FOLIO [17] provide coding and logical reasoning tasks for the subsequent generalization analysis.

Reference trajectories.

We use two types of reference trajectories to study first-token effects on reasoning length. Naturally sampled trajectories characterize first-token frequencies and their association with reasoning length. We focus on Okay, Alright, First, and To, which account for most naturally occurring firsts across our evaluated models and datasets (Appendix § 9). Forced first token trajectories begin with one of these long-associated (Okay, Alright) or short-associated (First, To) tokens, followed by freely sampled continuation. They serve as unmodified references for subsequent intervention experiments, with comparisons matched by question.

Sampling and evaluation.

We draw three samples per question and condition at temperature $0.6$ and top-$p=0.95$. Reasoning lengths are measured within an 8,192-token observation horizon; unfinished traces are retained at their observed lengths. We report total reasoning length for free generation and remaining length for prefix-preserving interventions. Additional details are provided in Appendix § 8.

How the First Token Shapes Reasoning Length

To understand how the first token shapes subsequent reasoning length, we first use prefix-preserving interventions to examine whether its influence persists after a reasoning path has formed. We then identify later generation states whose predictions are sensitive to the first-token condition. Finally, we use attention masking and distribution replacement to test whether direct reads of the first token at these states sustain length differences and whether changing their generation choices can reproduce the length effect.

Persistent First-Token Influence

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Setup.

To test whether the first-token effect persists beyond the initial selection of a reasoning path, we replace the first token of a forced first token trajectory while holding the subsequent prefix tokens fixed. For prefix lengths $K\in\{50,100,150,200\}$, we replace long-associated first token (Okay or Alright) with short-associated first token (To or First), and vice versa:

We sample three continuations from each edited prefix and compare their mean remaining reasoning length with an unchanged-prefix reference, averaging the observed source suffix $r_{K+1:L}$ and two newly sampled continuations. Further experimental details and results are provided in Appendix § 10.

The length effect extends beyond the initial text.

Figure 2 shows that changing the first token shifts the remaining reasoning length toward the tendency associated with the replacement first token. Specifically, replacing a long-associated first token with a short-associated one shortens the subsequent reasoning, while the reverse replacement lengthens it. If the first token affected reasoning length only by inducing different early text, preserving that text should eliminate its influence on subsequent generation. However, the effect remains evident even when the following 199 tokens are preserved. These results indicate that the first token’s influence on reasoning length cannot be explained solely by the early text it induces, and persists even when the intervening text is held fixed.

Model	Opening	Rem. tokens	Acc. (%)
Qwen-1.5B	Source	1,461	88.6
	To	419	86.3
	First	525	86.9
Qwen-7B	Source	1,019	94.8
	To	483	93.7
	First	347	94.5
Llama-8B	Source	1,348	89.0
	To	683	86.6
	First	666	85.9
Qwen-1.5B	Source	48	74.1
	Okay	510	75.4
	Alright	496	77.4
Qwen-7B	Source	43	82.8
	Okay	75	83.0
	Alright	62	82.4
Llama-8B	Source	47	54.5
	Okay	235	56.3
	Alright	194	55.4

Edited prefixes remain compatible with effective question answering.

Because the preserved prefix text was generated under the original first token, replacing that token may disrupt reasoning and thereby alter length. However, Table 1 shows that shortened continuations still answer most questions correctly, though less accurately than the matched source trajectories, while lengthened continuations generally maintain or improve mean accuracy. These results suggest that the length changes do not simply reflect a general breakdown in answering ability caused by prefix editing.

First-token Sensitivity Concentrates at Few Positions

Setup.

Since reasoning unfolds through successive next-token predictions, we investigate the first token’s influence on subsequent generation by examining how replacing it changes these predictive distributions. Using the controlled setting established in the previous section, we compare predictive distributions under different first-token conditions while keeping the subsequent reasoning prefix fixed. At position $t$, we define

and quantify the sensitivity of the next-token prediction to the first-token condition using Jensen–Shannon (JS) divergence [20]. For a long-associated first token $z_{\mathrm{long}}$ and a short-associated first token $z_{\mathrm{short}}$, we define:

We present First–Okay as a representative long–short pair; results for the other three pairs are provided in Appendix § 11.

