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

• Reasoning traces vary in length across problems and repeated generations, with differences affecting inference cost and potentially task performance.Source: §1 · p. 1
• Changing only the first token of a fixed reasoning prefix substantially changes the remaining reasoning length.Long-associated tokens increase remaining length, while short-associated tokens reduce it.Source: §1 · pp. 1–2
• First-token sensitivity in next-token predictions concentrates at a small set of positions that also show stronger attention to the first token.Source: §1 · p. 2
• Blocking sensitive positions’ attention to the first token reduces the reasoning-length gap between first-token conditions.Source: §1 · p. 2
• Replacing next-token distributions at sensitive positions with those from another first-token condition substantially changes subsequent reasoning length.Source: §1 · p. 2

• Budget forcing that suppresses termination and suppressing reflection-related tokens such as Wait and Hmm are reported to extend and shorten reasoning, respectively.Muennighoff et al. (2025) extend reasoning; Wang et al. (2025) shorten it.Source: §2 · p. 2
• Lin et al. (2025) and Nguyen et al. (2026) link first-token choices to reasoning length, with Nguyen et al. also connecting choices to reasoning modes with different lengths and accuracies.Source: §2 · p. 2
• Other approaches regulate reasoning length through budget forcing, length-constrained reinforcement learning, compressed traces, activation steering, attention-head edits, and representation transformations.The cited work also studies predicting reasoning length from question activations and modulating reasoning strength.Source: §2 · p. 2

3.1 Problem Formulation

• Reasoning length is L = |r|, the chain-of-thought length excluding reasoning delimiters and the final answer; the first reasoning token is z = r1.Source: §3.1 · p. 2

3.2 First-Token Effects on Reasoning Length

• On GSM8K, Okay or Alright beginnings have greater mean reasoning length than To or First beginnings, including when the first token is forced.Figure 1 reports natural first-token frequencies, mean lengths by natural first token, and mean lengths under forced first tokens; its bars identify tokens and show 95% bootstrap confidence intervals.Source: §3.2 · pp. 2–3, Figure 1 · p. 3

• The study evaluates three DeepSeek-R1 distilled models on 500 MATH-500 test questions and a fixed random sample of 500 GSM8K training questions, with HumanEval and FOLIO used for generalization analysis.Source: §4 · p. 3
• Natural trajectories characterize first-token frequencies and length associations, while forced trajectories begin with Okay, Alright, First, or To and provide matched-question references for interventions.The four tokens account for most naturally occurring first tokens across evaluated models and datasets.Source: §4 · p. 3
• The study draws three samples per question and condition at temperature 0.6 and top-p = 0.95, measuring lengths within an 8,192-token horizon and retaining unfinished traces at observed lengths.Free generation uses total length; prefix-preserving interventions use remaining length.Source: §4 · p. 3

5.1 Persistent First-Token Influence

• Replacing only the first token shifted remaining reasoning length toward that token’s associated tendency, even when the following 199 tokens were preserved.Shortened continuations still answered most questions correctly, though less accurately than matched source trajectories; lengthened continuations generally maintained or improved mean accuracy.Source: Figure 2 · p. 4, §5.1 · p. 4

5.2 First-token Sensitivity Concentrates at Few Positions

• The highest-JS 10% of positions accounted for approximately 69–82% of total JS across models and datasets, with sensitivity peaks also occurring later in generation.In the example trajectory, peaks were denser and larger early on but were not confined to the initial reasoning stage.Source: Figure 3 · p. 5, §5.2 · p. 5
• Higher-JS positions tended to attend more to the first token; after adjusting for position, mean within-trajectory Spearman correlations remained positive at 0.25–0.38.In the highest JS decile, first-token attention averaged the 77th–82nd within-trajectory percentile.Source: §5.2 · p. 5, Figure 4 · p. 6

5.3 Testing the Role of Sensitive Positions in Reasoning Length

• 51–96%: blocking first-token attention at JS-selected positions reduced the First–Okay reasoning-length gap across all three models and both datasets.The reduction came from shorter Okay continuations, longer First continuations, or both; a residual gap remained.Source: §5.3 · pp. 6–7, Figure 5 · p. 7
• 3.7–7.9 times: First-to-Okay distribution replacement increased mean length relative to its source baseline, while Okay-to-First replacement reduced it by 53–90%.These shifts occurred with the source first token retained and only selected-step sampling distributions changed.Source: §5.3 · p. 7
• JS-based selection changed the first-token length difference more than periodic intervention for both interventions, despite modifying fewer positions.The advantage was consistent across tested settings and indicates that intervention location mattered beyond the number of modified steps.Source: §5.3 · p. 7

6 Discussion

• First tokens can carry distinct length tendencies without explicitly specifying reasoning length; learned associations with broader generation patterns are one possible explanation.The discussion frames this association as a possibility, not an established mechanism.Source: §6 · pp. 7–8
• The first token offers a tractable entry point because its position is aligned and its values are concentrated, while intermediate tokens may depend more on context.The proposed strategy is to make controlled local substitutions, identify sensitive positions, and intervene on them.Source: §6 · p. 8
• Future work could test how individual sensitive positions combine, distinguish length effects from wording changes, and examine relevant contexts and internal representations.The discussion leaves open whether position contributions are independent, redundant, or synergistic.Source: §6 · p. 8

