Writing study: GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning

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Jinhao Jing, Zheng Ma, Jinwei Liang, Qiannian Zhao, Shuang Chen, Jing Yang, Prayag Tiwari, Jingjing Bai, Benyou Wang, Por L Yee, Zhan Su, Lewei Lu · 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: Datasets, benchmarks & measurement (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

35 physical pages

Before references / appendix

≈ 9.09 page-equivalents

Main figures / tables

5 / 6

Attached appendix figures / tables

12 / 11

Attached appendix span

≈ 20.91 page-equivalents

Before references / appendix: ≈ 25.97%References / intervening material: ≈ 14.29%Attached appendix: ≈ 59.74%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 physical single-column y/page-height, including equation-heavy pages.

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	≈ 1.35 pp.	3.86%
2 Related Work	3	≈ 1 pp.	2.86%
3 Methodology: Scalable and Symbolically-Verifiable Synthesis	4	≈ 0.37 pp.	1.06%
4 The GeoSym Synthesis Framework	4	≈ 1.2 pp.	3.43%
5 The GeoSym Dataset and Benchmark	5	≈ 2.04 pp.	5.83%
6 Experiments and Analysis	7	≈ 2.06 pp.	5.89%
7 Conclusion	9	≈ 0.34 pp.	0.97%
References	10	≈ 5 pp.	14.29%
A GeoSym127K Dataset Samples and Comparison	15	≈ 6 pp.	17.14%
B Extended details of the GeoSym framework	21	≈ 5 pp.	14.29%
C Detailed Dataset Statistics	26	≈ 3 pp.	8.57%
D The GeoSym-Bench Details	29	≈ 3.42 pp.	9.77%
E Experimental Details and Extended Analyses	32	≈ 3.08 pp.	8.8%
F Limitations	35	≈ 0.41 pp.	1.17%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Table 1 · p. 3
• Figure 2 · p. 5
• Table 2 · p. 5
• Figure 3 · p. 6
• Table 3 · p. 6
• Table 4 · p. 6
• Table 5 · p. 7
• Figure 4 · p. 8
• Table 6 · p. 8
• Figure 5 · p. 9

Attached appendix

• Figure 6 · p. 15
• Figure 7 · p. 16
• Figure 8 · p. 17
• Figure 9 · p. 18
• Figure 10 · p. 19
• Figure 11 · p. 20
• Table 7 · p. 21
• Table 8 · p. 22
• Table 9 · p. 22
• Table 10 · p. 23
• Table 11 · p. 26
• Table 12 · p. 27
• Figure 12 · p. 27
• Table 13 · p. 28
• Figure 13 · p. 28
• Table 14 · p. 28
• Figure 14 · p. 29
• Figure 15 · p. 30
• Figure 16 · p. 30
• Figure 17 · p. 31
• Table 15 · p. 33
• Table 16 · p. 34
• Table 17 · p. 35

Argument and organization

1. Problem and contribution

   Explains the tension between geometric complexity and trustworthy supervision, positioning symbolic generation and verified answers as separate from merely enlarging an image-question collection.

2. Argument sequence

   A formal symbolic representation precedes the four-stage generation pipeline; dataset composition, expert quality audit and downstream training effects are then presented as different evidence layers.

3. Evidence and verification

   Table 2 reports generated counts and answer-verified rationale counts separately, exposing attrition. Human auditing, main benchmark comparisons and equal-volume RL comparisons use separate tables.

Problem, claim and contribution

Explains the tension between geometric complexity and trustworthy supervision, positioning symbolic generation and verified answers as separate from merely enlarging an image-question collection.

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

Argument and section order

A formal symbolic representation precedes the four-stage generation pipeline; dataset composition, expert quality audit and downstream training effects are then presented as different evidence layers.

Sections 3–5, pp. 4–9 · Main paper

Figures, captions and visual explanation

Figure 2 separates the symbolic state definition from four numbered stages and retains color identities across builders, drawing, solving and language generation. Example geometry and symbolic expressions explain what flows between modules. Figure 3 combines token-length and difficulty histograms with a hierarchical geometry-category ring for the instruction subset, not the entire named corpus. The adjacent tables separate a 1,000-sample human quality audit from model accuracy on the curated benchmark, keeping validation and downstream utility as different evidence.

Figure 2, p. 5 (render inspected); Figure 3 and Tables 3–4, p. 6 (additional rendered inspection) · Main paper

Tables, comparisons and evidence

Table 2 reports generated counts and answer-verified rationale counts separately, exposing attrition. Human auditing, main benchmark comparisons and equal-volume RL comparisons use separate tables.

Tables 2–6, pp. 5–8 · Main paper

Appendix and reproducibility

The appendix provides symbolic grammar and task-generation details, but also includes a correct-final-answer/invalid-reasoning example that bounds what answer verification guarantees.

Appendix B, pp. 21–25; Figure 14 and Appendix D, pp. 29–32 · Main paper

Clarity and writing conventions

The strongest useful pattern is the separation of mathematical answer correctness, rationale quality and model utility. Absolute-integrity wording should be softened in light of the documented rationale failure.

Section 4, p. 5; Appendix D and Figure 14, p. 29 · Main paper

What to reuse—and what not to infer

Transferable lesson: A synthetic-data paper needs a generation diagram, composition/attrition table, independent quality audit and downstream evidence, with different validation claims kept distinct.

Boundary: A symbolic check of a final answer does not certify every reasoning step in the generated chain of thought; the source's own appendix supplies a counterexample.

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 scan across manuscript framing, section sequence, figure/table captions, selected argument/evaluation prose and conclusion; not exhaustive technical or proof verification. Sections 1–6, pp. 1–9: problem, related datasets, symbolic formulation, synthesis, benchmark/training evidence and conclusion. Source is the exact public author version listed below, not a verified accepted/camera-ready revision.

Appendix / supplement

Writing-oriented appendix/documentation scan: Appendices A–F, pp. 15–35: examples, grammar/solvers/prompts, statistics, validation/decontamination, training protocols, anomalies and limitations. Source code, data, model outputs and external video assets were not executed or independently validated.

Visually inspected PDF pages

5, 6

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 2605.16371v1; not verified identical to the accepted or camera-ready OpenReview revision · 35 pages