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Sensitivity is concentrated at a small fraction of positions.

Figure 3(a) shows that, across models and datasets, the highest-JS 10% of positions account for approximately 69–82% of total JS. Sensitivity to the first-token condition is therefore highly concentrated along reasoning trajectories, with a small fraction of positions accounting for most of the difference in predictive distributions. Figure 3(b) illustrates this pattern in an example trajectory. JS remains relatively low at most positions, interspersed with distinct peaks. Although these peaks are denser and larger early in generation, they also occur later, showing that high sensitivity is not confined to the initial reasoning stage. Additional concentration analyses are provided in Appendix § 11.

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High-JS positions are more strongly associated with the first token.

We further examine attention to the first token to assess whether high-JS positions are more strongly associated with it. Figure 4 shows that, across models, datasets, and first token conditions, positions with higher JS tend to assign greater attention to the first token. In the highest JS decile, first-token attention lies at the 77th–82nd within-trajectory percentile on average, and the mean within-trajectory Spearman correlation between JS and first-token attention ranges from 0.32 to 0.40. Since both quantities may vary systematically with generation position, we remove their linear position trends and find that the correlation remains positive, ranging from 0.25 to 0.38. These results indicate that high-JS positions not only exhibit greater predictive sensitivity to the first-token condition, but are also more strongly associated with the first token itself.

Testing the Role of Sensitive Positions in Reasoning Length

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Setup.

We perform two interventions to test whether sensitive positions contribute to the first-token length effect. Attention blocking masks attention to the first reasoning token whenever $J_t>\tau$. For every layer $\ell$ and head $h$, we set the corresponding pre-softmax attention logit to

while leaving all other logits unchanged before softmax. This tests whether direct attention to the first token at sensitive positions contributes to the length effect. Distribution replacement instead uses

where $z$ and $z'$ denote the source and alternative first tokens, respectively. Both distributions condition on the same subsequent reasoning prefix. We sample the next token from $\widetilde{p}_t$ to test whether changing predictions at sensitive positions shifts subsequent reasoning length. For both interventions, we focus on First and Okay as frequent short- and long-associated first tokens, respectively, using the same JS contrast as in § 5.2.

We use absolute thresholds because JS distributions differ across first token conditions and reasoning lengths. Selecting a fixed percentage would assign more intervention positions to longer chains, potentially including positions with low sensitivity. We evaluate both interventions at JS thresholds $\tau\in\{0.05,0.1,0.2\}$.

Model	Opening	Every 3	$0.2$	$0.1$	$0.05$
Qwen-1.5B	First	33.3	6.1	10.9	16.9
	Okay	33.4	5.2	9.7	15.7
Qwen-7B	First	33.4	6.2	10.4	16.1
	Okay	33.4	6.3	10.9	16.6
Llama-8B	First	33.3	9.5	16.2	23.2
	Okay	33.4	8.5	14.9	21.4
Qwen-1.5B	First	33.3	2.1	3.9	6.7
	Okay	33.3	0.6	1.6	3.9
Qwen-7B	First	33.3	4.9	8.1	12.0
	Okay	33.3	2.6	5.5	8.9
Llama-8B	First	33.3	5.3	9.5	13.9
	Okay	33.3	2.9	5.5	8.6

First-token attention at sensitive positions sustains the length effect.

Figure 5 shows that blocking attention to the first token at selected positions reduces the length gap between First and Okay by 51–96% relative to the unmodified baselines across all three models and both datasets. This reduction reflects shorter Okay continuations, longer First continuations, or both. On Qwen-1.5B/MATH, the change is driven mainly by lengthening First, with relatively little change in Okay. The intervention thus weakens the distinction between first token conditions rather than uniformly shortening reasoning, although a residual gap remains. In every model–dataset combination, JS-based selection reduces the gap more than periodic masking while intervening at a smaller fraction of positions (Table 2), supporting the importance of where attention is blocked.

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Distribution replacement redirects reasoning length.

