Writing study: Testable and Actionable Calibration for Full Swap Regret

← NeurIPS 2026 oral writing corpus

Konstantina Bairaktari, Lunjia Hu, Huy Nguyen, Jonathan Ullman · 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: ≈ 30.54 page-equivalents
Main figures / tables: 3 / 2
Attached appendix figures / tables: 0 / 0
Attached appendix span: ≈ 3.27 page-equivalents

Before references / appendix: ≈ 80.37%References / intervening material: ≈ 11.03%Attached appendix: ≈ 8.61%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Source-checked 2026-10-02: replace numbered requirements and property-list bullets with actual Sections 2-5 on pages 12, 13, 17 and 20. Complete the wrapped section labels. Acknowledgments and references start on page 31; references continue onto page 35 before Appendix A begins at position 34.726. No checklist is present in this author version.

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	2	≈ 10.31 pp.	27.13%
2 Preliminaries	12	≈ 1.27 pp.	3.34%
3 Basic Properties of SCDL	13	≈ 3.91 pp.	10.29%
4 Actionability of SCDL	17	≈ 2.51 pp.	6.61%
5 Continuity of SCDL	20	≈ 1.7 pp.	4.47%
6 Quadratic Relationship between SCDL and the Distance to Calibration	21	≈ 0.79 pp.	2.08%
7 Testability of SCDL	22	≈ 6.02 pp.	15.84%
8 Lower bound	28	≈ 0.91 pp.	2.39%
9 Experiments	29	≈ 1.93 pp.	5.08%
Acknowledgments	31	≈ 0.11 pp.	0.29%
References	31	≈ 4.19 pp.	11.03%
A Quadratic Gap between Smooth Calibration Error and Swap Regret	35	≈ 0.69 pp.	1.82%
B Power-2/3 Gap between Cutoff Calibration Error and Swap Regret	36	≈ 2.58 pp.	6.79%

All detected figure and table locations

Main text

Attached appendix

No recognized caption labels.

Argument and organization

Problem and contribution
The introduction defines two requirements that are easy to conflate: actionable predictions should control decision loss, while testable calibration should be estimable from finite samples. The paper then explains why choosing the decision response function is central to reconciling them.
Argument sequence
A long introduction supplies definitions, earlier trade-offs, the proposed SCDL properties and a technical overview. Preliminaries are followed by property-specific proof sections for actionability, continuity, distance to calibration and testability, then a lower bound and synthetic experiments.
Evidence and verification
Prediction-curve panels show the synthetic family before scatterplots relate calibration measures to swap regret. The scatterplots report Spearman correlations and encode the varied parameter, making the simulation's construction visible. A companion analysis of the complementary predictor tests whether an apparent relationship is specific to one setup.

Problem, claim and contribution

The introduction defines two requirements that are easy to conflate: actionable predictions should control decision loss, while testable calibration should be estimable from finite samples. The paper then explains why choosing the decision response function is central to reconciling them.

Sections 1.1–1.4, pp. 3–8 · Main paper

Argument and section order

A long introduction supplies definitions, earlier trade-offs, the proposed SCDL properties and a technical overview. Preliminaries are followed by property-specific proof sections for actionability, continuity, distance to calibration and testability, then a lower bound and synthetic experiments.

Sections 1–9, pp. 2–31 · Main paper

Figures, captions and visual explanation

A compact guarantee table compares full versus restricted actionability and estimation rates. Its row and column labels make the desired combination legible without requiring readers to reconstruct it from separate theorems; blue emphasis is also explained by text rather than carrying the only meaning.

Table 1, p. 7; rendered page inspected · Main paper

Tables, comparisons and evidence

Prediction-curve panels show the synthetic family before scatterplots relate calibration measures to swap regret. The scatterplots report Spearman correlations and encode the varied parameter, making the simulation's construction visible. A companion analysis of the complementary predictor tests whether an apparent relationship is specific to one setup.

Figures 1–3 and Section 9, pp. 29–31; p. 30 rendered and inspected · Main paper

Appendix and reproducibility

The major proof sequence stays in the long-form main text, while the appendix provides additional separation arguments about prior measures and swap regret. For a conference draft, these dependencies would need an explicit claim-to-proof map rather than copying the preprint's section lengths.

Sections 3–8 and appendices, pp. 13–28 and 35–38 · Main paper

Clarity and writing conventions

Properties are named consistently and guarantees are paired with their sample or response-function conditions. The empirical section reports exceptions in variance behavior rather than saying one estimator is always the most stable. Near-optimality remains qualified by its logarithmic gap.

Sections 1.4, 7–9, pp. 8 and 22–31 · Main paper

What to reuse—and what not to infer

Transferable lesson: When proposing a theoretical metric, summarize the guarantee trade-off in one table, then organize the proof and empirical illustration by those same properties.

Boundary: The 38-page author manuscript is not a NeurIPS formatting example or a verified accepted revision. Synthetic correlations illustrate the theory but do not prove universal empirical reliability; the current official record says Accept (oral) while exposing only a poster event.

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 distributed manuscript scan of Sections 1–9, physical pp. 1–31, in a long-form single-column author manuscript: section sequence, substantive prose windows, captions, comparison contracts and conclusions. Not exhaustive technical verification.
Appendix / supplement: Writing-oriented distributed scan of Proof appendices beginning partway through physical p. 35 and continuing through p. 38; references begin on p. 31 and continue onto p. 35 before Appendix A. Not independent proof checking; code and experiments were not executed.
Visually inspected PDF pages: 7, 30

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.

Public author arXiv manuscript 2605.17749v1; not verified identical to the accepted or camera-ready OpenReview revision · 38 pages