Writing study: Solving Time-Dependent Differential Equations with Physical Dynamical Systems

ICML overviewCorpus atlasBy contribution typeVisual galleryRules & templateWriting patternsPaper studies

← ICML 2026 oral writing corpus

Chuan Liu, Yijie Chen, Ruibing Song, Wenhao Huang, Chunshu Wu, Deqian Kong, Ying Nian Wu, Kaiyuan Yang, Ang Li, Tony Geng · 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: Efficiency, inference & systems (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

17 physical pages

Before references / appendix

≈ 8.6 page-equivalents

Main figures / tables

7 / 1

Attached appendix figures / tables

1 / 0

Attached appendix span

≈ 4.91 page-equivalents

Before references / appendix: ≈ 50.59%References / intervening material: ≈ 20.53%Attached appendix: ≈ 28.88%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	≈ 1.22 pp.	7.18%
2. Preliminaries	2	≈ 0.45 pp.	2.65%
3. Methodology	3	≈ 3.06 pp.	18%
4. Evaluation	6	≈ 2.04 pp.	12%
5. Related Work	8	≈ 0.86 pp.	5.06%
6. Conclusion	9	≈ 0.11 pp.	0.65%
Acknowledgements	9	≈ 0.17 pp.	1%
Impact Statement	9	≈ 0.05 pp.	0.29%
References	9	≈ 3.49 pp.	20.53%
A. Appendix	13	≈ 4.91 pp.	28.88%

All detected figure and table locations

Main text

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

Attached appendix

• Figure 8 · p. 16

Argument and organization

1. 1 Introduction; 2 Preliminaries

   Motivates continuous-time computation while retaining spatial discretization.

2. 3 Method

   Maps excitation, state-aware coefficients and higher-order integration to components before training and boundary handling.

3. 4 Evaluation; 5 Related Work; 6 Conclusion

   Separates predictive errors, hardware estimates and noise robustness.

Problem, claim and contribution

The motivating distinction is continuous physical-time evolution versus repeated digital stepping, not elimination of spatial discretization or learned-parameter fitting.

Introduction, p.1; Sections 3.1-3.2, pp.3-5 · Main paper

Argument and section order

The three modules are introduced as operators before their circuit mappings, supervised training and boundary-condition procedures.

Sections 3.1-3.4, pp.3-5 · Main paper

Figures, captions and visual explanation

The module schematic prints subsection pointers and preserves signal labels across panels; the results table groups short and long trajectories while latency plots use matched task columns.

Figure 3, p.4; Table 1 and latency plots, p.7 · Main paper

Tables, comparisons and evidence

Headline speed and energy gains combine software dynamics with component-level circuit characterization and estimated hardware power, not a fabricated full-system measurement.

Evaluation setup and latency/energy analysis, pp.6-8 · Main paper

Appendix and reproducibility

The supplement specifies staged quantization-aware training and early stopping, then acknowledges the connection cost of a fully coupled implementation.

Training details, p.15; implementation limitations, p.17 · Main paper

Clarity and writing conventions

The noise analysis identifies a thermal-noise model and bandwidth, so its favorable error result should not be generalized to every fabrication or device imperfection.

Noise robustness, p.8 · Main paper

What to reuse—and what not to infer

Transferable lesson: For a hardware-motivated paper, identify the measurement level of every efficiency number and separate the mathematical design from its physical realization.

Boundary: The reported system-level gains are estimates based on characterized components; query latency, power assumptions and I/O coverage must remain explicit when comparing to digital baselines.

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

Visually inspected PDF pages

4, 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 · 17 pages