Writing study: DISCO: Mitigating Bias in Deep Learning with Conditional Distance Correlation

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← ICML 2026 oral writing corpus

Emre Kavak, Tom Nuno Wolf, Christian Wachinger · Official ICML 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: Training, objectives & optimization (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

30 physical pages

Before references / appendix

≈ 9.23 page-equivalents

Main figures / tables

4 / 3

Attached appendix figures / tables

8 / 4

Attached appendix span

≈ 17.91 page-equivalents

Before references / appendix: ≈ 30.77%References / intervening material: ≈ 9.53%Attached appendix: ≈ 59.7%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Replace a prose cross-reference falsely detected as a caption with the actual caption from physical-page source text and coordinates.

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	≈ 1.6 pp.	5.33%
2. Causal Invariance	2	≈ 2.24 pp.	7.47%
3. Distance Correlation for Conditional Independence	5	≈ 2 pp.	6.67%
4. Experiments	7	≈ 2.13 pp.	7.1%
5. Conclusion	9	≈ 0.41 pp.	1.37%
6. Limitations and Ethical Considerations	9	≈ 0.38 pp.	1.27%
Acknowledgment	10	≈ 0.07 pp.	0.23%
Impact Statement	10	≈ 0.12 pp.	0.4%
References	10	≈ 2.85 pp.	9.5%
Appendix	13	≈ 0.03 pp.	0.1%
A. Use of LLMs	13	≈ 0.11 pp.	0.37%
B. Camera-Ready Changes	13	≈ 0.43 pp.	1.43%
C. Contextualization and Related Work	13	≈ 1.75 pp.	5.83%
D. Causal Graph and Assumptions	15	≈ 0.16 pp.	0.53%
E. Causal Invariance as Conditional Independence	15	≈ 3.86 pp.	12.87%
F. Proofs and Supplementary Definitions for Conditional Distance Correlation Background	19	≈ 2.67 pp.	8.9%
G. Exact Factorization and Proof of sDISCO	22	≈ 2 pp.	6.67%
H. Experiments	24	≈ 6.91 pp.	23.03%

All detected figure and table locations

Main text

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

Attached appendix

• Table 4 · p. 13
• Figure D.1 · p. 16
• Figure E.2 · p. 17
• Figure H.3 · p. 24
• Figure H.4 · p. 24
• Figure H.5 · p. 25
• Figure H.6 · p. 25
• Figure H.7 · p. 26
• Table 5 · p. 28
• Figure H.8 · p. 29
• Table 6 · p. 30
• Table 7 · p. 30

Argument and organization

1. 1 Introduction; 2 Causal Invariance

   Defines the causal graph, desired stability and assumptions before the optimization proxy.

2. 3 Conditional Distance Correlation

   Moves from population definitions to finite-sample estimators and a practical regularizer.

3. 4 Experiments; 5 Conclusion; 6 Limitations

   Separates balanced-test accuracy from controlled counterfactual analysis and observed-bias restrictions.

Problem, claim and contribution

The model treats selected mediators as unwanted shortcuts but explicitly allows stable useful mediators to be excluded from the bias set.

Introduction, p.1; Selective Mediation, p.4 · Main paper

Argument and section order

The causal theorem is followed immediately by positivity, selective-mediation and unobserved-confounding discussion before estimator construction.

Sections 2.1-3.1, pp.4-5 · Main paper

Figures, captions and visual explanation

Counterfactual sensitivity and target accuracy are paired beside the causal graph, while the main table shades naive backbones and labels distinct regression, balanced-accuracy and worst-group metrics.

Table 3 and Figure 4, p.8; Table 2, p.9 · Main paper

Tables, comparisons and evidence

Bias labels are used during training but not inference, and true counterfactual evaluation is confined to a controlled generator rather than inferred for every real dataset.

Section 3.3, p.6; Section 4.4, p.8 · Main paper

Appendix and reproducibility

A camera-ready disclosure records an earlier estimator implementation error, preserves old results and identifies the corrected main-text version.

Appendix B, p.13; complementary counterfactual analysis, p.29 · Main paper

Clarity and writing conventions

The limitation section separates theoretical assumptions from practical observed-label needs; stability is explicitly not sufficient for predictive usefulness.

Theorem discussion, p.4; Section 6, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: Put assumption failures before the practical estimator and preserve version-specific corrections so readers can distinguish the theorem, surrogate and implementation.

Boundary: A finite regularization penalty is not automatic satisfaction of the population constraint; unknown biases remain, and benchmark demographic labels are imperfect proxies rather than personal identity.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-10-07

Reading status

Writing-focused manuscript scan + selected visuals inspected

Main text

Writing-oriented scan of the main argument through physical p.9, with focused physical-page text inspection on 1, 3, 4, 5, 6, 7, 8, 9. Framing, section progression, mechanism/proof explanation, displays, comparison conditions and conclusions were inspected. This is not exhaustive technical reading, proof verification or reproduction.

Appendix / supplement

Appendix organization and main-text pointers were checked; focused text inspection of physical pages 13, 29. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

8, 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.

• Published proceedings PDF, PMLR volume 306, retrieved 2026-10-07 · 30 pages