Writing study: ReViT: Rotational-equivariant Vision Transformers for Neural PDE Solvers

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← ICML 2026 oral writing corpus

Hao Wei, Björn List, Nils Thuerey · 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

39 physical pages

Before references / appendix

≈ 9.24 page-equivalents

Main figures / tables

7 / 2

Attached appendix figures / tables

10 / 8

Attached appendix span

≈ 25.92 page-equivalents

Before references / appendix: ≈ 23.69%References / intervening material: ≈ 9.85%Attached appendix: ≈ 66.46%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	≈ 1.06 pp.	2.72%
2. Related Work	2	≈ 0.48 pp.	1.23%
3. Theoretical Analysis: Why ViTs fail	2	≈ 1.07 pp.	2.74%
4. Methodology of ReViT	3	≈ 2.43 pp.	6.23%
5. Results	6	≈ 3.4 pp.	8.72%
6. Discussion and Conclusions	9	≈ 0.27 pp.	0.69%
Acknowledgments	10	≈ 0.11 pp.	0.28%
Impact Statement	10	≈ 0.08 pp.	0.21%
References	10	≈ 3.84 pp.	9.85%
APPENDIX	14	≈ 0.33 pp.	0.85%
A. Results details	14	≈ 2.44 pp.	6.26%
B. Ablation study on Equivariance	16	≈ 2 pp.	5.13%
C. Local Bases	18	≈ 8.97 pp.	23%
D. Valid Rotation Range and Periodic Boundary Extension	27	≈ 1.58 pp.	4.05%
E. Rotation Aliasing in Discrete Lattices	29	≈ 1.28 pp.	3.28%
F. Experimental Details	30	≈ 3.47 pp.	8.9%
G. Approximate Equivariance Error Bound	34	≈ 0.35 pp.	0.9%
H. Equivariance Evaluation Metric Details	34	≈ 0.34 pp.	0.87%
I. Local vs. Global Bases	34	≈ 0.45 pp.	1.15%
J. Generality of ReViT	35	≈ 0.92 pp.	2.36%
K. Computational Complexity Analysis	36	≈ 0.32 pp.	0.82%
L. Data Scaling Experiment	36	≈ 0.32 pp.	0.82%
M. Architectural Advantage vs. Model Size	36	≈ 3.15 pp.	8.08%

All detected figure and table locations

Main text

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

Attached appendix

• Table 3 · p. 15
• Figure 8 · p. 16
• Figure 9 · p. 17
• Figure 10 · p. 18
• Figure 11 · p. 19
• Figure 12 · p. 20
• Table 4 · p. 26
• Figure 13 · p. 27
• Figure 14 · p. 28
• Figure 15 · p. 29
• Figure 16 · p. 30
• Figure 17 · p. 30
• Table 5 · p. 35
• Table 6 · p. 36
• Table 7 · p. 36
• Table 8 · p. 37
• Table 9 · p. 37
• Table 10 · p. 38

Argument and organization

1. Problem and contribution

   Identifies representational, tokenization and spatial obstacles to rotational equivariance rather than presenting one unexplained architectural module.

2. Argument sequence

   Each obstacle receives a corresponding local-coordinate or rebasing operation, followed by invariant-to-equivariant decoding and the hierarchical reference-basis construction.

3. Evidence and verification

   The arbitrary-angle evaluation actually compares orthogonal angular pairs to isolate exact grid-preserving symmetry; continuous non-grid-aligned rotations remain affected by interpolation.

Problem, claim and contribution

Identifies representational, tokenization and spatial obstacles to rotational equivariance rather than presenting one unexplained architectural module.

Sections 3-4, pp. 2-4 · Main paper

Argument and section order

Each obstacle receives a corresponding local-coordinate or rebasing operation, followed by invariant-to-equivariant decoding and the hierarchical reference-basis construction.

Sections 4.1-4.5, pp. 4-5 · Main paper

Figures, captions and visual explanation

The architecture separates invariant blocks, coordinate transitions and the shared basis pyramid; paired-angle bars and difference maps test equivariance independently of raw prediction error.

Figure 2, p. 5; Figures 5-6, p. 8; both PNGs inspected · Main paper

Tables, comparisons and evidence

The arbitrary-angle evaluation actually compares orthogonal angular pairs to isolate exact grid-preserving symmetry; continuous non-grid-aligned rotations remain affected by interpolation.

Section 5.4, p. 8; Appendix G-H, p. 34 · Main paper

Appendix and reproducibility

The supplement exposes degenerate basis handling, interpolation assumptions and a decoder/aggregation ablation that identifies activation-memory and accuracy tradeoffs.

Appendix C, pp. 18-25; G-H, p. 34; P, pp. 38-39 · Main paper

Clarity and writing conventions

Strict or perfect equivariance language is narrowed by the discrete-lattice discussion; preserving the group and resampling qualification is essential when summarizing the claim.

Section 5.4, p. 8; Appendix G, p. 34 · Main paper

What to reuse—and what not to infer

Transferable lesson: Map each architectural change to a stated invariance failure and evaluate the claimed symmetry separately from task accuracy.

Boundary: Grid-preserving C4 or octahedral symmetry is not exact equivariance under every continuous rotation; interpolation and degenerate local-frame cases must remain in scope.

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-focused distributed manuscript scan, not exhaustive technical/proof validation. Sections 1-5 and conclusion, pp. 1-9: equivariance barriers, local bases, invariant tokens, rebasing/hierarchy and scalar/vector PDE evaluations.

Appendix / supplement

Writing-focused appendix scan; code, data and external assets not executed. Appendices A-P, pp. 14-39: group/augmentation results, basis constructions, discrete-grid aliasing, setup, approximate bound, scaling and architectural variants.

Visually inspected PDF pages

5, 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 ICML 2026 proceedings PDF, PMLR volume 306; retrieved 2026-10-07. Public OpenReview decision notes were not independently reverified. · 39 pages