Writing study: Conformal Robustness Control: A New Strategy for Robust Decision

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← ICLR 2026 oral writing corpus

Yang Hu, Jieren Tan, Changliang Zou, Yajie Bao, Haojie Ren · Official ICLR 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: Learning & optimization algorithms (primary) · Theory & formal foundations.

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

29 physical pages

Before references / appendix

≈ 10.23 page-equivalents

Main figures / tables

5 / 1

Attached appendix figures / tables

2 / 5

Attached appendix span

≈ 15.89 page-equivalents

Before references / appendix: ≈ 35.28%References / intervening material: ≈ 9.93%Attached appendix: ≈ 54.79%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	≈ 1.29 pp.	4.45%
2 RELATED WORKS	2	≈ 0.7 pp.	2.41%
3 PREDICTION SET OPTIMIZATION WITH ROBUSTNESS CONTROL	3	≈ 3.05 pp.	10.52%
4 TEST-TIME DECISION WITH FINITE-SAMPLE ROBUSTNESS CONTROL	6	≈ 1.14 pp.	3.93%
5 EXPERIMENTS	7	≈ 2.94 pp.	10.14%
6 CONCLUSION AND DISCUSSION	10	≈ 0.19 pp.	0.66%
ACKNOWLEDGEMENTS	10	≈ 0.36 pp.	1.24%
REFERENCES	11	≈ 2.88 pp.	9.93%
A USAGE STATEMENT OF LARGE LANGUAGE MODEL	14	≈ 0.1 pp.	0.34%
B MORE DISCUSSION ON RELATED WORK	14	≈ 4.51 pp.	15.55%
C PROOF OF MAIN RESULTS IN SECTION 3.3	18	≈ 2.67 pp.	9.21%
D ADDITIONAL THEORETICAL RESULTS	21	≈ 4.2 pp.	14.48%
E EXPERIMENTAL DETAILS AND ADDITIONAL RESULTS	25	≈ 4.41 pp.	15.21%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 8
• Figure 3 · p. 8
• Table 1 · p. 9
• Figure 4 · p. 10
• Figure 5 · p. 10

Attached appendix

• Table 2 · p. 26
• Table 3 · p. 26
• Figure 6 · p. 27
• Table 4 · p. 28
• Figure 7 · p. 28
• Table 5 · p. 29
• Table 6 · p. 29

Argument and organization

1. Coverage is sufficient but not necessary

   Motivate direct decision-robustness constraints with a geometric counterexample.

2. Parameterized empirical optimization and theory

   Define the risk-certificate objective, differentiable surrogate and finite-sample deviation bounds.

3. Calibration and experiments

   Separate exact exchangeability-based calibration from uncalibrated optimization and compare certificates, losses, robustness and coverage.

Problem, claim and contribution

The introduction contrasts the desired event—loss below a certificate—with the stronger event that the outcome lies in a prediction set. This precise sufficient-versus-necessary distinction supplies the entire motivation.

Equations 1–2 and Figure 1, pp. 1–2. · Main paper

Argument and section order

The paper proceeds from unrestricted policy/set equivalence to tractable parameterized sets, empirical optimization and explicit regularity assumptions. A separate section then introduces Cal-CRC rather than attaching exact finite-sample validity to the optimizer without qualification.

Sections 3–4, pp. 3–7. · Main paper

Figures, captions and visual explanation

Figure 1 combines a symbolic decision flow with matched two-dimensional geometry. Brown prediction sets and blue acceptable-loss regions visibly differ, and the caption gives the common nominal level and loss function.

Figure 1, p. 2. · Main paper

Tables, comparisons and evidence

Table 1 pairs certificate and realized loss with robustness at two nominal levels, so lower loss is not the only reported outcome. Figures 2–3 additionally show coverage, demonstrating the conceptual distinction empirically.

Figures 2–3, p. 8; Table 1, p. 9. · Main paper

Appendix and reproducibility

Appendices distinguish proof dependencies, smoothed-objective bias and implementation choices. E.7 compares CRC, calibrated CRC and calibration alone, showing that the guaranteed variant can sacrifice some certificate efficiency.

Appendices C–D, pp. 18–25; E.1 and E.7, pp. 25–26 and 29. · Main paper

What to reuse—and what not to infer

Transferable lesson: When replacing a conservative proxy constraint, display the proxy and actual target side by side, then label which algorithm enjoys which form of validity.

Boundary: The finite-sample theorem is marginal over exchangeable data, not a guarantee conditional on every individual covariate or under time-series shift. Uncalibrated CRC has an estimated robustness gap; exact Cal-CRC requires extra label-space calibration. Real-data split/compute details are limited, and sigmoid-transformed battery-loss plots obscure effect magnitudes.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-09-19

Reading status

Full text + selected visuals inspected

Main text

Sections 1–6, pp. 1–10; acknowledgments/references pp. 10–13.

Appendix / supplement

Appendices A–E.7, pp. 14–29: related formulations, calibrated algorithm, all proofs, VC/smoothed bounds, implementations and additional experiments.

Visually inspected PDF pages

2, 9

• ICLR 2026 official proceedings PDF, retrieved 2026-09-19 · 29 pages