Writing study: Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models

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← ICLR 2026 oral writing corpus

Li Sun, Zhenhao Huang, Silei Chen, Lanxu Yang, Junda Ye, Sen Su, Philip Yu · 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: Architecture & representation design (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

41 physical pages

Before references / appendix

≈ 10.11 page-equivalents

Main figures / tables

6 / 1

Attached appendix figures / tables

2 / 21

Attached appendix span

≈ 22.89 page-equivalents

Before references / appendix: ≈ 24.66%References / intervening material: ≈ 19.51%Attached appendix: ≈ 55.83%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	≈ 1.24 pp.	3.02%
2 RELATED WORK	2	≈ 0.66 pp.	1.61%
3 NOTATIONS AND PRELIMINARIES	3	≈ 0.6 pp.	1.46%
4 THEORY: CONSTRUCTING A UNIFIED, SMOOTH MANIFOLD	4	≈ 2.59 pp.	6.32%
5 GRAPHGLUE: GEOMETRIC MULTI-DOMAIN GRAPH PRE-TRAINING	6	≈ 1.58 pp.	3.85%
6 EXPERIMENTS	8	≈ 2.41 pp.	5.88%
7 CONCLUSION	10	≈ 0.41 pp.	1%
REFERENCES	11	≈ 8 pp.	19.51%
A NOTATIONS	19	≈ 1 pp.	2.44%
B PROOFS	20	≈ 6 pp.	14.63%
C BACKGROUND: DIFFERENTIAL GEOMETRY ON RIEMANNIAN MANIFOLDS	26	≈ 3 pp.	7.32%
D ALGORITHMS	29	≈ 1.5 pp.	3.66%
E RELATED WORK	30	≈ 1.24 pp.	3.02%
F EMPIRICAL DETAILS	31	≈ 2.7 pp.	6.59%
G ADDITIONAL RESULTS	34	≈ 5.57 pp.	13.59%
H REPRODUCIBILITY STATEMENT	40	≈ 1.39 pp.	3.39%
I ETHICS STATEMENT	41	≈ 0.08 pp.	0.2%
J DECLARATION OF LLM USAGE	41	≈ 0.08 pp.	0.2%
K BROADER IMPACT	41	≈ 0.35 pp.	0.85%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 6
• Table 1 · p. 9
• Figure 3 · p. 9
• Figure 4 · p. 9
• Figure 5 · p. 10
• Figure 6 · p. 10

Attached appendix

• Table 2 · p. 19
• Table 3 · p. 29
• Table 4 · p. 30
• Table 5 · p. 30
• Table 6 · p. 32
• Table 7 · p. 34
• Table 8 · p. 34
• Table 9 · p. 34
• Table 10 · p. 34
• Table 11 · p. 34
• Table 12 · p. 34
• Table 13 · p. 35
• Table 14 · p. 35
• Table 15 · p. 35
• Table 16 · p. 36
• Table 17 · p. 36
• Figure 7 · p. 37
• Table 18 · p. 37
• Table 19 · p. 38
• Table 20 · p. 38
• Table 21 · p. 38
• Table 22 · p. 39
• Figure 8 · p. 39

Argument and organization

1. Motivation and geometric construction

   Frames multi-domain graph transfer as compatible local geometry, then introduces frames, transport and regularizers.

2. Pretraining and adaptation

   Converts the construction into prototype-based batching, a frozen encoder and Riemannian mixture-of-experts adaptation.

3. Experiments and technical appendices

   Separates few-shot transfer, diagnostic trends and ablations from proofs, background and implementation details.

Problem, claim and contribution

The argument distinguishes learning shared structure across graph domains from adapting to a held-out domain, giving the method two explicit responsibilities.

Sections 1 and 5, pages 1–2 and 6–8. · Main paper

Argument and section order

Definitions and numbered theorems precede each implementable loss. This creates a traceable concept-to-objective chain, but a theorem label must not substitute for checking its assumptions.

Section 4, pages 3–6; Appendix B, pages 20–25. · Main paper

Figures, captions and visual explanation

Figure 2 uses a two-row training/adaptation diagram, repeated domain colors, prototype shapes and frozen/trainable symbols. Its brief caption leaves several symbols dependent on surrounding prose.

Figure 2, page 6. · Main paper

Tables, comparisons and evidence

Table 1 groups columns by task and shot count and reports uncertainty over ten splits. It also preserves exceptions: GraphGlue does not lead 5-shot Arxiv or 1-shot PROTEINS.

Table 1, page 9; protocol in Appendix F.3, page 33. · Main paper

Appendix and reproducibility

A contents page, notation table, pseudocode and dataset-specific hyperparameters make the long supplement navigable. Figure 8's smooth surfaces come from t-SNE followed by RBF interpolation, not a direct proof of learned smoothness.

Pages 17–19, 28, 33–34; Appendix G.1, page 34 and Figure 8, page 39. · Main paper

Clarity and writing conventions

Consistency checking is essential: Appendix B.5 changes the sign between Equations 51 and 52 for the same determinant ratio; the full-model PROTEINS 1-shot entry is 59.87 in Table 18 but 55.87 in Table 22.

Page 25, Equations 51–52; Tables 18 and 22, pages 37 and 39. · Main paper

What to reuse—and what not to infer

Transferable lesson: Reuse the staged explanation from geometric intuition to an explicit loss and then to an adaptation protocol; pair the overview figure with a self-contained legend and claim-linked evaluation.

Boundary: Do not reuse the geometric guarantees as established facts. The displayed reciprocal expansion and ratio inequalities conflict internally; theorem assumptions and numerical inconsistencies require specialist verification. Interpolated manifold pictures and limited scaling sweeps are not independent mathematical validation.

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 1–10, Sections 1–7; references on pages 11–16.

Appendix / supplement

Pages 17–41, appendix contents and Appendices A–K, including every proof, algorithm, experimental table and reproducibility statement.

Visually inspected PDF pages

6, 9, 25, 39

• ICLR 2026 official proceedings PDF, retrieved 2026-09-19 · 41 pages