Writing study: Guaranteed Optimal Compositional Explanations for Neurons

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← ICML 2026 oral writing corpus

Biagio La Rosa, Leilani H. Gilpin · 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: 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

43 physical pages

Before references / appendix

≈ 9.04 page-equivalents

Main figures / tables

1 / 4

Attached appendix figures / tables

9 / 5

Attached appendix span

≈ 31.91 page-equivalents

Before references / appendix: ≈ 21.02%References / intervening material: ≈ 4.77%Attached appendix: ≈ 74.21%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	≈ 1.17 pp.	2.72%
2. Related Work	2	≈ 0.36 pp.	0.84%
3. Optimal Compositional Explanations	2	≈ 4.35 pp.	10.12%
4. Analysis	7	≈ 2.5 pp.	5.81%
5. Conclusion	9	≈ 0.15 pp.	0.35%
Impact Statement	9	≈ 0.13 pp.	0.3%
References	10	≈ 2.04 pp.	4.74%
A. Proof Equivalence Alignment-IoU Score	12	≈ 0.55 pp.	1.28%
B. Complete Results	12	≈ 0.91 pp.	2.12%
C. Optimal Algorithm	13	≈ 3.3 pp.	7.67%
D. Beam Search Algorithm	16	≈ 0.39 pp.	0.91%
E. Estimating Quantities	17	≈ 4.08 pp.	9.49%
F. Proof of Optimality	21	≈ 7.94 pp.	18.47%
G. Other Neuron and Concept-Based Explanations	29	≈ 0.98 pp.	2.28%
H. Further Insights and Discussion	30	≈ 1.44 pp.	3.35%
I. Examples of Explanations Difference	31	≈ 12.31 pp.	28.63%

All detected figure and table locations

Main text

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

Attached appendix

• Table 5 · p. 13
• Table 6 · p. 14
• Table 7 · p. 15
• Table 8 · p. 16
• Table 9 · p. 16
• Figure 2 · p. 33
• Figure 3 · p. 34
• Figure 4 · p. 35
• Figure 5 · p. 36
• Figure 6 · p. 37
• Figure 7 · p. 38
• Figure 8 · p. 39
• Figure 9 · p. 40
• Figure 10 · p. 41

Argument and organization

1. Problem and contribution

   Asks whether beam-search explanations actually maximize alignment, explicitly defining feasible runtime relative to the existing setting rather than promising unrestricted tractability.

2. Argument sequence

   The objective and three search-space assumptions precede decomposition, bounds and algorithm; evaluation then separates search efficiency from explanation semantics.

3. Evidence and verification

   Runtime extrapolation for breadth-first search is footnoted with its assumed per-node time, while explanation categories distinguish changed concepts, changed operators and equal-score alternatives.

Problem, claim and contribution

Asks whether beam-search explanations actually maximize alignment, explicitly defining feasible runtime relative to the existing setting rather than promising unrestricted tractability.

Introduction, p. 2 · Main paper

Argument and section order

The objective and three search-space assumptions precede decomposition, bounds and algorithm; evaluation then separates search efficiency from explanation semantics.

Sections 3-4, pp. 2-9 · Main paper

Figures, captions and visual explanation

A small color-coded binary table grounds the fundamental set quantities; the analysis page separates frequency of differing solutions from their IoU increments.

Table 1, p. 3; Tables 3-4, p. 8; both PNGs inspected · Main paper

Tables, comparisons and evidence

Runtime extrapolation for breadth-first search is footnoted with its assumed per-node time, while explanation categories distinguish changed concepts, changed operators and equal-score alternatives.

Section 4.2 and footnote 2, p. 8 · Main paper

Appendix and reproducibility

Operator-by-operator derivations support the admissibility proof, and complete optimal/beam pseudocode appears after detailed qualitative examples.

Appendix E, pp. 17-20; F, pp. 21-29; algorithms, pp. 42-43 · Main paper

Clarity and writing conventions

Definitions, observations and assumptions distinguish exact quantities from estimates, and prose explicitly names the sample-versus-aggregate precision/cost tradeoff.

Sections 3.1-3.2, pp. 3-6 · Main paper

What to reuse—and what not to infer

Transferable lesson: For an optimality claim, expose the search space and objective first, then separate certified objective quality from semantic interpretation.

Boundary: Optimal IoU within the chosen concept vocabulary, logic and dataset is not a causal or universally complete neuron explanation; extrapolated exhaustive runtimes are not measured runs.

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-focused distributed manuscript scan, not exhaustive technical/proof validation. Sections 1-5, pp. 1-9: exact explanation objective, IoU decomposition, admissible bounds, optimal/beam algorithms and explanation analysis.

Appendix / supplement

Writing-focused appendix scan; code, data and external assets not executed. Appendices A-I and final algorithms, pp. 12-43: equivalence, results, search implementations, bound derivations, admissibility/optimality proofs and differing explanation examples.

Visually inspected PDF pages

3, 8

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 ICML 2026 proceedings PDF, PMLR volume 306; retrieved 2026-10-07. Public OpenReview decision notes were not independently reverified. · 43 pages