Writing study: Exchangeability of GNN Representations with Applications to Graph Retrieval

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← ICLR 2026 oral writing corpus

Kartik Nair, Indradyumna Roy, Soumen Chakrabarti, Anirban Dasgupta, Abir De · 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: Theory & formal foundations (primary) · Inference, algorithms & systems efficiency.

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

66 physical pages

Before references / appendix

≈ 10.28 page-equivalents

Main figures / tables

4 / 1

Attached appendix figures / tables

17 / 3

Attached appendix span

≈ 48.89 page-equivalents

Before references / appendix: ≈ 15.58%References / intervening material: ≈ 10.35%Attached appendix: ≈ 74.08%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Extraction notes: Figure numbering discontinuity; see source note; Table numbering discontinuity; see source note. Zero means no recognized caption, not independently verified absence.

Source-bound correction: Caption audit 2026-09-19, HQcCd0laFq: no missing captions were found. This source uses one shared sequential counter for figures and tables. Rendered page 8 shows Figure 1, Table 2 and Figure 3; page 50 shows Tables 6 and 7; page 61 shows Figure 18, Table 19 and Figure 20. The extracted union covers every integer 1 through 25 exactly once. Per-kind numbering-gap flags are expected for this source and must not be filled with invented figures or tables. Preserve 21 figures and 4 tables (main: 4 figures/1 table; appendix: 17 figures/3 tables).

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	≈ 1.09 pp.	1.65%
2 PRELIMINARIES	2	≈ 0.82 pp.	1.24%
3 EXCHANGEABILITY OF GNN REPRESENTATIONS	3	≈ 2.17 pp.	3.29%
4 APPLICATIONS TO GRAPH RETRIEVAL	5	≈ 2.71 pp.	4.11%
5 EXPERIMENTS	8	≈ 2.42 pp.	3.67%
6 CONCLUSIONS	10	≈ 0.39 pp.	0.59%
ETHICS STATEMENT	11	≈ 0.08 pp.	0.12%
REPRODUCIBILITY STATEMENT	11	≈ 0.09 pp.	0.14%
REFERENCES	11	≈ 6.82 pp.	10.33%
A BROADER IMPACT	18	≈ 0.16 pp.	0.24%
B LIMITATIONS	18	≈ 0.23 pp.	0.35%
C LLM USAGE	18	≈ 0.1 pp.	0.15%
D RELATED WORK	18	≈ 1.51 pp.	2.29%
E PROOFS AND OTHER TECHNICAL DETAILS	20	≈ 25 pp.	37.88%
F LIST OF GNNS	45	≈ 5 pp.	7.58%
G ADDITIONAL DETAILS ABOUT EXPERIMENTS	50	≈ 4 pp.	6.06%
H ADDITIONAL EXPERIMENTS	54	≈ 12.89 pp.	19.53%

All detected figure and table locations

Main text

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

Attached appendix

• Table 6 · p. 50
• Table 7 · p. 50
• Figure 8 · p. 54
• Figure 9 · p. 54
• Figure 10 · p. 55
• Figure 11 · p. 56
• Figure 12 · p. 58
• Figure 13 · p. 58
• Figure 14 · p. 59
• Figure 15 · p. 59
• Figure 16 · p. 60
• Figure 17 · p. 60
• Figure 18 · p. 61
• Table 19 · p. 61
• Figure 20 · p. 61
• Figure 21 · p. 62
• Figure 22 · p. 63
• Figure 23 · p. 63
• Figure 24 · p. 65
• Figure 25 · p. 66

Argument and organization

1. Exchangeability theory

   Establishes coordinate permutation symmetry over initialization and training before deriving retrieval consequences.

2. GraphHash and experiments

   Converts a transport-score approximation into indexing/query algorithms and tests both symmetry diagnostics and retrieval.

Problem, claim and contribution

The object of symmetry is embedding coordinates across randomly initialized and trained networks, not graph nodes. Defining this probability space early prevents readers from confusing exchangeability with independent features.

Sections 2–3, pp. 2–5 · Main paper

Argument and section order

A lemma-to-theorem progression connects parameter permutations, gradients, training distributions, and representations before introducing the application. The appendix then works through optimizers, classifiers, normalization, and architecture exceptions.

Section 3; Appendix E.1, pp. 20–32; Appendix F, pp. 45–49 · Main paper

Figures, captions and visual explanation

Two adjacent algorithm boxes share notation while separating offline indexing from online querying. Explicitly carrying stored projections and frequencies into the query algorithm makes deployment dependencies inspectable.

Algorithms 1–2, p. 7 · Main paper

Tables, comparisons and evidence

Marginal density overlays are correctly introduced as a necessary condition, followed by a joint-distribution MMD diagnostic and a mean-matrix rank plot. These are distinct empirical checks rather than interchangeable demonstrations.

Section 5.1, Figures 1 and 3, Table 2, p. 8 · Main paper

Appendix and reproducibility

Matched-objective baseline retraining is a useful supplement: retrieval methods receive representations trained for their own score. The full multi-dataset panels expose where trade-offs differ instead of hiding them in one average.

Appendix H.2.8, pp. 64–66; Figure 24, p. 65 · Main paper

Clarity and writing conventions

Metric terminology requires care: Figure 25's caption says top 10000, but its axes say NDCG at 1K. A final cross-check of axis labels, captions, and protocol definitions would eliminate this ambiguity.

Figure 25, p. 66; evaluation definitions in Appendix G · Main paper

What to reuse—and what not to infer

Transferable lesson: State the exact random object and assumptions, then give separate evidence for each logical link; place deployment algorithms side by side when they share persisted state.

Boundary: A rank-at-most-one expectation does not imply every trained embedding collapses. Concentration also assumes bounded norms and regularity, and the practical learned maps/hash projections differ from the ideal random-hash construction. Reading the proofs is not independent proof certification.

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

Pages 1–11, Sections 1–6 and ethics/reproducibility statements; references 11–16

Appendix / supplement

Pages 17–66, appendices A–H, including all proofs, architecture cases, protocols, and supplementary experiments

Visually inspected PDF pages

7, 8, 65

• ICLR 2026 final proceedings · 66 pages