Writing study: Gaussian certified unlearning in high dimensions: A hypothesis testing approach

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← ICLR 2026 oral writing corpus

Aaradhya Pandey, Arnab Auddy, Haolin Zou, Arian Maleki, Sanjeev Kulkarni · 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

38 physical pages

Before references / appendix

≈ 10.11 page-equivalents

Main figures / tables

5 / 1

Attached appendix figures / tables

9 / 0

Attached appendix span

≈ 23.89 page-equivalents

Before references / appendix: ≈ 26.61%References / intervening material: ≈ 10.53%Attached appendix: ≈ 62.87%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 AND THEORETICAL CONTRIBUTIONS	1	≈ 1.99 pp.	5.24%
2 THE MACHINE UNLEARNING PROBLEM: PRIVACY AND ACCURACY	3	≈ 1.02 pp.	2.68%
3 FORMAL DEFINITIONS OF CERTIFIABILITY AND ACCURACY	4	≈ 2.13 pp.	5.61%
4 NEWTON-BASED MACHINE UNLEARNING: THEORETICAL GUARANTEES	6	≈ 1.76 pp.	4.63%
5 EXPERIMENTS VALIDATING OUR THEORETICAL CONTRIBUTIONS	8	≈ 2.12 pp.	5.58%
6 CONCLUSION AND FUTURE DIRECTIONS OF RESEARCH	10	≈ 0.47 pp.	1.24%
REFERENCES	11	≈ 4 pp.	10.53%
A APPENDIX OF GAUSSIAN CERTIFIED UNLEARNING IN HIGH DIMENSIONS: A	15	≈ 0.14 pp.	0.37%
B MOTIVATIONS BEHIND OUR APPROACH ON A HIGH LEVEL	15	≈ 2.17 pp.	5.71%
C GAUSSIAN CERTIFIABILITY AND CONNECTIONS WITH RELATED NOTIONS	17	≈ 1.86 pp.	4.89%
D ASSUMPTIONS ON THE UNREGULARIZED INDIVIDUAL LOSS L,	19	≈ 3.45 pp.	9.08%
E NOISY NEWTON-BASED UNLEARNING MECHANISM	22	≈ 0.51 pp.	1.34%
F MAIN THEORETICAL RESULT: ASSUMPTIONS AND CONCLUSIONS	23	≈ 6.36 pp.	16.74%
G PROOFS IN THE CASE OF GAUSSIAN FEATURES	29	≈ 3.66 pp.	9.63%
H AN EXTENSION OF THE PROOF IN THE CASE OF SUB-GAUSSIAN FEATURES	33	≈ 0.25 pp.	0.66%
I ADDITIONAL NUMERICAL EXPERIMENTS	33	≈ 5.5 pp.	14.47%

All detected figure and table locations

Main text

• Table 1 · p. 3
• Figure 1 · p. 8
• Figure 2 · p. 9
• Figure 3 · p. 9
• Figure 4 · p. 10
• Figure 5 · p. 10

Attached appendix

• Figure 6 · p. 33
• Figure 7 · p. 34
• Figure 8 · p. 34
• Figure 9 · p. 35
• Figure 10 · p. 36
• Figure 11 · p. 36
• Figure 12 · p. 37
• Figure 13 · p. 37
• Figure 14 · p. 38

Argument and organization

1. Why existing assumptions fail

   A ridge-regression calculation motivates changing the certifiability framework before introducing the proposed definition.

2. Formal guarantee and validation

   Hypothesis-testing definitions lead to a one-step Newton mechanism, explicit assumptions, two guarantees, and controlled simulations.

Problem, claim and contribution

The introduction identifies a precise proportional-dimensional failure of standard assumptions rather than broadly claiming prior unlearning methods do not work.

Pages 2–3, ridge example and Table 1. · Main paper

Argument and section order

Privacy and accuracy are posed as separate questions and then answered by separate theorems before one combined conclusion.

Pages 7–8, section 4.3. · Main paper

Figures, captions and visual explanation

The first three-panel plot fixes deletion sizes across panels and uses log–log axes to test the predicted dimension scaling directly.

Page 8, Figure 1. · Main paper

Tables, comparisons and evidence

A later page juxtaposes higher-dimensional simulations with two real datasets, visibly distinguishing assumption-aligned evidence from a robustness check.

Page 10, Figures 4–5. · Main paper

Appendix and reproducibility

The appendix explains why conditioning and comparison distributions are chosen, maps competing assumptions carefully, and separates practical calibration heuristics from proved guarantees.

Appendices B–D and F.3, pages 15–29. · Main paper

Clarity and writing conventions

Named assumptions and explicit equation references make the scope of each theorem auditable, though repeated advocacy and duplicated exposition lengthen the supplement.

Section 4.2; appendices C, F. · Main paper

What to reuse—and what not to infer

Transferable lesson: When changing an evaluation or guarantee, first demonstrate the specific failure of the old formulation and explicitly trace the new definition through theorem, experiment, and practical calibration.

Boundary: Do not convert conditional Gaussian certifiability into a blanket privacy or legal-compliance claim. The proved results concern smooth convex regularized GLMs with distributional assumptions; scalable Hessian approximations, neural-network extensions, and rigorous practical calibration remain open.

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; references pages 11–14.

Appendix / supplement

Pages 15–38, appendices A–I: motivations, certifiability relationships, assumption comparisons, algorithm/restated results, calibration discussion, Gaussian/sub-Gaussian proofs, additional experiments.

Visually inspected PDF pages

8, 10

• ICLR 2026 final proceedings · 38 pages