Figure 6 shows bidirectional length shifts across all three models and both datasets. Replacing distributions from First with those from Okay lengthens reasoning, whereas the reverse replacement shortens it. Across models, datasets, and tested thresholds, First-to-Okay replacement increases mean length to 3.7–7.9 times its source baseline, while Okay-to-First replacement reduces it by 53–90%. These shifts occur while retaining the source first token and changing only the sampling distributions at selected steps. At every tested threshold, JS-based replacement produces larger mean shifts toward the alternative first token than periodic replacement, despite a lower intervention rate (Table tab:distribution-intervention-rates). Thus, changing predictions within the candidate set can redirect subsequent reasoning length without changing the first token itself.

Targeting sensitive positions is more effective than broad periodic intervention.

For both attention blocking and distribution replacement, JS-based selection produces larger changes in the first token dependent length difference than periodic intervention despite modifying a smaller fraction of positions (Table 2 and tab:distribution-intervention-rates). This consistent advantage across two distinct interventions shows that their effects cannot be explained simply by the number of modified generation steps. Instead, where the intervention is applied matters: positions that are more sensitive to the first-token condition exert a stronger aggregate influence on the resulting length difference.

Discussion

The first-token effect raises a broader question about how local choices shape generation as a whole. A token need not explicitly specify a desired length to influence how much reasoning follows. Our results offer a starting point for considering how such connections arise and whether they extend to other tokens.

Local expressions and global generation properties.

first tokens such as First and Okay do not explicitly specify reasoning length, yet they exhibit distinct length tendencies whose influence persists beyond the early text they induce. One possible explanation is that models learn associations between local expressions and sequence-level characteristics during training. For example, an expression that frequently co-occurs with longer reasoning may favor more extended continuations without conveying an explicit length instruction. From this perspective, a token’s influence may reflect both its literal meaning and learned associations with broader generation patterns. Examining these associations may help explain how small differences in local expression relate to substantial differences in sequence-level behavior.

The first token as an entry point.

Similar persistent influences may occur throughout generation, with the first token providing a tractable setting for observation and intervention. Its position is aligned across trajectories, and its values are concentrated in a small set of common first tokens. These properties enable consistent substitutions and allow us to trace their effects on subsequent predictions and overall length. Tokens at intermediate positions may play similar roles, although their identities and functions depend more strongly on the surrounding context. Studying the first token therefore offers a research strategy that can be explored more broadly: introduce controlled local substitutions, identify sensitive positions in subsequent generation, and intervene to examine how these dependencies contribute to global generation properties.

Future work.

A next step is to investigate how the contributions of individual positions within the candidate set combine to shape reasoning length. Finer-grained interventions could distinguish positions with substantial effects on length from those that primarily alter local wording, and determine whether their contributions are independent, redundant, or synergistic. Analyses of the surrounding context and internal representations could further reveal which generation states make earlier cues influential and how predictive changes at these positions alter the subsequent course of reasoning. This would extend the set-level intervention evidence toward a more specific account of how local dependencies contribute to global generation properties.

Conclusion

We investigate how the first reasoning token influences subsequent reasoning length. Its effect persists when the intervening text is held fixed, while predictive sensitivity is concentrated at a small fraction of positions. Attention blocking and distribution replacement at these positions respectively attenuate length differences and redirect reasoning length. Together, these findings support a role for the selected candidate set in sustaining the first-token length effect.

Limitations

Model scope.

All three models studied in this work belong to the DeepSeek-R1 distilled series. Although they differ in size and backbone architecture, they share the same source model for distillation. Whether persistent first-token influence and concentrated sensitivity also occur in other model families and under different training procedures remains to be established.

From sensitive positions to reasoning length.

We characterize the relationship between the first token and subsequent sensitive positions, and establish their contribution to the length effect through set-level interventions. This evidence concerns the selected set as a whole, leaving the contributions of individual positions unresolved. Finer-grained interventions are needed to determine which positions within the set drive the observed length changes.

Experimental Setup Details

Prompt templates.

The prompts used for each dataset are shown below.

Aggregation and uncertainty.

