Writing study: CoEvol-NO: State and Coordinate Co-Evolution with an Error-Driven Predictor-Corrector Paradigm for Neural Operator Transformer

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← ICML 2026 oral writing corpus

Jianqiao Zeng, Ruocheng Wang, Yanzhi Liu, Hao Xiong, Junchi Yan · 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

≈ 9.15 page-equivalents

Main figures / tables

3 / 10

Attached appendix figures / tables

5 / 9

Attached appendix span

≈ 14.86 page-equivalents

Before references / appendix: ≈ 33.89%References / intervening material: ≈ 11.07%Attached appendix: ≈ 55.04%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	≈ 0.98 pp.	3.63%
2. Related Work	2	≈ 0.94 pp.	3.48%
3. Preliminary	3	≈ 0.49 pp.	1.81%
4. Methodology	4	≈ 1.66 pp.	6.15%
5. Experiment	5	≈ 3.9 pp.	14.44%
6. Conclusion and Limitation	9	≈ 0.32 pp.	1.19%
Impact Statement	10	≈ 0.05 pp.	0.19%
Acknowledgments	10	≈ 0.05 pp.	0.19%
References	10	≈ 2.99 pp.	11.07%
A. Theoretical Analysis and Derivations	13	≈ 2.37 pp.	8.78%
B. Theoretical Motivation for the Prediction Target Selection	15	≈ 0.84 pp.	3.11%
C. CoEvol-NO Algorithm	16	≈ 0.41 pp.	1.52%
D. Stability and Conditioning Analysis of Update Mechanisms	16	≈ 1.33 pp.	4.93%
E. Full Gradient Ablation: 8-Combination Study	18	≈ 0.38 pp.	1.41%
F. Full Momentum Ablation	18	≈ 0.62 pp.	2.3%
G. Comparison with Attention Residuals (AttnRes)	19	≈ 0.33 pp.	1.22%
H. Extended Scaling Analysis	19	≈ 2.13 pp.	7.89%
I. Statistical Significance and Stability	21	≈ 0.18 pp.	0.67%
J. In-depth Visualization of Latent Dynamics	21	≈ 3.65 pp.	13.52%
K. Experimental Details	25	≈ 1.36 pp.	5.04%
L. Efficiency Analysis	26	≈ 0.42 pp.	1.56%
M. Runtime and Memory Benchmarks	27	≈ 0.83 pp.	3.07%

All detected figure and table locations

Main text

• Figure 1 · p. 1
• Figure 2 · p. 2
• Table 1 · p. 3
• Figure 3 · p. 6
• Table 2 · p. 6
• Table 3 · p. 6
• Table 4 · p. 7
• Table 5 · p. 8
• Table 6 · p. 8
• Table 7 · p. 8
• Table 8 · p. 9
• Table 9 · p. 9
• Table 10 · p. 9

Attached appendix

• Table 11 · p. 18
• Table 12 · p. 18
• Table 13 · p. 19
• Table 14 · p. 19
• Figure 4 · p. 19
• Table 15 · p. 20
• Table 16 · p. 21
• Figure 5 · p. 21
• Figure 6 · p. 22
• Figure 7 · p. 23
• Table 17 · p. 25
• Table 18 · p. 26
• Figure 8 · p. 26
• Table 19 · p. 27

Argument and organization

1. 1 Introduction; 2 Related Work; 3 Preliminaries

   Frames competing mesh/state interaction designs before the predictor-corrector analogy.

2. 4 Methodology

   Separates exact latent-state correction, approximate mesh updates and optimizer enhancements.

3. 5 Experiments; 6 Conclusion and Limitation

   Tests benchmark quality, component choices, resolution transfer, shifts and cross-architecture applicability.

Problem, claim and contribution

The architecture is motivated by a proposed geometry-versus-memory trade-off, but layer-wise latent evolution should not be confused with directly verified physical-time dynamics.

Abstract, p.1; Section 4.2, p.4 · Main paper

Argument and section order

Prediction and correction receive separate definitions, and the ideal representation is explicitly replaced by a learned target rather than intermediate ground truth.

Remark 3.1 and Section 4.2, p.4 · Main paper

Figures, captions and visual explanation

The ablation table separates exact and approximate updates and labels loss variants; adjacent transfer tables make resolution and physical-condition shifts distinct evaluation axes.

Tables 5-7, p.8 · Main paper

Tables, comparisons and evidence

The result captions identify copied versus reimplemented baselines, while the OOD table retains worse field/coefficient errors despite improved rank correlation.

Table 2, p.6; Table 7 and discussion, p.8 · Main paper

Appendix and reproducibility

The gradient derivation supports the stated mesh-size complexity, and the runtime supplement reports an approximately 1.7-fold constant overhead despite linear scaling.

Appendix A.1, p.13; Appendix L, p.26 · Main paper

Clarity and writing conventions

The limitation paragraph admits that exact correction on every module can hurt and that conditioning and deep-network behavior remain unresolved.

Conclusion and Limitation, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: Separate asymptotic scaling from measured constant cost, and report accuracy, ranking and distribution-shift results without merging their different conclusions.

Boundary: Linear complexity holds with latent size and feature width controlled; PCA trajectories and improved PDE errors do not prove recovery of physical laws or universal stability.

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, 26. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

4, 8

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