Writing study: Information Shapes Koopman Representation

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← ICLR 2026 oral writing corpus

Xiaoyuan Cheng, Wenxuan Yuan, Yiming Yang, Yuanzhao Zhang, Sibo Cheng, Yi He, Zhuo Sun · Official ICLR 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: Learning & optimization algorithms (primary) · Theory & formal foundations.

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

50 physical pages

Before references / appendix

≈ 10.28 page-equivalents

Main figures / tables

6 / 2

Attached appendix figures / tables

16 / 10

Attached appendix span

≈ 35.79 page-equivalents

Before references / appendix: ≈ 20.56%References / intervening material: ≈ 7.86%Attached appendix: ≈ 71.58%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	≈ 1.6 pp.	3.2%
2 PRELIMINARIES	3	≈ 0.56 pp.	1.12%
3 METHOD	3	≈ 3.75 pp.	7.5%
4 EXPERIMENTS	7	≈ 3.22 pp.	6.44%
5 CONCLUSION	10	≈ 0.28 pp.	0.56%
ACKNOWLEDGMENTS	11	≈ 0.17 pp.	0.34%
REFERENCES	11	≈ 3.93 pp.	7.86%
A NOTATION	15	≈ 0.89 pp.	1.78%
B A GENTLE INTRODUCTION TO APPENDIX	16	≈ 1 pp.	2%
C MORE LITERATURE REVIEW RELATED TO KOOPMAN REPRESENTATION	17	≈ 0.45 pp.	0.9%
D LIMITATIONS AND FUTURE DIRECTIONS	17	≈ 0.55 pp.	1.1%
E KEY TECHNICAL DEFINITIONS AND RELATED PROPERTIES	18	≈ 2 pp.	4%
F THEORETICAL FRAMEWORK	20	≈ 12 pp.	24%
G PRACTICAL DETAILS, IMPLEMENTATION AND EXPERIMENTAL DETAILS	32	≈ 18.89 pp.	37.78%

All detected figure and table locations

Main text

• Table 1 · p. 2
• Figure 1 · p. 5
• Table 2 · p. 8
• Figure 2 · p. 9
• Figure 3 · p. 9
• Figure 4 · p. 9
• Figure 5 · p. 10
• Figure 6 · p. 10

Attached appendix

• Table 3 · p. 15
• Figure 7 · p. 18
• Figure 8 · p. 20
• Figure 9 · p. 26
• Table 4 · p. 28
• Figure 10 · p. 36
• Figure 11 · p. 37
• Figure 12 · p. 37
• Table 5 · p. 38
• Figure 13 · p. 39
• Figure 14 · p. 39
• Figure 15 · p. 40
• Table 6 · p. 41
• Table 7 · p. 41
• Figure 16 · p. 42
• Figure 17 · p. 43
• Figure 18 · p. 44
• Figure 19 · p. 45
• Figure 20 · p. 46
• Figure 21 · p. 47
• Table 8 · p. 48
• Table 9 · p. 48
• Figure 22 · p. 48
• Table 10 · p. 49
• Table 11 · p. 49
• Table 12 · p. 49

Argument and organization

1. Three representation desiderata and five theoretical questions

   Connects temporal coherence, structural consistency and predictive sufficiency to a sequence of propositions.

2. Practical objective and proposition-led experiments

   Labels each loss term by purpose and organizes empirical analysis as questions referring back to propositions.

Problem, claim and contribution

Table 1 translates the familiar information-bottleneck formulation into a dynamical prediction setting before introducing additional Koopman constraints.

Table 1 and introduction, page 2. · Main paper

Argument and section order

The five-proposition progression provides a clear argument map: information loss, prediction discrepancy, spectral decomposition, concentration and anti-collapse. Appendix B restates this as five reader questions.

Sections 3.1–3.3, pages 4–7; Appendix B, page 16. · Main paper

Figures, captions and visual explanation

Figure 1 combines an encoder–linear-operator–decoder diagram, geometric information decomposition and water-filling cartoons; matching labels help link mechanism and regularization.

Figure 1, page 5. · Main paper

Tables, comparisons and evidence

Table 2 groups metrics by task and horizon, marking best and second-best cells and retaining cases where PFNN wins. Figures 2–3 supply geometric evidence complementary to forecasting scores.

Table 2 and Figures 2–3, pages 8–9. · Main paper

Appendix and reproducibility

Separate stochastic and deterministic algorithms, task-specific transition structures, model tables and baseline links make the general formulation inspectable as distinct implementations.

Algorithms 1–2 and Tables 5, 10–12, pages 32–38 and 49–50. · Main paper

Clarity and writing conventions

Question-led experimental interpretation is a useful organizing device, but wording that an empirical table verifies a mathematical bound exceeds what the comparison alone demonstrates.

Section 4, first result-analysis question, page 8. · Main paper

What to reuse—and what not to infer

Transferable lesson: Make each theoretical motivation correspond to a labeled objective term and a distinct empirical diagnostic, then provide implementation-specific algorithms in the appendix.

Boundary: Do not reuse the theory as an independently validated guarantee. Fact F.1 claims an entropy inequality from data processing for a stochastic encoder, which is not generally valid; the proof's encoded-state conditional independences also require reconciliation with the generative chain in Equation 2. Gaussian latent assumptions, metric-label inconsistencies and non-winning control results require explicit qualification.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-09-19

Reading status

Full text + selected visuals inspected

Main text

Pages 1–10, Sections 1–5; acknowledgments, reproducibility and references on pages 11–14.

Appendix / supplement

Pages 15–50, Appendices A–G: notation, roadmap, literature, limitations, definitions, all six proof subsections, AE/VAE algorithms, task settings, additional results and architectures.

Visually inspected PDF pages

5, 8

• ICLR 2026 official proceedings PDF, retrieved 2026-09-19 · 50 pages