Forced-opening means average repetitions within questions, then questions. Natural conditional means pool trajectories by observed opening. For the first-token effect figures, 95% confidence intervals use 10,000 bootstrap resamples of whole questions, retaining all their trajectories. Experiment-specific aggregation and bootstrap settings are given in the corresponding appendices.

Computing infrastructure.

We conducted our experiments on NVIDIA RTX A6000 GPUs with 48 GB of memory and NVIDIA A800 GPUs with 80 GB of memory.

Additional First-Token Effects

Figure 7 extends Figure 1 to MATH-500, HumanEval, and FOLIO using the reference trajectories described in Appendix § 8.

The four selected openings account for 92.1–96.8% of natural trajectories on GSM8K, 99.8–100% on MATH-500, and 100% on HumanEval and FOLIO. Although the first-token distribution under natural sampling varies across datasets, forced-opening generation reveals similar reasoning-length contrasts across all four datasets. These results suggest that the first-token effect on reasoning length occurs across diverse tasks.

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Additional Prefix-Preserving Intervention Results

We supplement § 5.1 with length results on MATH-500, HumanEval, and FOLIO, together with accuracy evaluations across all four datasets.

Additional Length Results

Long-to-short comparisons retain questions for which both source trajectories exceed 200 tokens; short-to-long comparisons retain completed sources with at least $K$ tokens. Both directions compare mean remaining lengths under a common horizon of $8{,}192-K$ tokens, including unfinished continuations. We average repetitions within sources, eligible sources within questions, and then questions, using identical weights for the references. In the accompanying tables, questions counts distinct problems and sources counts eligible original trajectories before continuation resampling, with up to two source first tokens per question.

Figure 8 reports the MATH-500 results. For long-to-short comparisons, all 164 HumanEval problems are retained, alongside 499, 489, and 488 FOLIO questions for Qwen-1.5B, Qwen-7B, and Llama-8B, respectively. Short-to-long source coverage varies with $K$.

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Length effects beyond mathematical tasks.

Figure 9 and Figure 10 show bidirectional mean length changes, with weaker relative shortening on HumanEval than on FOLIO. At $K=200$, HumanEval long-to-short ratios range from 0.87 to 0.95, with all six 95% intervals below one, while short-to-long ratios range from 1.23 to 1.59. FOLIO shows larger relative changes, with corresponding ratios of 0.58–0.85 and 1.71–3.04. These results extend the persistence observation to coding and logical reasoning, while showing that its magnitude depends on the task and replacement.

Accuracy Evaluation

Accuracy is evaluated on the same eligible sources as the length comparisons, with each sampled continuation scored separately. Unfinished reasoning and missing or unparseable answers count as incorrect.

GSM8K and MATH-500.

Table 3 and Table 4 report accuracy on the mathematical datasets. For GSM8K, we extract answers after </think>, prioritizing the last complete \boxed expression and otherwise the last number, with fractions and unit formatting normalized. For MATH-500, extraction prioritizes boxed answers and otherwise uses an explicit final-answer section when available; Markdown emphasis, ordinal suffixes, and degree notation are normalized.

HumanEval and FOLIO.

Tables tab:transfer-accuracy-humaneval and tab:transfer-accuracy-folio report accuracy on the additional datasets. HumanEval programs are extracted from final answers, retaining generated imports and helper functions as well as imports supplied in the task prompt. Programs are evaluated against all supplied task tests in an isolated environment; test failures or execution exceeding 3 seconds of CPU time or 8 seconds of wall-clock time count as incorrect. FOLIO predictions are extracted from final-answer labels, prioritizing explicit answers over labels mentioned within explanations.

