Writing study: PRISM: Gauge-Invariant Tangent-Space Differentially Private LoRA

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← ICML 2026 oral writing corpus

Shihao Wang, Xueru Zhang · 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: Theory & formal analysis (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

35 physical pages

Before references / appendix

≈ 9.08 page-equivalents

Main figures / tables

4 / 5

Attached appendix figures / tables

17 / 3

Attached appendix span

≈ 22.38 page-equivalents

Before references / appendix: ≈ 25.94%References / intervening material: ≈ 10.11%Attached appendix: ≈ 63.94%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	≈ 1.35 pp.	3.86%
2. Problem Formulation	2	≈ 1.75 pp.	5%
3. Proposed Method: PRISM	4	≈ 3.34 pp.	9.54%
4. Experiments	7	≈ 2.11 pp.	6.03%
Acknowledgements	9	≈ 0.05 pp.	0.14%
Impact Statement	9	≈ 0.15 pp.	0.43%
References	10	≈ 3.54 pp.	10.11%
A. Theory and Proofs	13	≈ 12.06 pp.	34.46%
B. Experimental Setup	25	≈ 0.96 pp.	2.74%
C. Additional Diagnostics and Analysis	26	≈ 9.36 pp.	26.74%

All detected figure and table locations

Main text

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

Attached appendix

• Table 6 · p. 26
• Table 7 · p. 26
• Table 8 · p. 27
• Figure 5 · p. 27
• Figure 6 · p. 28
• Figure 7 · p. 28
• Figure 8 · p. 28
• Figure 9 · p. 29
• Figure 10 · p. 30
• Figure 11 · p. 30
• Figure 1 · p. 30
• Figure 12 · p. 31
• Figure 13 · p. 31
• Figure 14 · p. 32
• Figure 15 · p. 32
• Figure 16 · p. 33
• Figure 17 · p. 33
• Figure 18 · p. 34
• Figure 19 · p. 34
• Figure 20 · p. 35

Argument and organization

1. 1 Introduction; 2 Problem Formulation

   Explains non-identifiable LoRA factors and separates three failure mechanisms.

2. 3 Proposed Method: PRISM

   Maps each named issue to tangent projection, intrinsic noising or DP-aware preconditioning with explicit theorem pointers.

3. 4 Experiments; Limitations

   Separates task utility, rank/backbone sensitivity, measured overhead and three mechanism diagnostics.

Problem, claim and contribution

Three desiderata define the target before the method; the comparison table distinguishes gauge invariance, additive perturbations and LoRA-scale efficiency.

Table 1 and Section 2, physical pp.2–4 · Main paper

Argument and section order

Issue I–III labels recur in diagnosis, method subsections and experiments, making the claimed problem-to-intervention mapping easy to audit.

Sections 2–3, pp.3–7; mechanism diagnostics, p.9 · Main paper

Figures, captions and visual explanation

The diagnostic page separately plots intrinsic-noise amplification, gauge sensitivity, a predicted scaling relation and preconditioned noise rather than using only final task scores.

Figures 1–4, p.9 · Main paper

Tables, comparisons and evidence

The runtime table specifies hardware, warmup and measured updates and reports roughly doubled step time despite nearly unchanged memory; the utility discussion explicitly admits non-winning tasks.

Tables 3–5 and result interpretation, p.8 · Main paper

Appendix and reproducibility

Accounting details state clipping, subsampling and composition; experimental configuration and additional diagnostics are separate from the long sequence of mathematical lemmas.

Appendices A.25–A.30 and B.1, pp.24–25 · Main paper

Clarity and writing conventions

Backbone family labels are qualified with text-only inputs, preventing a reader from mistaking a multimodal model-family name for a multimodal evaluation.

Table 3 caption and scaling discussion, p.8 · Main paper

What to reuse—and what not to infer

Transferable lesson: Give each proposed failure mode a named intervention and a matching diagnostic, while disclosing utility exceptions and measured implementation overhead.

Boundary: This writing scan does not certify privacy, arbitrary-gauge invariance or implementation correctness. The DP result has explicit clipping/subsampling/accounting assumptions; Appendix A.30 treats orthogonal gauge transformations, so its scope should not silently be broadened to every invertible transformation or every adaptive update.

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-focused scan across physical PDF pp.1–9, covering framing, section progression, definitions, method/evidence explanations, captions and scope. Physical pages extracted individually to avoid form-feed pagination errors. Selected full-page rasters inspected; not exhaustive line-by-line technical verification or experimental reproduction.

Appendix / supplement

Appendix structure A–C inventoried, with selected detail reading of privacy accounting, rank-space moments and adaptive-preconditioner statements A.25–A.30 (pp.24–25), and experimental setup B.1 (p.25). Full proofs and implementations were not independently audited; impact text continues onto p.10 before references.

Visually inspected PDF pages

8, 9

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 · 35 pages