7 Conclusion

• Changing the first token alters subsequent reasoning length even when the intervening prefix text is held fixed.The conclusion also reports that these changes preserve effective question answering.Source: §7 · p. 8
• Predictive sensitivity is concentrated at a small fraction of positions; attention blocking there attenuates length differences, while distribution replacement redirects reasoning length.Together, these interventions support a role for the selected candidate set in sustaining the first-token length effect.Source: §7 · p. 8

Limitations

• All three studied models are DeepSeek-R1 distilled models sharing one source model, so transfer to other model families or training procedures remains unestablished.The models differ in size and backbone architecture.Source: Limitations · p. 9
• Set-level interventions establish a contribution from the selected sensitive positions as a group, but leave individual positions’ effects unresolved.Finer-grained interventions are needed to identify which positions drive the length changes.Source: Limitations · p. 9

A Experimental Setup Details

• The appendix lists dataset prompt templates, aggregation and bootstrap procedures, and the GPU hardware used for experiments.First-token-effect figures use 95% confidence intervals from 10,000 whole-question bootstrap resamples, retaining all trajectories.Source: A Experimental Setup Details · p. 11

B Additional First-Token Effects

• The four selected openings cover 92.1–96.8% of GSM8K natural trajectories, 99.8–100% on MATH-500, and 100% on HumanEval and FOLIO; forced openings show similar length contrasts across all four datasets.The appendix describes these findings as suggesting that first-token effects occur across diverse tasks.Source: B Additional First-Token Effects · p. 11

C Additional Prefix-Preserving Intervention Results

• The appendix supplements prefix-preserving intervention results with reasoning-length results on MATH-500, HumanEval, and FOLIO and accuracy evaluations across all four datasets.Source: C Additional Prefix-Preserving… · p. 11

C.1 Additional Length Results

• Long-to-short comparisons retain sources exceeding 200 tokens; both directions use an 8,192 − K-token horizon and equal question weighting.The averaging procedure first groups repetitions within sources and eligible sources within questions.Source: §C.1 · p. 11

C.2 Accuracy Evaluation

• Accuracy evaluation uses the same eligible sources, scores sampled continuations separately, and counts unfinished reasoning or missing or unparseable answers as incorrect.Answer extraction is dataset-specific; HumanEval programs are run against supplied tests.Source: §C.2 · pp. 11–12

C.3 Illustrative Prefix-Preserving Interventions

• Prefix-preserving replacement figures compare edited continuation lengths with matched unchanged-prefix references, with 95% question-bootstrap intervals.For HumanEval, the reference uses three unchanged-prefix continuations.Source: Figure 8 · p. 13, Figure 9 · p. 13

C.1 Additional Length Results

• At K = 200, HumanEval long-to-short ratios are 0.87–0.95 (all six 95% intervals below one), versus FOLIO’s 0.58–0.85; short-to-long ratios are 1.23–1.59 and 1.71–3.04.The comparisons extend the persistence observation to coding and logical reasoning, with effect magnitude depending on task and replacement.Source: §C.1 · p. 11, Figure 9 · p. 13, Figure 10 · p. 14

C.3 Illustrative Prefix-Preserving Interventions

• At K = 200, illustrative edits shorten or lengthen continuations across GSM8K, HumanEval, and FOLIO while retaining the same answer or solution.The FOLIO short-to-long example shows a modest increase, with variation across three edited samples.Source: Figure 11 · p. 19, Figure 12 · p. 19, Figure 13 · p. 20

D.1 Concentration Across First-Token Pairs

• Across GSM8K and MATH, concentration analysis extends to First–Alright, To–Okay, and To–Alright pairs; curves mark the highest-JS 10% of positions.Tail analyses exclude the first 50 positions and rerank and renormalize the remaining positions within each trajectory.Source: §D.1 · p. 22, Figure 17 · p. 22

D.2 Attention Across First-Token Pairs

• Across the three pairs, higher-JS positions receive greater first-token attention under both short-associated and long-associated conditions.Attention is measured separately under each first-token condition.Source: §D.2 · p. 22, Figure 18 · p. 23

D.3 Sensitivity Along Individual Trajectories

• Example trajectories show intermittent sensitivity peaks, including beyond the first 50 positions; examples were selected without inspecting JS values.Selection used complete, untruncated trajectories with L > 50 across all three models, choosing lengths near model-wise medians.Source: §D.3 · pp. 22–23

E.1 Attention Blocking

• The authors suggest weaker first-token effects and fewer selected positions may limit intervention impact on HumanEval.These are proposed factors for the less consistent HumanEval results.Source: §E.1 · p. 23
• On FOLIO, all tested JS thresholds reduce the length gap more than periodic masking; on HumanEval, the relative results vary by model.Periodic masking outperforms all tested thresholds for Qwen-7B and Llama-8B, while thresholds 0.2 and 0.1 outperform it for Qwen-1.5B.Source: §E.1 · p. 23, Figure 21 · p. 26, Table 7 · p. 26
• In one GSM8K case, blocking attention narrows the length gap and makes First and Okay trajectories more similar in content and wording; all four trajectories answer correctly.Without intervention, the Okay trajectory repeatedly checks the result while the First trajectory presents it directly.Source: §E.1 · p. 24, Figure 22 · p. 27

E.2 Distribution Replacement

• On FOLIO, all tested JS thresholds produce larger intended-direction length shifts than periodic replacement; HumanEval effectiveness varies across models and directions.The authors suggest weaker first-token effects and a smaller fraction of selected positions may contribute to HumanEval variation.Source: §E.2 · p. 25, Figure 23 · p. 28, Table 9 · p. 28