black!109cLong-to-short (Okay / Alright$\rightarrow$To / First)
Model	$K$	Questions / sources	Reference	To	First
			Length	Acc.	Length	Acc.	Length	Acc.
Qwen-1.5B	50	500 / 1000	1,608.6	88.5	274.5	86.3	343.2	87.6
	100	500 / 1000	1,565.4	89.2	358.5	86.7	432.5	87.8
	150	500 / 1000	1,472.6	89.9	404.5	87.1	489.8	87.8
	200	500 / 1000	1,461.2	88.6	419.5	86.3	524.7	86.9
Qwen-7B	50	500 / 1000	1,138.5	95.0	414.2	94.8	306.7	94.4
	100	500 / 1000	1,096.9	94.9	490.7	94.1	336.6	94.5
	150	500 / 1000	1,059.4	94.9	507.5	93.5	349.4	94.3
	200	500 / 1000	1,019.2	94.8	482.6	93.7	347.2	94.5
Llama-8B	50	500 / 1000	1,503.8	88.5	579.8	84.9	567.7	85.1
	100	500 / 1000	1,442.1	88.7	681.8	85.8	680.3	85.8
	150	500 / 1000	1,430.8	88.0	686.5	86.4	682.6	86.2
	200	500 / 1000	1,348.0	89.0	683.3	86.6	665.6	85.9
black!109cShort-to-long (To / First$\rightarrow$Okay / Alright)
Model	$K$	Questions / sources	Reference	Okay	Alright
			Length	Acc.	Length	Acc.	Length	Acc.
Qwen-1.5B	50	500 / 999	117.7	82.8	744.4	85.4	734.7	86.2
	100	492 / 932	70.4	83.0	441.7	85.0	421.7	84.8
	150	352 / 562	47.6	80.2	374.4	81.8	356.0	82.1
	200	165 / 223	48.1	74.1	510.4	75.4	495.9	77.4
Qwen-7B	50	500 / 999	120.2	92.0	181.0	92.9	180.4	93.4
	100	496 / 929	74.9	92.2	102.4	92.9	101.8	92.9
	150	372 / 597	49.5	89.6	79.1	90.6	68.2	90.3
	200	170 / 240	43.2	82.8	75.4	83.0	62.3	82.4
Llama-8B	50	500 / 1000	108.4	71.3	306.9	76.2	271.8	75.5
	100	483 / 894	64.3	70.9	192.9	74.4	150.9	73.1
	150	328 / 494	46.8	64.7	170.8	67.9	151.0	67.5
	200	138 / 181	47.5	54.5	235.2	56.3	193.9	55.4

black!109cLong-to-short (Okay / Alright$\rightarrow$To / First)
Model	$K$	Questions / sources	Reference	To	First
			Length	Acc.	Length	Acc.	Length	Acc.
Qwen-1.5B	50	500 / 1000	3,503.2	78.0	1,367.5	73.5	1,872.0	76.0
	100	500 / 1000	3,452.4	77.8	1,810.6	75.4	2,174.3	77.0
	150	500 / 1000	3,406.4	78.7	1,872.7	75.1	2,248.6	77.1
	200	500 / 1000	3,342.6	78.5	1,968.3	76.4	2,234.3	77.3
Qwen-7B	50	500 / 1000	2,959.6	88.3	2,132.8	88.4	1,652.1	87.1
	100	500 / 1000	2,914.7	88.3	2,227.3	88.2	1,772.6	87.3
	150	500 / 1000	2,837.4	88.5	2,290.6	87.3	1,847.4	88.1
	200	500 / 1000	2,796.3	88.6	2,278.1	88.2	1,859.2	87.8
Llama-8B	50	500 / 1000	3,253.0	81.7	2,235.6	79.3	2,253.3	79.7
	100	500 / 1000	3,233.4	81.3	2,301.6	81.0	2,305.9	80.5
	150	500 / 1000	3,179.5	80.9	2,351.7	80.7	2,346.3	80.5
	200	500 / 1000	3,101.2	81.4	2,368.0	80.8	2,339.2	81.1
black!109cShort-to-long (To / First$\rightarrow$Okay / Alright)
Model	$K$	Questions / sources	Reference	Okay	Alright
			Length	Acc.	Length	Acc.	Length	Acc.
Qwen-1.5B	50	500 / 989	354.0	66.5	2,805.8	77.6	2,794.6	77.4
	100	500 / 973	312.0	65.9	2,429.9	76.5	2,451.8	76.7
	150	472 / 870	275.6	66.0	2,302.0	75.4	2,288.2	76.0
	200	420 / 736	266.2	62.8	2,260.0	70.9	2,239.5	72.1
Qwen-7B	50	500 / 995	333.1	75.8	1,785.8	86.4	1,743.6	86.5
	100	496 / 978	282.8	75.1	1,314.8	84.2	1,237.5	84.4
	150	473 / 884	257.1	74.3	1,104.8	83.2	1,046.1	82.2
	200	412 / 735	240.4	71.3	1,104.2	79.9	1,073.5	78.4
Llama-8B	50	500 / 994	336.8	58.6	2,272.3	78.1	2,219.4	77.6
	100	495 / 966	296.5	58.0	1,913.1	75.1	1,860.4	73.5
	150	462 / 867	269.3	56.1	1,836.6	71.0	1,814.7	70.1
	200	398 / 707	278.1	53.4	1,991.5	66.8	1,835.3	65.5

