Writing study: Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale
← NeurIPS 2026 oral writing corpus
Shashaank Aiyer, Yishay Mansour, Shay Moran, Han Shao, Tom Waknine · Official NeurIPS 2026 oral record
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
- 32 physical pages
- Before references / appendix
- ≈ 29.09 page-equivalents
- Main figures / tables
- 1 / 0
- Attached appendix figures / tables
- 0 / 0
- Attached appendix span
- No boundary detected; not assumed zero
Extraction notes: No attached appendix boundary detected. Zero means no recognized caption, not independently verified absence.
Source-bound correction: Top-level heading and reference/appendix boundaries checked against source PDF text. Bibliography titles/author initials, numbered contribution/property bullets, diagram steps, equations and TOC entries are not substantive headings. Section spans are page-coordinate estimates, not ink area or prose-only length. This is an author manuscript mirror, not a verified accepted-version template. Source layout uses physical single-column y/page-height, including equation-heavy pages.
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 | ≈ 6.31 pp. | 19.72% |
| 2 Related Work | 8 | ≈ 1 pp. | 3.13% |
| 3 Proof Overviews | 9 | ≈ 4 pp. | 12.5% |
| 4 Proofs of Scale-Sensitive Learnability Results | 13 | ≈ 10.13 pp. | 31.66% |
| 5 Proofs of Evaluability Results | 23 | ≈ 6.33 pp. | 19.78% |
| 6 Acknowledgements | 29 | ≈ 0.54 pp. | 1.69% |
| References | 30 | ≈ 2.91 pp. | 9.09% |
All detected figure and table locations
Main text
Attached appendix
No recognized caption labels.
Argument and organization
- Problem and contribution
Starts from the exact scale at which familiar PAC-learning equivalences remain valid; the contribution is stated in explicit gamma-dependent terms before discussing consequences for generative-model evaluation.
- Argument sequence
An extended results overview is followed by related work, proof ideas and full numbered proof sections. This long-form arXiv organization must not be mistaken for the conference submission page budget.
- Evidence and verification
Evidence consists of equivalence statements, upper/lower bounds and constructive arguments, not benchmark accuracy. Qualitative evaluability conclusions explicitly distinguish finite and infinite domains.
Problem, claim and contribution
Starts from the exact scale at which familiar PAC-learning equivalences remain valid; the contribution is stated in explicit gamma-dependent terms before discussing consequences for generative-model evaluation.
Section 1, pp. 1–6 · Main paper
Argument and section order
An extended results overview is followed by related work, proof ideas and full numbered proof sections. This long-form arXiv organization must not be mistaken for the conference submission page budget.
Sections 1–5, pp. 1–28 · Main paper
Figures, captions and visual explanation
Figure 1 illustrates the lower-bound distribution construction with four stacked bar-pattern panels and the same symbolic mass levels, making the difference between reference distributions and sampled mixtures visible.
Figure 1, p. 25 (render inspected) · Main paper
Tables, comparisons and evidence
Evidence consists of equivalence statements, upper/lower bounds and constructive arguments, not benchmark accuracy. Qualitative evaluability conclusions explicitly distinguish finite and infinite domains.
Section 1.1, pp. 5–6; Sections 4–5, pp. 13–28 · Main paper
Appendix and reproducibility
Verification detail is in the main numbering, with proof references linking early theorem statements to later arguments; no missing appendix should be encoded as a zero-length technical verification burden.
Sections 4–5, pp. 13–28 · Main paper
Clarity and writing conventions
Scale parameters and quantifiers are retained in the statement of each relationship; discussion differentiates exact-scale equivalence from quantitative sample-complexity improvements. The rendered application-motivation page introduces integral probability metrics in a centered display and then states evaluability with explicit quantifiers and two model-selection implications. The prose explains the difference between comparing two models and estimating their distances, making the notation do explanatory work without requiring a decorative architecture figure.
Section 1, pp. 1–8; Section 1.1, p. 5 (additional rendered inspection) · Main paper
What to reuse—and what not to infer
Transferable lesson: A theorem-centered paper can use one carefully chosen construction figure; prioritize precise assumptions, scales and proof navigation over a conventional experimental section.
Boundary: This thirty-two-page author preprint is not a verified accepted-paper layout. Its section lengths cannot serve as a NeurIPS main-text template or quota.
Apply this lesson using the argument and evidence worksheet.
Inspection record and sources
- Checked
- 2026-10-02
- Reading status
- Writing-focused manuscript scan + selected visuals inspected
- Main text
- Writing-oriented scan across manuscript framing, section sequence, figure/table captions, selected argument/evaluation prose and conclusion; not exhaustive technical or proof verification. Sections 1–6, pp. 1–29; references pp. 29–32. This public preprint has proofs in numbered main sections rather than an attached appendix. Source is the exact public author version listed below, not a verified accepted/camera-ready revision.
- Appendix / supplement
- Writing-oriented appendix/documentation scan: No separately labeled appendix in the inspected thirty-two-page public manuscript; proofs occupy Sections 4–5, pp. 13–28. Source code, data, model outputs and external video assets were not executed or independently validated.
- Visually inspected PDF pages
- 5, 25
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.