Writing study: Addressing divergent representations from causal interventions on neural networks

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← ICLR 2026 oral writing corpus

Satchel Grant, Simon Jerome Han, Alexa Tartaglini, Christopher Potts · 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: Empirical analysis, diagnosis & auditing (primary) · Learning & optimization algorithms.

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

27 physical pages

Before references / appendix

≈ 10.33 page-equivalents

Main figures / tables

3 / 0

Attached appendix figures / tables

6 / 0

Attached appendix span

≈ 12.89 page-equivalents

Before references / appendix: ≈ 38.26%References / intervening material: ≈ 14%Attached appendix: ≈ 47.74%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	≈ 1.59 pp.	5.89%
2 BACKGROUND AND RELATED WORK	3	≈ 1.5 pp.	5.56%
3 ARE DIVERGENT REPRESENTATIONS A COMMON PHENOMENON?	4	≈ 1.26 pp.	4.67%
4 WHEN ARE DIVERGENT REPRESENTATIONS HARMLESS OR PERNICIOUS?	5	≈ 2.89 pp.	10.7%
5 HOW MIGHT WE AVOID DIVERGENT REPRESENTATIONS?	8	≈ 1.9 pp.	7.04%
6 DISCUSSION AND LIMITATIONS	10	≈ 0.45 pp.	1.67%
7 ACKNOWLEDGMENTS	11	≈ 0.09 pp.	0.33%
8 LLM USAGE STATEMENT	11	≈ 0.13 pp.	0.48%
REFERENCES	11	≈ 3.78 pp.	14%
A APPENDIX	15	≈ 12.89 pp.	47.74%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 5
• Figure 3 · p. 10

Attached appendix

• Figure 5 · p. 20
• Figure 4 · p. 22
• Figure 6 · p. 24
• Figure 7 · p. 25
• Figure 8 · p. 26
• Figure 9 · p. 27

Argument and organization

1. Background and prevalence of divergence

   Define intervention operations before testing whether they leave natural representation distributions.

2. Harmless versus pernicious divergence

   Use explicit constructions to distinguish a behavioral result from a mechanistic claim.

3. Mitigation and limitations

   Present counterfactual-latent regularization as an initial remedy rather than a universal guarantee.

Problem, claim and contribution

Three introduction questions become successive sections: prevalence, consequences, and mitigation. This keeps a conceptual critique from becoming an undirected catalog of failures.

Section 1, p. 1; Sections 3–5 · Main paper

Argument and section order

The argument separates existence of divergence from its harmfulness; the claim-dependent null-space discussion prevents a simplistic off-manifold-equals-invalid conclusion.

Sections 3–4, pp. 4–8 · Main paper

Figures, captions and visual explanation

Figure 1 pairs hidden-pathway arrows with decision-region geometry, giving two complementary intuitions for the same failure mode.

Figure 1, p. 2 · Main paper

Tables, comparisons and evidence

Figure 3 assembles the regularizer, representation plots, accuracy/divergence trade-off, and transfer result; its caption identifies which panels use real-model versus synthetic settings.

Figure 3, p. 10 · Main paper

Appendix and reproducibility

Metric definitions, model/layer choices, synthetic task partitions, and hyperparameter grids make the toy demonstrations auditable rather than merely illustrative.

Appendix A.1–A.6, pp. 15–27 · Main paper

Clarity and writing conventions

The limitations explicitly acknowledge the absence of a general harmful-divergence classifier and the narrow scope of the modified loss.

Section 6, p. 10 · Main paper

What to reuse—and what not to infer

Transferable lesson: Organize a methodological critique around separate questions of existence, relevance, and mitigation, and state exactly which scientific claim each counterexample challenges.

Boundary: Do not present reduced divergence as proof of faithful mechanisms. Several appendix details need checking before reuse: the stated Gaussian covariance is not positive semidefinite, the patch-closure proof's update order is inconsistent with its definition, and the Section 4.2.1 projection claim does not follow transparently from the displayed example.

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, disclosure, references pp. 11–14

Appendix / supplement

Appendix A.1–A.6 and Figures 4–9, pp. 15–27

Visually inspected PDF pages

2, 10

• ICLR 2026 official proceedings PDF, retrieved 2026-09-19 · 27 pages