black!109cLong-to-short (Okay / Alright$\rightarrow$To / First)
Model	$K$	Questions / sources	Reference	To	First
			Length	Acc.	Length	Acc.	Length	Acc.
Qwen-1.5B	50	164 / 328	3,554.1	64.7	3,140.9	64.9	3,092.6	63.9
	100	164 / 328	3,589.9	63.7	3,263.8	63.2	3,165.6	64.2
	150	164 / 328	3,441.8	64.6	3,116.0	66.5	3,106.7	66.6
	200	164 / 328	3,426.0	65.0	3,186.4	64.7	3,133.2	62.7
Qwen-7B	50	164 / 328	2,758.8	85.9	2,651.8	83.1	2,085.9	83.7
	100	164 / 328	2,671.6	85.9	2,530.3	86.2	2,236.1	84.5
	150	164 / 328	2,613.4	86.9	2,542.3	86.2	2,264.2	84.2
	200	164 / 328	2,586.6	85.1	2,452.8	86.5	2,249.8	85.1
Llama-8B	50	164 / 328	2,707.7	84.5	2,260.0	81.7	2,166.9	81.3
	100	164 / 328	2,631.9	84.5	2,304.7	81.9	2,196.7	81.6
	150	164 / 328	2,675.0	82.6	2,244.6	82.8	2,233.9	82.7
	200	164 / 328	2,551.4	83.5	2,252.8	82.6	2,261.0	81.6
black!109cShort-to-long (To / First$\rightarrow$Okay / Alright)
Model	$K$	Questions / sources	Reference	Okay	Alright
			Length	Acc.	Length	Acc.	Length	Acc.
Qwen-1.5B	50	157 / 293	2,601.3	67.9	3,335.1	67.5	3,330.8	68.9
	100	157 / 293	2,629.0	66.7	3,240.3	68.6	3,221.1	68.6
	150	157 / 293	2,657.2	66.5	3,085.1	67.5	3,086.4	67.4
	200	157 / 290	2,456.9	68.2	3,021.9	68.3	3,076.1	67.2
Qwen-7B	50	161 / 312	1,684.1	84.4	2,605.5	85.1	2,630.6	85.1
	100	161 / 312	1,727.9	84.5	2,528.6	86.0	2,471.6	86.2
	150	161 / 308	1,686.3	84.5	2,419.2	87.2	2,500.5	86.4
	200	157 / 297	1,690.3	84.4	2,373.1	85.7	2,423.7	85.8
Llama-8B	50	160 / 190	1,402.2	76.1	2,442.9	85.4	2,421.8	83.9
	100	159 / 189	1,423.7	76.2	2,379.0	81.8	2,267.4	81.0
	150	157 / 184	1,262.1	76.2	2,331.6	82.8	2,153.8	82.1
	200	148 / 171	1,431.3	76.5	2,278.7	83.3	2,119.2	81.1

