Writing study: ThreadWeaver: Adaptive Threading for Efficient Parallel Reasoning in Language Models

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← ICML 2026 oral writing corpus

Long Lian, Sida Wang, Felix Juefei-Xu, Tsu-Jui Fu, Xiuyu Li, Adam Yala, Trevor Darrell, Alane Suhr, Yuandong Tian, Xi Victoria Lin · Official ICML 2026 oral record

Observed writing choices, not acceptance rules. This study examines the inspected manuscript version. It does not establish why the paper was accepted or that its presentation choices should be copied unchanged.

Figure, table and section ledger

Editorial contribution type: Efficiency, inference & systems (primary).

Layout extraction, not a required paper template. Counts are distinct caption labels; a multi-panel figure counts once. Section spans are estimated from heading positions, including floats and whitespace. Method and limitations.

Canonical PDF

36 physical pages

Before references / appendix

≈ 8.38 page-equivalents

Main figures / tables

5 / 5

Attached appendix figures / tables

2 / 6

Attached appendix span

≈ 24.91 page-equivalents

Before references / appendix: ≈ 23.28%References / intervening material: ≈ 7.53%Attached appendix: ≈ 69.19%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Wrapped main heading labels restored from the immediately following same-size source line in the physical PDF. Heading start positions are unchanged. Newly detected unnumbered impact/singular-acknowledgment statements are retained from the size-aware source extraction; authored heading corrections are unchanged.

Section-by-section lengths and source pages

The title/abstract/front matter precede the first numbered heading. A span ends at the next detected top-level heading, not at the last sentence; end-page whitespace is included. References and statements are listed separately. These are not measurements of text-only or artwork area.

Top-level heading	Starts on PDF page	Estimated span	Share of entire PDF
1 Introduction	1	≈ 1.16 pp.	3.22%
2 Model	2	≈ 1.53 pp.	4.25%
3 Parallel Trajectory Curation for Supervised Fine-tuning	4	≈ 0.41 pp.	1.14%
4 Reinforcement Learning	4	≈ 1.31 pp.	3.64%
5 Experiments	6	≈ 2.36 pp.	6.56%
6 Related work	8	≈ 0.71 pp.	1.97%
7 Conclusion	9	≈ 0.12 pp.	0.33%
Acknowledgements	9	≈ 0.09 pp.	0.25%
Impact Statement	9	≈ 0.05 pp.	0.14%
References	9	≈ 2.71 pp.	7.53%
A Preliminaries	12	≈ 1.14 pp.	3.17%
B Derivations for P-GRPO	13	≈ 1.24 pp.	3.44%
C Implementation Details	14	≈ 2.35 pp.	6.53%
D Dataset Statistics	16	≈ 0.75 pp.	2.08%
E Additional Results	17	≈ 7.23 pp.	20.08%
F Reasoning Trajectory Annotation Pipeline for ThreadWeaver	24	≈ 10.85 pp.	30.14%
G Discussion: Reward Hacking	35	≈ 0.44 pp.	1.22%
H Future Directions	36	≈ 0.91 pp.	2.53%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 3
• Figure 3 · p. 3
• Figure 4 · p. 4
• Table 1 · p. 7
• Figure 5 · p. 7
• Table 2 · p. 7
• Table 3 · p. 7
• Table 4 · p. 8
• Table 5 · p. 8

Attached appendix

• Figure 6 · p. 15
• Table 6 · p. 16
• Table 7 · p. 17
• Table 8 · p. 18
• Table 9 · p. 19
• Table 10 · p. 20
• Table 11 · p. 20
• Figure 7 · p. 23

Argument and organization

1. Problem and claim

   Maps three obstacles—training trajectories, inference-engine dependence and parallelization incentives—to three corresponding contributions, keeping the efficiency claim attached to a sequential reasoning baseline.

2. Argument sequence

   Introduces the trajectory format and inference state machine before data construction and P-GRPO. Algorithm 1 therefore refers to a previously explained execution object rather than introducing a second opaque pipeline.

3. Evidence and verification

   Separates average per-problem speedup, ratio of mean token latencies and measured wall-clock time. Table 3 reports 1.14× wall-clock speedup on 50 MATH problems, while the adjacent protocol discloses one sequential GPU versus four parallel GPUs.

Problem, claim and contribution

Maps three obstacles—training trajectories, inference-engine dependence and parallelization incentives—to three corresponding contributions, keeping the efficiency claim attached to a sequential reasoning baseline.

Abstract and Introduction, pp. 1–2 · Main paper

Argument and section order

Introduces the trajectory format and inference state machine before data construction and P-GRPO. Algorithm 1 therefore refers to a previously explained execution object rather than introducing a second opaque pipeline.

Sections 2–4, pp. 2–5 · Main paper

Figures, captions and visual explanation

The paired example and request/completion timeline reuse colors for shared context and independent threads. Stop conditions label each inference step, while the caption distinguishes parallel thread contents from sequential framing tokens.

Figures 2–3, physical p. 3; raster inspected · Main paper

Tables, comparisons and evidence

Separates average per-problem speedup, ratio of mean token latencies and measured wall-clock time. Table 3 reports 1.14× wall-clock speedup on 50 MATH problems, while the adjacent protocol discloses one sequential GPU versus four parallel GPUs.

Section 5.2, p. 6; Tables 1–3 and Section 5.5, physical p. 7; raster inspected · Main paper

Appendix and reproducibility

Derivations and execution specifications precede stagewise ablations, full worked trajectories and exact rewriting prompts. The separate limitations and future-directions sections keep prospective ideas apart from demonstrated behavior.

Appendices A–H, pp. 12–36 · Main paper

Clarity and writing conventions

The distribution discussion retains mild slowdowns and near-parity tasks, explaining them through sequential portions and orchestration overhead rather than implying universal acceleration.

Sections 5.2 and 5.4, pp. 6–7 · Main paper

What to reuse—and what not to infer

Transferable lesson: Pair a concrete execution trace with explicitly different efficiency denominators, and disclose the extra hardware that buys lower latency.

Boundary: The 1.53× token-latency headline is not the measured overall wall-clock gain, and approximately matched accuracy is not superiority on every benchmark.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-10-07

Reading status

Writing-focused manuscript scan + selected visuals inspected

Main text

Writing-focused scan of main Sections 1–7, physical pp. 1–9, including metric definitions, algorithm, state-machine figures, comparison tables and limitations.

Appendix / supplement

Structural scan of Appendices A–H, pp. 12–36: objective derivation, execution steps, data/training recipes, additional comparisons, worked traces, prompts, limitations and future directions. Long prompts and derivations were not independently validated.

Visually inspected PDF pages

3, 7

This is a writing-focused scan of the manuscript and the stated supplementary scope: framing, organization, visual explanation, evidence presentation and wording. It is not a line-by-line proof audit, reproduction of results or exhaustive scientific review.

• Published proceedings PDF, PMLR volume 306, retrieved 2026-10-07 · 36 pages