Writing study: Geometric Flow Grounding: A Unified Manifold Decoupling Framework for Dynamics Discovery and Verification

ICML overviewCorpus atlasBy contribution typeVisual galleryRules & templateWriting patternsPaper studies

← ICML 2026 oral writing corpus

Chang Yu, Yuxuan Luo, Yixuan Du, Yuqing Zhou, Siyuan Li, Jingbo Zhou, Jiawei Jiang, Zhen Lei, Stan Z. Li · 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: Architecture & representation (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

27 physical pages

Before references / appendix

≈ 9.04 page-equivalents

Main figures / tables

6 / 6

Attached appendix figures / tables

2 / 5

Attached appendix span

≈ 14.91 page-equivalents

Before references / appendix: ≈ 33.48%References / intervening material: ≈ 11.3%Attached appendix: ≈ 55.22%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	≈ 1.24 pp.	4.59%
2. Preliminaries	2	≈ 0.56 pp.	2.07%
3. Method	3	≈ 2.33 pp.	8.63%
4. Experiments	5	≈ 3.14 pp.	11.63%
5. Related Work	8	≈ 0.45 pp.	1.67%
6. Conclusion and Future Work	9	≈ 0.39 pp.	1.44%
Acknowledgements	9	≈ 0.1 pp.	0.37%
Impact Statement	9	≈ 0.21 pp.	0.78%
References	10	≈ 3.04 pp.	11.26%
A. Theoretical Proofs	13	≈ 2.09 pp.	7.74%
B. Datasets and Evaluation Metrics	15	≈ 2.49 pp.	9.22%
C. Network Architectures and Training Details	17	≈ 5.42 pp.	20.07%
D. Supplementary Experiments and Analysis	23	≈ 2.67 pp.	9.89%
E. Detailed Case-specific Related Work	25	≈ 2.25 pp.	8.33%

All detected figure and table locations

Main text

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

Attached appendix

• Table 7 · p. 23
• Table 8 · p. 23
• Table 9 · p. 24
• Figure 8 · p. 25
• Figure 7 · p. 25
• Table 10 · p. 26
• Table 11 · p. 27

Argument and organization

1. 1 Introduction; 2 Preliminaries

   Distinguishes smoothing drift from integration drift and defines learned geometry.

2. 3 Method

   States tangent-space assumptions, presents a projection argument and implements dual state/dynamics streams.

3. 4 Experiments; 5 Related Work; 6 Conclusion

   Maps the common formulation to ODE, RNA-velocity and video cases with domain-specific objectives and limitations.

Problem, claim and contribution

The unifying claim is geometric consistency with a learned decoder manifold, not access to the true manifold or a uniquely identified latent system.

Assumption 3.1, p.3; Limitation, p.9 · Main paper

Argument and section order

A proof sketch separates ideal orthogonal projection from the practical Jacobian-vector construction, and a domain-objective table explains what changes across applications.

Theorem 3.2 and Sections 3.3-3.4, pp.4-5 · Main paper

Figures, captions and visual explanation

The overview consistently separates blue state and green velocity codebooks, linked by a red JVP arrow; RNA plots use matched embeddings and highlighted regions beside distinct atom activations.

Figure 2, p.3; Figures 4-5, p.7 · Main paper

Tables, comparisons and evidence

Geometric coherence is distinguished from lineage-direction metrics, and the video table separately reports the standalone signal and its combination with an existing detector.

Table 3, p.6; Table 4, p.7 · Main paper

Appendix and reproducibility

The supplement gives the generator-specific train/validation/test protocol and a degradation experiment, making the scope of unseen-generator claims inspectable.

Appendix B.3, p.17; Appendix D.3, p.25 · Main paper

Clarity and writing conventions

The video discussion preserves the combined model’s lower F1 despite stronger recall/AUROC, whereas universal and hallucination-free language needs the later manifold assumptions.

Section 4.3, p.8; Limitation, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: When proposing one framework across domains, show the common operator, the changing supervision and the distinct validation target for each case.

Boundary: Tangency to learned geometry is not guaranteed physical correctness; RNA streamlines and enrichment are not lineage experiments, and the complete video pipeline includes training and pretrained-model assumptions.

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-oriented scan of the main argument through physical p.9, with focused physical-page text inspection on 1, 3, 4, 5, 6, 7, 8, 9. Framing, section progression, mechanism/proof explanation, displays, comparison conditions and conclusions were inspected. This is not exhaustive technical reading, proof verification or reproduction.

Appendix / supplement

Appendix organization and main-text pointers were checked; focused text inspection of physical pages 13, 17, 25. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

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 · 27 pages