Writing study: Surprises in Proper Positive-Only Learning
← NeurIPS 2026 oral writing corpus
Shai Ben-David, Farnam Mansouri, Anay Mehrotra, Manolis Zampetakis · 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
- 38 physical pages
- Before references / appendix
- ≈ 13.09 page-equivalents
- Main figures / tables
- 0 / 0
- Attached appendix figures / tables
- 0 / 0
- Attached appendix span
- ≈ 20.91 page-equivalents
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 | ≈ 3.08 pp. | 8.11% |
| 2 Preliminaries | 4 | ≈ 1 pp. | 2.63% |
| 3 Characterizing Conditions | 5 | ≈ 1.72 pp. | 4.53% |
| 4 Our Results | 7 | ≈ 2.15 pp. | 5.66% |
| 5 Technical Overview | 9 | ≈ 3.24 pp. | 8.53% |
| 6 Conclusion and Future Work | 12 | ≈ 1.26 pp. | 3.32% |
| References | 14 | ≈ 4 pp. | 10.53% |
| A Additional Preliminaries | 18 | ≈ 0.66 pp. | 1.74% |
| B Relationships Between Conditions | 18 | ≈ 4.57 pp. | 12.03% |
| C Proof of Main Results | 23 | ≈ 4.77 pp. | 12.55% |
| D Proof of Additional Separation Results | 28 | ≈ 10.91 pp. | 28.71% |
All detected figure and table locations
Main text
No recognized caption labels.
Attached appendix
No recognized caption labels.
Argument and organization
- 1 Introduction and related work
Sets up proper versus improper positive-only learnability.
- 2 Preliminaries
Defines the learning model and notation.
- 3 Characterizing Conditions
Builds the hierarchy of exterior separability conditions.
- 4 Our Results
States characterization, randomness, separation and stability results.
- 5 Technical Overview
Explains the main proof strategy before the full appendix.
- 6 Conclusion and Future Work
Summarizes differences from ordinary PAC learning and open directions.
Problem, claim and contribution
The motivating question separates proper from improper positive-only learning, so a familiar finite-VC characterization cannot be silently transferred from ordinary PAC learning. The introduction makes the unresolved distinction the organizing question.
PDF pp.1–3, Section 1 · Main paper
Argument and section order
Definitions and the hierarchy of exterior conditions precede the main equivalence. The paper then treats randomness, deterministic rules, consistency, and stability as distinct consequences before giving a technical overview and full proofs.
PDF pp.4–11, Sections 2–5 · Main paper
Figures, captions and visual explanation
The two inspected main pages use an implication chain, numbered equivalence statements, and short explanatory paragraphs instead of charts. Proposition 2 shows the exact/uniform/distributional hierarchy immediately above the main characterization. A theory paper does not need an artificial architecture figure.
PDF p.7, Proposition 2 and Theorems 3–4; p.9, Theorems 8–9 · Main paper
Tables, comparisons and evidence
Theorems distinguish sufficiency, necessity, and separation by counterexample. In particular, stability returns to the stronger exact exterior condition; putting that result beside the general characterization prevents collapsing all settings into one slogan.
PDF pp.7–9, Theorems 4–9 · Main paper
Appendix and reproducibility
The appendix is claim-indexed: relationships between conditions, the main characterization and randomness proofs, then additional separations including consistency and stable learners. The main text explains proof ideas while specific theorem references lead to the full arguments.
PDF pp.18–38, Appendices A–D; Section C.1 and Sections D.4–D.5 · Main paper
Clarity and writing conventions
The manuscript names the learning model and logical condition in each result, and contrasts it with ordinary PAC learning in nearby prose. Definitions are linked forward into theorem statements rather than relying only on theorem numbering.
PDF pp.7–9, explanatory text around Theorems 4 and 9 · Main paper
What to reuse—and what not to infer
Transferable lesson: For a characterization paper, make the implication structure and quantifiers inspectable before sending readers to long proofs.
Boundary: Proper, improper, randomized, deterministic, consistent, and stable learning are different guarantees. These writing observations are not a verification of all proofs. The arXiv mirror has not been established as the accepted conference revision.
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 source scan of framing, argument roadmap, selected substantive passages, method/theorem statements, main figure/table captions, evidence and limits across PDF pp.1–12. Two selected main-body pages were actually inspected as rendered images. This is not exhaustive line-by-line technical verification or experiment reproduction. Title and all author names compared against official program metadata and manuscript first page; matching authors, with capitalization, middle initials or expanded given names where applicable.
- Appendix / supplement
- Appendix structure, theorem-restatement and proof openings, and main-text-to-proof links were checked; long proofs were not verified line by line.
- Visually inspected PDF pages
- 7, 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.