Writing study: Cross-Domain Lossy Compression via Rate- and Classification-Constrained Optimal Transport

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← ICLR 2026 oral writing corpus

Nam Nguyen, Thinh Nguyen, Bella Bose · 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: Theory & formal foundations (primary) · Learning & optimization algorithms.

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

≈ 9.17 page-equivalents

Main figures / tables

6 / 0

Attached appendix figures / tables

13 / 15

Attached appendix span

≈ 35.84 page-equivalents

Before references / appendix: ≈ 18.34%References / intervening material: ≈ 9.98%Attached appendix: ≈ 71.68%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.	2.12%
2 SYSTEM MODEL AND ONE-SHOT SETTING RESULTS	2	≈ 2.59 pp.	5.18%
3 SYSTEM MODEL AND ASYMPTOTIC SETTING RESULTS	5	≈ 2.5 pp.	5%
4 RELATED WORKS	7	≈ 0.61 pp.	1.22%
5 EXPERIMENTAL RESULTS	8	≈ 1.36 pp.	2.72%
6 CONCLUSION	9	≈ 0.48 pp.	0.96%
REFERENCES	10	≈ 4.98 pp.	9.96%
A THEORETICAL RESULTS	15	≈ 15.95 pp.	31.9%
B EXPERIMENTAL RESULTS	31	≈ 15 pp.	30%
C ADDITIONAL EXPERIMENTAL RESULTS	46	≈ 4.89 pp.	9.78%

All detected figure and table locations

Main text

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

Attached appendix

• Figure 7 · p. 32
• Figure 8 · p. 33
• Figure 9 · p. 34
• Figure 10 · p. 35
• Figure 11 · p. 36
• Figure 12 · p. 38
• Figure 13 · p. 39
• Table 1 · p. 41
• Table 2 · p. 41
• Table 3 · p. 42
• Table 4 · p. 42
• Table 5 · p. 42
• Table 6 · p. 43
• Table 7 · p. 44
• Table 8 · p. 44
• Table 9 · p. 44
• Table 10 · p. 45
• Table 11 · p. 45
• Table 12 · p. 45
• Figure 14 · p. 46
• Figure 15 · p. 46
• Figure 16 · p. 47
• Figure 17 · p. 47
• Figure 18 · p. 48
• Figure 19 · p. 49
• Table 13 · p. 49
• Table 14 · p. 49
• Table 15 · p. 50

Argument and organization

1. Constrained transport and coding

   Defines separate marginal, rate and label-information requirements.

2. One-shot and asymptotic regimes

   Organizes Bernoulli and Gaussian claims under distinct coding assumptions.

3. Neural implementation and empirical trade-offs

   Maps theoretical quantities to practical surrogate losses.

Problem, claim and contribution

The motivation distinguishes restoring a target distribution from reproducing a degraded input. However, the distortion remains between input and reconstruction, so the reader must keep distributional restoration separate from paired clean-target error.

§§1–2, pp.1–3; §5.1, p.8 · Main paper

Argument and section order

Numbered definitions separate one-shot entropy constraints from asymptotic mutual information. The practical rate upper bound and later entropy-model estimate are different quantities, and should retain their units instead of sharing an unexplained rate axis.

Definitions2–3, pp.3,5; §5.1, p.8; AppendixB.1, p.31 · Main paper

Figures, captions and visual explanation

Figure5 links the dither add/subtract path, discriminator, classifier and distortion loss explicitly. Figure18 then places classification accuracy beside conditional-entropy estimates, although labeling a learned-posterior estimate exact overstates what the experiment establishes.

Figure5, p.8; AppendixC.4 and Figure18, p.48 · Main paper

Tables, comparisons and evidence

Appendix tables expose non-monotonic experimental points hidden by general monotonic wording. The Kodak comparison also acknowledges that BM3D has no rate penalty, but supplies no bitrate column, preventing verification of a matched-rate superiority claim.

Tables1–5, pp.41–42; Tables11–12, p.45; Table15, p.50 · Main paper

Appendix and reproducibility

Reading the proofs reveals substantive issues requiring clarification: AppendixA.1.2 replaces H(S|Y) by an average conditional on the shared seed, and AppendixA.1.3 assigns finite mutual information to Y=X for a nondegenerate continuous Gaussian.

AppendixA.1.2, pp.16–17; AppendixA.1.3 Case4, p.21 · Main paper

Clarity and writing conventions

Synthetic samples drawn from a theorem-prescribed coupling check that construction's behavior, not optimality over all couplings. The conclusion's confirmed-theory wording is therefore too strong, especially alongside the unresolved entropy and feasibility issues.

§6, p.9; AppendixC.3, pp.47–48 · Main paper

What to reuse—and what not to infer

Transferable lesson: For theory-to-system papers, preserve the exact conditioning variables, feasible regimes and operational rate units all the way from definitions to figures; empirical agreement is not a substitute for a valid derivation.

Boundary: Full reading is not proof certification. Several supplied formulas and architecture descriptions require correction or reconciliation before scientific reuse. Fluorescence nuclei experiments are not WSI pathology validation; unsupervised restoration still uses semantic labels and target-distribution information in the described objectives.

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

pp.1–9, §§1–6; references pp.10–14

Appendix / supplement

pp.15–50, A–C: complete supplied proofs, rate estimation, restoration protocols, architecture tables, synthetic checks and additional comparisons

Visually inspected PDF pages

8, 48

• official ICLR 2026 proceedings PDF · 50 pages