Writing study: Characterizing, Evaluating, and Optimizing Complex Reasoning

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← ICML 2026 oral writing corpus

Haoran Zhang, Yafu Li, Zhi Wang, Zhilin Wang, Shunkai Zhang, Xiaoye Qu, Yu Cheng · 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: Training, objectives & optimization (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

68 physical pages

Before references / appendix

≈ 8.36 page-equivalents

Main figures / tables

6 / 3

Attached appendix figures / tables

12 / 3

Attached appendix span

≈ 54.91 page-equivalents

Before references / appendix: ≈ 12.29%References / intervening material: ≈ 6.96%Attached appendix: ≈ 80.75%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

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	≈ 1.47 pp.	2.16%
2. Related Work	2	≈ 0.55 pp.	0.81%
3. Characterizing Reasoning Trace Quality	3	≈ 0.82 pp.	1.21%
4. Evaluating Reasoning Traces	4	≈ 1.2 pp.	1.76%
5. Optimizing Reasoning with Thinking	5	≈ 2.93 pp.	4.31%
6. Analysis	8	≈ 0.79 pp.	1.16%
7. Conclusion	9	≈ 0.14 pp.	0.21%
Acknowledgements	9	≈ 0.06 pp.	0.09%
Impact Statement	9	≈ 0.05 pp.	0.07%
References	9	≈ 4.73 pp.	6.96%
A. Optimal Policy Invariance of TRM-Guided Reward Shaping	14	≈ 1.47 pp.	2.16%
B. Lower Bound on Policy Improvement	15	≈ 4.72 pp.	6.94%
C. Discussion	20	≈ 1.04 pp.	1.53%
D. Details of Step Partitioning	21	≈ 0.42 pp.	0.62%
E. Details of DAG Construction	21	≈ 1.79 pp.	2.63%
F. Details of Preference Dataset Construction	23	≈ 0.82 pp.	1.21%
G. Experimental Details	24	≈ 2.16 pp.	3.18%
H. Ablation Study	26	≈ 0.12 pp.	0.18%
I. Brief Introduction of Bradley–Terry Loss	26	≈ 0.47 pp.	0.69%
J. Prompt Design	27	≈ 9 pp.	13.24%
K. Case Study	36	≈ 32.91 pp.	48.4%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 3
• Figure 3 · p. 5
• Table 1 · p. 6
• Figure 4 · p. 7
• Table 2 · p. 7
• Figure 5 · p. 8
• Figure 6 · p. 8
• Table 3 · p. 8

Attached appendix

• Figure 7 · p. 22
• Figure 8 · p. 23
• Figure 9 · p. 24
• Table 4 · p. 25
• Table 5 · p. 26
• Table 6 · p. 26
• Figure 10 · p. 28
• Figure 11 · p. 29
• Figure 12 · p. 30
• Figure 13 · p. 31
• Figure 14 · p. 32
• Figure 15 · p. 33
• Figure 16 · p. 34
• Figure 17 · p. 35
• Figure 18 · p. 37

Argument and organization

1. 1 Introduction; 2 Related Work; 3 Characterizing Reasoning Trace Quality

   Maps three questions to a macro/micro by efficiency/effectiveness definition of trace quality.

2. 4 Evaluating Reasoning Traces; 5 Optimizing Reasoning

   Builds DAG abstractions and pairwise labels, then trains a reward model and uses it for selection and gated RL reward.

3. 6 Analysis; 7 Conclusion

   Checks learned trace preferences, training trajectories and compute overhead separately from final-answer scores.

Problem, claim and contribution

Verified-correct traces are used to train a quality preference model, explicitly separating within-correct-trace preferences from binary answer correctness.

Sections 1 and 5.1, physical pp.2,5 · Main paper

Argument and section order

The quality taxonomy comes before graph construction and reward optimization, so the evaluation instrument is defined before its use as a learning signal.

Sections 3–5, pp.3–7 · Main paper

Figures, captions and visual explanation

The DAG illustration explains progression, branching and merging, with separate macro summaries and a micro dominant path; the result table groups policy models and task families.

Figure 3, p.5; Figure 4 and Table 2, p.7 · Main paper

Tables, comparisons and evidence

Preference accuracy counts ties as incorrect in the main validation table, whereas the appendix reliability check excludes ties. Offline label construction is separately costed rather than included in the 49-GPU-hour RL figure.

Table 1, p.6; Table 3, p.8; Appendices G.4–G.5, p.25 · Main paper

Appendix and reproducibility

Formal shaping statements, graph-construction details, exact evaluation prompts, human/LLM agreement checks and worked traces are separated into distinct appendix functions.

Appendices A, D–K; selected pp.14,25–26 · Main paper

Clarity and writing conventions

Main claims of optimal-policy invariance point to an appendix potential-based formulation; the mapping and assumptions require technical verification beyond a writing scan.

Theorem 5.1, p.7; Appendix A, p.14 · Main paper

What to reuse—and what not to infer

Transferable lesson: Define a quality construct before training a model to optimize it, and keep label reliability, downstream accuracy and construction cost as separate evidence.

Boundary: A judge-derived trace preference is not direct access to internal reasoning or proof faithfulness. Do not repeat the 19.3-point example without checking its task label: the 44.7-to-64.0 trajectory appears under AIME25 in Figure 4 although adjacent prose names AIME24. The shaping guarantees were not independently validated.

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 across physical PDF pp.1–9, covering framing, section progression, definitions, method/evidence explanations, captions and scope. Physical pages extracted individually to avoid form-feed pagination errors. Selected full-page rasters inspected; not exhaustive line-by-line technical verification or experimental reproduction.

Appendix / supplement

Appendix structure inventoried; selected reading of potential-based shaping formulation A (p.14), reliability and offline-cost details G.3–G.5 (p.25), and larger-model/coefficient results G.6–I (p.26). Long proofs and full case-study traces were not independently verified.

Visually inspected PDF pages

5, 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 · 68 pages