Writing study: InfoNCE Induces Gaussian Distribution

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← ICLR 2026 oral writing corpus

Roy Betser, Eyal Gofer, Meir Yossef Levi, Guy Gilboa · 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) · Empirical analysis, diagnosis & auditing.

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

22 physical pages

Before references / appendix

≈ 10.42 page-equivalents

Main figures / tables

4 / 2

Attached appendix figures / tables

7 / 0

Attached appendix span

≈ 8.27 page-equivalents

Before references / appendix: ≈ 47.36%References / intervening material: ≈ 15.05%Attached appendix: ≈ 37.59%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Independent PDF text and boundary audit: appendix navigation/overview begins before first lettered substantive heading. Physical heading coordinates taken from source-pinned Poppler bbox.

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	≈ 1.13 pp.	5.14%
2 RELATED WORK	2	≈ 0.85 pp.	3.86%
3 SETUP	3	≈ 1.27 pp.	5.77%
4 GAUSSIANITY FROM INFONCE	4	≈ 3.63 pp.	16.5%
5 EXPERIMENTS	8	≈ 2.21 pp.	10.05%
6 DISCUSSION AND CONCLUSION	10	≈ 0.53 pp.	2.41%
ETHICS STATEMENT	11	≈ 0.23 pp.	1.05%
ACKNOWLEDGMENTS	11	≈ 0.08 pp.	0.36%
REFERENCES	11	≈ 3.18 pp.	14.45%
LLM USAGE	14	≈ 0.14 pp.	0.64%
OVERVIEW	14	≈ 0.37 pp.	1.68%
A HGR MAXIMAL CORRELATION AND THE ALIGNMENT BOUND	15	≈ 1.65 pp.	7.5%
B REGULARIZED SURROGATE PROOFS	16	≈ 0.75 pp.	3.41%
C ALIGNMENT-PLATEAU PROOFS	17	≈ 1.08 pp.	4.91%
D EXACT ALIGNMENT BOUND IN PLATEAU DISCUSSION	18	≈ 0.59 pp.	2.68%
E EXPERIMENTAL DETAILS	19	≈ 3.83 pp.	17.41%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 6
• Figure 3 · p. 8
• Figure 4 · p. 9
• Table 1 · p. 9
• Table 2 · p. 10

Attached appendix

• Figure 5 · p. 18
• Figure 6 · p. 20
• Figure 7 · p. 21
• Figure 8 · p. 21
• Figure 9 · p. 21
• Figure 10 · p. 22
• Figure 11 · p. 22

Argument and organization

1. Question and two routes

   The marginal-law question is distinguished from identifiability and class separation, then studied via plateau assumptions and a regularized surrogate.

2. Diagnostics

   Synthetic controls, CIFAR-10 objective comparisons, and pretrained-model observations test progressively less idealized settings.

Problem, claim and contribution

The introduction converts a familiar alignment/uniformity story into a precise distributional question and explains why closed-form Gaussian quantities would be useful.

Pages 1–3, introduction and related work. · Main paper

Argument and section order

Two named analytical routes and visibly labelled assumptions let readers distinguish an idealized training plateau from a modified population objective.

Pages 4–7, section 4. · Main paper

Figures, captions and visual explanation

The opening image-to-encoder-to-cloud cartoon communicates the headline quickly, but contains little information about the assumptions or low-dimensional-projection scope.

Page 2, Figure 1. · Main paper

Tables, comparisons and evidence

Three aligned training curves separate radial concentration, AD statistic, and coordinate-wise DP acceptance; the adjacent table states test thresholds and normalization.

Page 9, Figure 4 and Table 1. · Main paper

Appendix and reproducibility

Proofs are grouped by analytical route; the experimental appendix records augmentation distributions and separately presents alternative histogram views.

Appendices A–E, pages 15–22. · Main paper

Clarity and writing conventions

The conclusion explicitly says optimization dynamics and attainment of the population minimizers are not proved, an important restraint after the broad title.

Page 10, section 6. · Main paper

What to reuse—and what not to infer

Transferable lesson: Separate alternative explanatory routes and their assumptions, and choose empirical diagnostics that map one-to-one onto the theoretical ingredients.

Boundary: Coordinate-wise failure to reject normality is not proof of joint Gaussianity. The theorem concerns population/large-dimensional limits under stated feasibility or regularization assumptions; DINO observations are empirical extensions, not evidence that DINO optimizes InfoNCE.

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 1–11, sections 1–6 and ethics/reproducibility; references pages 11–14.

Appendix / supplement

Pages 14–22, overview and appendices A–E: HGR alignment bound, regularized surrogate, spherical projection proofs, plateau extension, all experimental details/diagnostics.

Visually inspected PDF pages

2, 9

• ICLR 2026 final proceedings · 22 pages