Writing study: High-dimensional Analysis of Synthetic Data Selection

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← ICLR 2026 oral writing corpus

Parham Rezaei, Filip Kovačević, Francesco Locatello, Marco Mondelli · 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

52 physical pages

Before references / appendix

≈ 10.16 page-equivalents

Main figures / tables

1 / 3

Attached appendix figures / tables

1 / 10

Attached appendix span

≈ 36.89 page-equivalents

Before references / appendix: ≈ 19.54%References / intervening material: ≈ 9.52%Attached appendix: ≈ 70.94%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	≈ 1.28 pp.	2.46%
2 RELATED WORK	2	≈ 0.91 pp.	1.75%
3 PRELIMINARIES	3	≈ 1.07 pp.	2.06%
4 THEORETICAL RESULTS	4	≈ 3.08 pp.	5.92%
5 EXPERIMENTAL RESULTS	7	≈ 2.46 pp.	4.73%
6 CONCLUSION	10	≈ 0.31 pp.	0.6%
ETHICS STATEMENT	10	≈ 0.1 pp.	0.19%
REPRODUCIBILITY STATEMENT	10	≈ 0.09 pp.	0.17%
ACKNOWLEDGEMENTS	10	≈ 0.33 pp.	0.63%
REFERENCES	11	≈ 4.95 pp.	9.52%
A PROOFS OF THE THEORETICAL RESULTS	16	≈ 26.58 pp.	51.12%
B MODEL SHIFT	42	≈ 5.42 pp.	10.42%
C ADDITIONAL NUMERICAL RESULTS	48	≈ 4.89 pp.	9.4%

All detected figure and table locations

Main text

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

Attached appendix

• Table 4 · p. 48
• Table 5 · p. 49
• Figure 2 · p. 49
• Table 6 · p. 49
• Table 7 · p. 50
• Table 8 · p. 50
• Table 9 · p. 50
• Table 10 · p. 51
• Table 11 · p. 51
• Table 12 · p. 51
• Table 13 · p. 52

Argument and organization

1. Motivation, related work and problem setting

   Turns synthetic-data selection into a precisely defined mixed-distribution risk question.

2. Theoretical analysis

   Separates under- and over-parameterized regimes, explaining assumptions before optimization implications.

3. Experimental results and appendices

   Tests the resulting covariance heuristic across training paradigms, then supplies proofs and controlled stress tests.

Problem, claim and contribution

The introduction poses a selection question rather than another generator proposal; its explicit classwise abstraction makes the theory-to-practice gap visible early.

Sections 1 and 3, pp. 1–4 · Main paper

Argument and section order

The theory explains which term vanishes and why before presenting each risk formula. The synthetic-only countercase usefully prevents an unconditional claim that means never matter.

Section 4.1, Theorems 4.1–4.3 and Proposition 4.2 · Main paper

Figures, captions and visual explanation

Figure 1 aligns three controlled interventions with matched theoretical curves, empirical points and one-standard-deviation bands; the caption supplies dimensions and covariance construction.

Figure 1, p. 7 · Main paper

Tables, comparisons and evidence

Table 1 keeps selectors as rows and scratch, distillation and pretrained regimes as columns, with no-synthetic and real-data reference bounds separated by rules.

Table 1, p. 8 · Main paper

Appendix and reproducibility

The appendix moves from proof dependencies to a model-shift extension, then named experimental questions: collapsed generators, feature extractors, sample budgets and alternative search procedures.

Appendices A–C, pp. 16–52 · Main paper

Clarity and writing conventions

Captions distinguish outperforming from matching baselines. The conclusion acknowledges missing between-class interactions, although its future-work model-shift statement should acknowledge the extension already in Appendix B.

Tables 1–3; Section 6; Appendix B · Main paper

What to reuse—and what not to infer

Transferable lesson: Connect each theoretical insight to a controlled empirical intervention, and organize extra experiments by the alternative explanation they test.

Boundary: Do not turn covariance matching into a universal guarantee: over-parameterized optimality assumes an isotropic target, and classwise linear theory does not prove neural multiclass behavior. Clarify whether dimension refers to original features or the actual 32-dimensional PCA selection space.

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

Pages 1–10, Sections 1–6 and ethics/reproducibility statements

Appendix / supplement

Pages 16–52, Appendices A–C: complete proofs, model-shift extension, implementation and all additional experiments

Visually inspected PDF pages

7, 8

• ICLR 2026 final proceedings · 52 pages