Writing study: Learning Eigenstructures of Unstructured Data Manifolds

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← CVPR 2026 oral writing corpus

Roy Velich, Arkadi Piven, David Bensaid, Daniel Cremers, Thomas Dagès, Ron Kimmel · Official CVPR 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

14 physical pages

Before references / appendix

≈ 8.05 page-equivalents

Main figures / tables

9 / 1

Attached appendix figures / tables

0 / 0

Attached appendix span

≈ 2.62 page-equivalents

Before references / appendix: ≈ 57.5%References / intervening material: ≈ 23.79%Attached appendix: ≈ 18.71%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	≈ 0.83 pp.	5.93%
2. Related Works	2	≈ 0.88 pp.	6.29%
3. Method	3	≈ 2.79 pp.	19.93%
4. Experiments	5	≈ 2.81 pp.	20.07%
5. Conclusion	8	≈ 0.39 pp.	2.79%
References	9	≈ 3.33 pp.	23.79%
A. Godil, J. Han, H. Johan, L. Lai, B. Li, C. Li, H. Li,	12	≈ 2.62 pp.	18.71%

All detected figure and table locations

Main text

• Figure 1 · p. 4
• Figure 2 · p. 6
• Figure 3 · p. 6
• Figure 4 · p. 6
• Figure 5 · p. 6
• Table 1 · p. 7
• Figure 6 · p. 7
• Figure 7 · p. 7
• Figure 8 · p. 8
• Figure 9 · p. 8

Attached appendix

No recognized caption labels.

Separate source files—excluded from canonical-PDF totals

A separate author version may repeat main text and references. Whole-file lengths and counts are not extra appendix material and are never added to the canonical PDF totals. Read the study's source scope for which sections received substantive reading versus layout inspection.

Additional source 1

Separate PDF (or ZIP containing it): whole-file layout of 27 physical pages; 20 detected figures and 12 tables. These may include overlapping main-text material.

Located appendix only: starts on physical p.1; ≈ 26.94 page-equivalents, 20 figure labels and 12 table labels. This interval is distinct from the whole file.

Detected heading	PDF page	Estimated span
Supplementary Material	1	≈ 0.02 pp.
A. Additional Theory	1	≈ 0.97 pp.
B. Additional Details on Our Framework	2	≈ 0.61 pp.
C. Additional Experimental Details and Re-	2	≈ 25.35 pp.

• Table 2 · p. 4
• Table 3 · p. 5
• Table 4 · p. 6
• Figure 10 · p. 7
• Figure 11 · p. 9
• Figure 12 · p. 10
• Figure 14 · p. 12
• Figure 15 · p. 13
• Figure 16 · p. 14
• Figure 17 · p. 15
• Figure 18 · p. 16
• Figure 19 · p. 17
• Figure 20 · p. 18
• Figure 21 · p. 18
• Figure 22 · p. 19
• Table 5 · p. 19
• Table 6 · p. 20
• Table 7 · p. 20
• Table 8 · p. 21
• Table 9 · p. 21
• Table 10 · p. 22
• Table 11 · p. 22
• Table 12 · p. 23
• Table 13 · p. 23
• Figure 23 · p. 24
• Figure 24 · p. 24
• Figure 25 · p. 25
• Figure 26 · p. 25
• Figure 27 · p. 26
• Figure 28 · p. 26
• Figure 29 · p. 27
• Figure 30 · p. 27

Argument and organization

1. 3. Method

   Introduces foundations, a neural spectral basis, and optimal-approximation training.

2. 4. Experiments

   Progresses from a toy interval through geometric shapes to high-dimensional feature manifolds.

Problem, claim and contribution

The opening identifies explicit operator discretization/eigendecomposition as the conventional dependency to bypass, while retaining spectral applications.

Section 1 · Main paper · Additional source 2

Argument and section order

Definitions and the approximation argument precede architecture; a progressive reconstruction algorithm makes the abstract objective executable.

§3; Algorithm 1 p. 5 · Main paper · Additional source 2

Figures, captions and visual explanation

The overview combines probe-function smoothing, a learned orthogonal basis, and weighted projection into the loss; shape panels then show the basis itself rather than only final scores.

Figure 1 p. 4; Figures 6–7 p. 7 · Main paper · Additional source 2

Tables, comparisons and evidence

The paper labels single-shape overfitting and unseen-shape generalization separately, and compares multiple truncation levels to an oracle operator.

Table 1 and §4 p. 7 · Main paper · Additional source 2

Appendix and reproducibility

The supplement distinguishes per-shape tuned from fixed probe settings and supplies dataset-wise means/variability, helping readers interpret apparent oracle agreement.

Supplement Table 2; Figures 21–22; Tables 6–13 · Main paper · Additional source 2

Clarity and writing conventions

The limitations explicitly say probe functions impose an implicit operator and training is expensive, qualifying broad dimensionality claims.

§5 p. 8 · Main paper · Additional source 2

What to reuse—and what not to infer

Transferable lesson: For an abstract geometric method, use a simple analytically interpretable case, visible intermediate bases, and clearly separate fitted from transfer settings.

Boundary: Agreement with a selected oracle and attractive embeddings do not establish universal recovery of every manifold operator.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-09-26

Reading status

Writing-focused manuscript scan + selected visuals inspected

Main text

Manuscript-wide writing scan of main PDF pp. 1–8: framing, section structure, method exposition, figure/table captions, evaluation organization and conclusions; not an exhaustive technical proof audit or reproduction.

Appendix / supplement

Scanned 27 supplementary pages on theory, projection details, overfitting versus generalization protocols, probe parameters, costs, extensive basis/reconstruction examples, and manifold-learning tables; no independent proof verification.

Visually inspected PDF pages

4, 7

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.

• Official CVPR 2026 CVF proceedings PDF; retrieved 2026-09-26 · 14 pages
• Official CVPR 2026 separate supplementary PDF; retrieved 2026-09-26 · 27 pages