Writing study: Lottery Prior: Randomized Neural Compression for Zero-Shot Inverse Problems

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← ICML 2026 oral writing corpus

Haotian Wu, Di You, Pier Luigi Dragotti, Deniz Gunduz · 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: Training, objectives & optimization (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

37 physical pages

Before references / appendix

≈ 9.15 page-equivalents

Main figures / tables

6 / 6

Attached appendix figures / tables

10 / 14

Attached appendix span

≈ 24.92 page-equivalents

Before references / appendix: ≈ 24.73%References / intervening material: ≈ 7.92%Attached appendix: ≈ 67.35%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Join wrapped printed heading text using adjacent source lines; original heading start coordinates 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	≈ 2.58 pp.	6.97%
2. Related work	3	≈ 0.44 pp.	1.19%
3. Theoretical Foundations of Compression-Based Inverse Solvers	4	≈ 1.4 pp.	3.78%
4. Lottery Prior	5	≈ 1.54 pp.	4.16%
5. Experimental results	7	≈ 2.51 pp.	6.78%
6. Conclusion and future work	9	≈ 0.26 pp.	0.7%
Impact Statement	10	≈ 0.05 pp.	0.14%
Acknowledgments	10	≈ 0.05 pp.	0.14%
References	10	≈ 2.94 pp.	7.95%
Appendix	13	≈ 0.2 pp.	0.54%
A. Proof of theorem and corollary	13	≈ 6 pp.	16.22%
B. Implementation details	19	≈ 4.8 pp.	12.97%
C. Visualization	24	≈ 0.32 pp.	0.86%
D. Ablation studies and more experiments	24	≈ 2.74 pp.	7.41%
E. Detailed datapoints	27	≈ 10.86 pp.	29.35%

All detected figure and table locations

Main text

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

Attached appendix

• Table 7 · p. 21
• Figure 7 · p. 22
• Table 8 · p. 24
• Table 9 · p. 25
• Table 10 · p. 25
• Table 11 · p. 25
• Table 12 · p. 26
• Table 13 · p. 26
• Table 14 · p. 26
• Figure 8 · p. 27
• Figure 9 · p. 28
• Figure 10 · p. 29
• Figure 11 · p. 30
• Figure 12 · p. 31
• Figure 13 · p. 32
• Figure 14 · p. 33
• Figure 15 · p. 34
• Figure 16 · p. 35
• Table 15 · p. 36
• Table 16 · p. 36
• Table 17 · p. 37
• Table 18 · p. 37
• Table 19 · p. 37
• Table 20 · p. 37

Argument and organization

1. 1 Introduction; 2 Related Work

   Reformulates single-observation restoration as compression-regularized fitting with randomized priors.

2. 3 Theoretical Foundations; 4 Lottery Prior

   Separates finite-codebook guarantees from entropy, mask and ensemble implementation.

3. 5 Experimental Results; 6 Conclusion and Future Work

   Moves from core inverse tasks to adaptation, cost and operator-dependent limitations.

Problem, claim and contribution

The abstract defines zero-shot as recovery from one degraded observation without external training data, clarifying the resource constraint behind the compact-model claim.

Abstract, p.1 · Main paper

Argument and section order

The theory discussion distinguishes measurement-domain guarantees from signal-domain guarantees requiring a restricted injectivity assumption, before introducing the learned practical codebook.

Section 3.3 and Section 4 opening, p.5 · Main paper

Figures, captions and visual explanation

The codec schematic connects a rate-distortion example to latent modulation and a masked network; restoration panels use matching crop boxes across original, corrupted and reconstructed images.

Figure 3, p.3; Figures 5-6, p.8 · Main paper

Tables, comparisons and evidence

The demosaicing table labels pretrained and fine-tuned foundation-prior comparators and retains their stronger results; runtime distinguishes per-step cost, required optimization steps and multi-prior ensembling.

Tables 4 and 6 with discussion, p.9 · Main paper

Appendix and reproducibility

The appendix begins with a contents roadmap and explicitly limits the stated maximum-likelihood derivation and guarantees to Gaussian linear inverse problems despite broader empirical noise tests.

Appendix contents and A.1, p.13 · Main paper

Clarity and writing conventions

The bound comparison states operating regimes where a prior result is tighter, while the conclusion admits that severely ill-conditioned operators remain challenging.

Remark 3.4, p.5; limitations, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: Separate theorem assumptions from the adaptive implementation and report optimization/ensemble costs alongside compact parameter counts.

Boundary: Fixed-codebook Gaussian guarantees do not automatically certify every learned-codebook, Poisson or nonlinear experiment; fewer effective parameters do not eliminate per-image optimization.

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, 5, 7, 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. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

3, 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 · 37 pages