Writing study: Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers

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← ICML 2026 oral writing corpus

Zander W. Blasingame, Chen Liu · 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: Theory & formal analysis (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

73 physical pages

Before references / appendix

≈ 9.19 page-equivalents

Main figures / tables

9 / 1

Attached appendix figures / tables

11 / 8

Attached appendix span

≈ 57.91 page-equivalents

Before references / appendix: ≈ 12.59%References / intervening material: ≈ 8.08%Attached appendix: ≈ 79.33%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Source-checked physical-page text restores wrapped top-level heading labels on pp. 3. Heading starts and measured positions are unchanged; this is label completeness, not a new section. Newly detected unnumbered impact/singular-acknowledgment statements are retained from the size-aware source extraction; authored heading corrections are unchanged.

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	≈ 0.9 pp.	1.23%
2. Preliminaries	2	≈ 1.03 pp.	1.41%
3. Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers	3	≈ 3.41 pp.	4.67%
4. Empirical Results	6	≈ 2.94 pp.	4.03%
5. Related Work	9	≈ 0.16 pp.	0.22%
6. Conclusion	9	≈ 0.26 pp.	0.36%
Acknowledgements	10	≈ 0.08 pp.	0.11%
Impact Statement	10	≈ 0.08 pp.	0.11%
References	10	≈ 5.89 pp.	8.07%
Appendices	16	≈ 1.47 pp.	2.01%
A. Detailed Discussion on Related Work	17	≈ 7.8 pp.	10.68%
B. Stochastic Runge-Kutta Methods	25	≈ 5.42 pp.	7.42%
C. Derivation of Rex	30	≈ 12.78 pp.	17.51%
D. Convergence Order Proofs	43	≈ 1.91 pp.	2.62%
E. Relation to Other Solvers for Diffusion Models	45	≈ 7.62 pp.	10.44%
F. Implementation Details	53	≈ 5.6 pp.	7.67%
G. Experimental Details	58	≈ 5.14 pp.	7.04%
H. Additional Results	63	≈ 10.18 pp.	13.95%

All detected figure and table locations

Main text

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

Attached appendix

• Table 2 · p. 24
• Figure 10 · p. 45
• Table 3 · p. 62
• Table 4 · p. 63
• Table 5 · p. 64
• Table 6 · p. 65
• Table 7 · p. 65
• Table 8 · p. 66
• Figure 11 · p. 66
• Table 9 · p. 67
• Figure 12 · p. 68
• Figure 13 · p. 68
• Figure 14 · p. 69
• Figure 15 · p. 69
• Figure 16 · p. 69
• Figure 17 · p. 70
• Figure 18 · p. 71
• Figure 19 · p. 72
• Figure 20 · p. 73

Argument and organization

1. Problem and contribution

   Separates closed-form algebraic reversibility from implicit inversion and from merely storing the trajectory, making the target property precise.

2. Argument sequence

   Reparameterization precedes the reversible coupling, then a boxed construction and separate convergence statements lead to reconstruction and downstream tests.

3. Evidence and verification

   Editing results explain omitted identity-collapse outputs, while component ablations retain variants with better inversion error but worse editing quality.

Problem, claim and contribution

Separates closed-form algebraic reversibility from implicit inversion and from merely storing the trajectory, making the target property precise.

Section 2.1, p. 2 · Main paper

Argument and section order

Reparameterization precedes the reversible coupling, then a boxed construction and separate convergence statements lead to reconstruction and downstream tests.

Sections 3-4, pp. 3-8 · Main paper

Figures, captions and visual explanation

Tinted proposition/theorem boxes distinguish construction from guarantees; radar captions disclose normalized ranges, the inverted LPIPS axis and raw-table destinations.

Proposition 3.2/Theorem 3.3, p. 5; Figures 8-9, p. 8; both PNGs inspected · Main paper

Tables, comparisons and evidence

Editing results explain omitted identity-collapse outputs, while component ablations retain variants with better inversion error but worse editing quality.

Section 4.3, p. 8; Appendix H.7 and Table 9, p. 67 · Main paper

Appendix and reproducibility

A detailed contents page supports the long derivation chain; Brownian reconstruction profiling is followed by latent-space failures, including a stochastic data-parameterization overflow case.

Appendix overview, p. 16; H.6-H.8, pp. 66-67 · Main paper

Clarity and writing conventions

The narrative explicitly distinguishes an ODE convergence-order result from stochastic constructions and accompanies exact-inversion language with finite-precision experiments.

Section 3.3, pp. 5-6; Appendix H.8, p. 67 · Main paper

What to reuse—and what not to infer

Transferable lesson: Separate algebraic identity, numerical stability and downstream usefulness, and preserve ablations where those objectives move in opposite directions.

Boundary: Algebraic reversibility does not prevent overflow or guarantee stable latent distributions; radar area depends on normalization and LPIPS to the whole original image is not a localized preservation certificate.

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 1-6, pp. 1-9: reversibility definitions, reparameterized solver construction, ODE/SDE properties, finite-precision reconstruction, generation/editing and molecular sampling.

Appendix / supplement

Writing-focused appendix scan; code, data and external assets not executed. Appendix navigation p. 16 and A-H, pp. 17-73: stability comparisons, stochastic integrators, derivations/proofs, solver correspondences, implementation, profiling, ablations and uncurated samples.

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. · 73 pages