Writing study: Discount Model Search for Quality Diversity Optimization in High-Dimensional Measure Spaces

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← ICLR 2026 oral writing corpus

Bryon Tjanaka, Henry Chen, Matthew Fontaine, Stefanos Nikolaidis · 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: Learning & optimization algorithms (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

≈ 10.42 page-equivalents

Main figures / tables

2 / 2

Attached appendix figures / tables

10 / 5

Attached appendix span

≈ 20.89 page-equivalents

Before references / appendix: ≈ 26.72%References / intervening material: ≈ 19.72%Attached appendix: ≈ 53.56%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	≈ 1.88 pp.	4.82%
2 PROBLEM FORMULATION	3	≈ 0.19 pp.	0.49%
3 BACKGROUND	3	≈ 1.11 pp.	2.85%
4 UNDERSTANDING DISTORTION IN HIGH-DIMENSIONAL MEASURE SPACES	4	≈ 0.72 pp.	1.85%
5 DISCOUNT MODEL SEARCH	5	≈ 1.7 pp.	4.36%
6 DOMAINS	7	≈ 1.47 pp.	3.77%
7 EXPERIMENTS	8	≈ 1.81 pp.	4.64%
8 CONCLUSION	10	≈ 0.32 pp.	0.82%
9 ETHICS STATEMENT	10	≈ 0.36 pp.	0.92%
10 REPRODUCIBILITY STATEMENT	11	≈ 0.13 pp.	0.33%
ACKNOWLEDGMENTS	11	≈ 0.09 pp.	0.23%
REFERENCES	11	≈ 7.69 pp.	19.72%
A RELATED WORK	19	≈ 1.08 pp.	2.77%
B RESULTS	20	≈ 8.92 pp.	22.87%
C HYPERPARAMETERS	29	≈ 2.17 pp.	5.56%
D ABLATION STUDY	31	≈ 4.52 pp.	11.59%
E DOMAIN DETAILS	35	≈ 2.84 pp.	7.28%
F IMPLEMENTATION	38	≈ 0.46 pp.	1.18%
G DIFFERENTIABLE QUALITY DIVERSITY IN QDDM DOMAINS	39	≈ 0.89 pp.	2.28%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 3
• Table 1 · p. 8
• Table 2 · p. 10

Attached appendix

• Figure 3 · p. 22
• Figure 4 · p. 23
• Figure 5 · p. 24
• Figure 6 · p. 24
• Figure 7 · p. 25
• Figure 8 · p. 26
• Table 3 · p. 27
• Table 4 · p. 27
• Table 5 · p. 28
• Table 6 · p. 29
• Figure 9 · p. 32
• Figure 10 · p. 33
• Table 7 · p. 33
• Figure 11 · p. 34
• Figure 12 · p. 36

Argument and organization

1. A concrete stagnation failure

   Derives the need for continuous discount values from archive-cell collisions.

2. Formal QD and algorithm lineage

   Separates solution space, measure space and archive improvement.

3. Method, new setting, controlled comparisons

   Introduces DMS before dataset-specified measure domains and quantitative tests.

Problem, claim and contribution

The hiker example distinguishes optimizing one image from seeking a diverse archive, making the unusual optimization objective understandable.

Sections 1–2, pp. 1–3 · Main paper

Argument and section order

The algorithm is introduced after explaining precisely how CMA-MAE and DDS differ, so the reader can isolate the changed component.

Sections 3–5, pp. 3–7 · Main paper

Figures, captions and visual explanation

Figure 1 contrasts piecewise-constant and smooth discount functions using the same two candidate solutions, then attaches an empirical stagnation plot.

Figure 1, p. 2 · Main paper

Tables, comparisons and evidence

The main results report both quality-diversity score and coverage, preventing high coverage with very poor objective values from appearing successful.

Table 1 and Section 7.1, pp. 8–9 · Main paper

Appendix and reproducibility

A dedicated comparability subsection explains score normalization, iteration counts, archive sizes and dimensionality differences from previous papers.

Appendix B.1, pp. 20–21 · Main paper

Clarity and writing conventions

Negative and null findings are explicit: MNIST does not significantly beat CMA-MAE, hiker coverage stays low, and wall-clock overhead is separately tabulated.

Section 7.1 and Table 2, pp. 9–10 · Main paper

What to reuse—and what not to infer

Transferable lesson: Explain the exact failure mechanism with a matched before/after schematic, then pair effectiveness metrics with resource costs and an explicit comparability note.

Boundary: DMS is black-box search with an online learned discount, not a newly trained image generator. Hiker coverage is only 3.77%, and comparisons there are not significant against both MAP-Elites variants. The CLIP metric and source datasets also determine what counts as diversity.

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

PDF pp. 1–11, Sections 1–10

Appendix / supplement

PDF pp. 19–39, Appendices A–G, including all domain definitions, ablations and statistical tables

Visually inspected PDF pages

2, 8

• Official ICLR 2026 proceedings conference PDF; PDF creation metadata: Thu Apr 30 13:46:58 2026 EDT · 39 pages