black!109cLong-to-short (Okay / Alright$\rightarrow$To / First)
Model	$K$	Questions / sources	Reference	To	First
			Length	Acc.	Length	Acc.	Length	Acc.
Qwen-1.5B	50	499 / 998	1,580.1	44.6	884.7	42.1	796.9	41.5
	100	499 / 998	1,531.2	44.0	881.3	42.4	810.5	41.3
	150	499 / 998	1,515.9	43.4	856.0	44.1	804.4	42.2
	200	499 / 998	1,402.6	43.6	869.9	42.2	816.5	42.6
Qwen-7B	50	489 / 978	835.2	51.2	704.2	49.0	570.4	48.1
	100	489 / 978	785.8	50.4	657.0	50.1	562.4	48.5
	150	489 / 978	748.0	49.9	609.0	49.8	524.2	48.6
	200	489 / 978	676.8	50.4	575.9	49.3	484.9	48.6
Llama-8B	50	488 / 976	934.2	49.1	622.6	47.9	563.1	46.8
	100	488 / 976	880.9	49.6	597.5	47.8	549.8	47.0
	150	488 / 976	820.8	49.4	570.4	47.6	516.8	47.7
	200	488 / 976	775.0	49.1	541.9	48.3	486.1	47.2
black!109cShort-to-long (To / First$\rightarrow$Okay / Alright)
Model	$K$	Questions / sources	Reference	Okay	Alright
			Length	Acc.	Length	Acc.	Length	Acc.
Qwen-1.5B	50	500 / 999	234.6	40.3	581.9	42.6	531.6	41.7
	100	500 / 995	188.6	40.3	489.6	42.4	463.6	42.1
	150	491 / 920	144.5	40.6	404.6	41.6	387.9	41.6
	200	441 / 753	128.7	38.3	391.5	40.2	358.5	40.3
Qwen-7B	50	500 / 1000	245.6	46.6	390.5	49.4	372.8	48.8
	100	500 / 990	193.8	46.9	310.0	50.1	308.9	48.8
	150	485 / 913	155.9	44.5	265.0	47.1	252.0	46.9
	200	434 / 761	124.0	42.3	223.8	45.5	226.3	44.6
Llama-8B	50	500 / 1000	201.3	43.5	327.6	47.6	311.1	46.5
	100	500 / 991	153.4	44.3	265.6	46.9	241.0	46.2
	150	486 / 914	110.8	42.5	198.0	44.2	184.0	44.9
	200	415 / 688	87.2	39.1	165.6	40.7	149.3	39.3

Illustrative Prefix-Preserving Interventions

Figures fig:prefix-case-prefix–Figure 13 show Qwen-7B cases in both directions on GSM8K, HumanEval, and FOLIO at $K=200$. QIDs are zero-based dataset row indices and coincide with numeric task IDs for HumanEval.

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Additional Sensitivity Results

Concentration Across First-Token Pairs

Figure 14 extends the concentration analysis to First–Alright, To–Okay, and To–Alright.

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Attention Across First-Token Pairs

Figure 15 and Figure 16 extend the attention analysis to the same three pairs. JS compares the paired first-token conditions on a fixed subsequent prefix; attention is measured separately under each condition. Higher-JS positions receive greater first-token attention across all three pairs.

Vector (PDF)

Vector (PDF)

Sensitivity Along Individual Trajectories

Figure 17 extends the example in Figure 3(b) to three models and two datasets. The curves show intermittent peaks, including peaks beyond the initial 50 positions. For each dataset, the example is selected from complete, untruncated natural trajectories with $L>50$ in all three models, using proximity to the model-wise median lengths without inspecting JS values.

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Additional Intervention Results

Attention Blocking

Vector (PDF)

Model	Source	Base	Every 3	$0.2$	$0.1$	$0.05$
Qwen-1.5B	First	2,910	2,941 (33.3)	3,047 (0.6)	3,145 (1.3)	3,035 (2.7)
	Okay	3,717	3,536 (33.3)	3,516 (0.2)	3,509 (0.6)	3,635 (1.3)
Qwen-7B	First	1,622	2,041 (33.3)	1,752 (2.2)	1,889 (4.0)	2,018 (6.5)
	Okay	2,797	2,763 (33.3)	2,746 (0.3)	2,716 (0.7)	2,757 (1.6)
Llama-8B	First	1,655	2,109 (33.3)	1,853 (1.6)	1,864 (3.3)	1,979 (6.0)
	Okay	2,633	2,730 (33.3)	2,777 (0.2)	2,802 (0.6)	2,629 (1.4)
Qwen-1.5B	First	291	494 (33.3)	660 (1.0)	735 (1.9)	980 (3.4)
	Okay	1,679	1,676 (33.3)	1,466 (0.5)	1,410 (1.1)	1,434 (2.7)
Qwen-7B	First	283	422 (33.3)	680 (0.9)	663 (1.7)	682 (3.3)
	Okay	926	891 (33.3)	910 (0.6)	891 (1.1)	909 (2.3)
Llama-8B	First	250	268 (33.3)	457 (6.0)	492 (11.1)	497 (18.0)
	Okay	993	898 (33.3)	672 (4.8)	648 (9.5)	671 (15.9)

