Writing study: Thinking with Images as Continuous Policy: Numerical Visual Chain-of-Thought

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← NeurIPS 2026 oral writing corpus

Kesen Zhao, Beier Zhu, Junbao Zhou, Xingyu Zhu, Zhongqi Yue, Hanwang Zhang · Official NeurIPS 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

12 physical pages

Before references / appendix

≈ 8.19 page-equivalents

Main figures / tables

5 / 3

Attached appendix figures / tables

1 / 0

Attached appendix span

≈ 1.96 page-equivalents

Before references / appendix: ≈ 68.25%References / intervening material: ≈ 15.42%Attached appendix: ≈ 16.33%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Top-level heading and reference/appendix boundaries checked against source PDF text. Bibliography titles/author initials, numbered contribution/property bullets, diagram steps, equations and TOC entries are not substantive headings. Section spans are page-coordinate estimates, not ink area or prose-only length. This is an author manuscript mirror, not a verified accepted-version template. Source layout uses two-column reading order.

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	≈ 1.33 pp.	11.08%
2. Related Work	3	≈ 0.45 pp.	3.75%
3. Method	3	≈ 2.06 pp.	17.17%
4. Experiments	5	≈ 3.2 pp.	26.67%
5. Conclusion	8	≈ 0.34 pp.	2.83%
References	9	≈ 1.86 pp.	15.5%
A. Implementation Details	11	≈ 1.71 pp.	14.25%
B. More Visualization Results	12	≈ 0.13 pp.	1.08%
C. LLM Usage Statement	12	≈ 0.12 pp.	1%

All detected figure and table locations

Main text

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

Attached appendix

• Figure 6 · p. 12

Argument and organization

1. Problem and contribution

   Contrasts coordinate-token semantics and fixed patch granularity with a continuous spatial action space.

2. Argument sequence

   Defines the numerical head, supervised regression and policy optimization before Gaussian/Laplace choices and evaluations.

3. Evidence and verification

   The ablation page separates coordinate-policy choice, uncertainty parameterization, localization IoU and final-answer performance.

Problem, claim and contribution

Contrasts coordinate-token semantics and fixed patch granularity with a continuous spatial action space.

Introduction; Figure 2 · Main paper

Argument and section order

Defines the numerical head, supervised regression and policy optimization before Gaussian/Laplace choices and evaluations.

Section 3; Section 4 · Main paper

Figures, captions and visual explanation

A shared image/question anchors three paradigm panels; discrete token choices, patch grids and a continuous density make the representational difference visible.

Figure 2, p. 2 · Main paper

Tables, comparisons and evidence

The ablation page separates coordinate-policy choice, uncertainty parameterization, localization IoU and final-answer performance.

Tables 2–3; Figures 3–4, p. 7 · Main paper

Appendix and reproducibility

Additional derivation and bounding-box examples extend the mechanism and qualitative evidence without replacing the main comparison.

Appendices A–B · Main paper

Clarity and writing conventions

The evaluation explicitly distinguishes single tool calls from dagger-marked multistep settings.

Table 1 caption; evaluation protocol · Main paper

What to reuse—and what not to infer

Transferable lesson: Use one worked input to compare representations, then measure the intermediate localization claim separately from answer accuracy.

Boundary: The author PDF uses 'Continuous Actions' in its title/header rather than the accepted inventory's 'Continuous Policy'; its two-column format is not verified NeurIPS final formatting.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-10-02

Reading status

Writing-focused manuscript scan + selected visuals inspected

Main text

Writing-oriented distributed manuscript scan of Sections 1–5, pp. 1–8; impact/reference material pp. 9–11: abstract/framing, section sequence, substantive text windows, captions, evidence organization and conclusion; not exhaustive technical verification.

Appendix / supplement

Writing-oriented scan of Supplementary derivation and additional localization examples ending on p. 12; code and experiments were not executed.

Visually inspected PDF pages

2, 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.

• Public author arXiv manuscript 2602.23959v1; not verified identical to the accepted or camera-ready OpenReview revision · 12 pages