Extension to additional datasets.

Figure fig:transfer-attention and Table Figure 18 present the results on FOLIO and HumanEval. On FOLIO, the results follow the same pattern as on the mathematical datasets, with all tested JS thresholds reducing the length gap more than periodic masking. The results on HumanEval are less consistent: periodic masking outperforms all tested JS thresholds for Qwen-7B and Llama-8B, whereas thresholds of 0.2 and 0.1 outperform periodic masking for Qwen-1.5B. Two factors may contribute to this difference. First, the first-token length effect is weaker on HumanEval than on the other tasks, leaving less room for gap reduction. Second, the same JS thresholds select a substantially smaller fraction of positions on HumanEval, which may limit the impact of the intervention.

Case Study.

Figure 19 compares reasoning trajectories beginning with First and Okay for the same GSM8K question. Without intervention, the First trajectory presents the solution and answer directly, whereas the Okay trajectory repeatedly checks the result, exhibiting a tendency toward overthinking. Blocking attention to the first token at sensitive positions narrows the length gap and makes the two trajectories more similar in both content and wording. This example illustrates how the intervention weakens the first-token length effect, alongside changes in reasoning behavior.

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Distribution Replacement

Table tab:distribution-intervention-rates reports distribution-replacement rates on the mathematical datasets, using the same averaging and eligible-position denominators.

Vector (PDF)

Model	Source	Base	Every 3	$0.2$	$0.1$	$0.05$
Qwen-1.5B	First	2,910	3,105 (33.3)	3,123 (0.3)	3,157 (0.7)	3,343 (1.4)
	Okay	3,717	3,407 (33.3)	3,574 (0.3)	3,418 (1.0)	3,302 (2.8)
Qwen-7B	First	1,622	2,606 (33.3)	2,346 (0.4)	2,403 (0.9)	2,425 (1.7)
	Okay	2,797	2,565 (33.3)	2,572 (1.1)	2,384 (3.3)	2,258 (7.4)
Llama-8B	First	1,655	2,374 (33.3)	2,241 (0.4)	2,396 (1.0)	2,456 (1.9)
	Okay	2,633	2,621 (33.3)	2,608 (0.7)	2,300 (3.0)	2,120 (7.0)
Qwen-1.5B	First	291	593 (33.3)	691 (1.4)	905 (2.0)	1,098 (3.2)
	Okay	1,679	1,114 (33.3)	541 (4.2)	397 (8.7)	324 (14.9)
Qwen-7B	First	283	507 (33.3)	567 (1.4)	648 (2.6)	743 (4.4)
	Okay	926	668 (33.3)	381 (4.3)	322 (8.4)	305 (14.6)
Llama-8B	First	250	445 (33.3)	572 (1.8)	705 (3.1)	808 (5.7)
	Okay	993	752 (33.3)	347 (5.3)	277 (10.6)	257 (18.1)

Extension to additional datasets.

Figure fig:transfer-distribution and table Figure 20 present the distribution replacement results on FOLIO and HumanEval. On FOLIO, the results follow the same pattern as on the mathematical datasets, with all tested JS thresholds producing larger length shifts in the intended direction than periodic replacement. On HumanEval, the relative effectiveness varies across models and replacement directions. Two factors may contribute to this variation: the first-token length effect is weaker on HumanEval, and the same JS thresholds select a substantially smaller fraction of positions, potentially limiting the impact of distribution replacement.