Writing study: Compactness and Consistency: A Conjoint Framework for Deep Graph Clustering

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← ICLR 2026 oral writing corpus

Wei Ju, Siyu Yi, Kangjie Zheng, Yifan Wang, Ziyue Qiao, Li Shen, Yongdao Zhou, Xiaochun Cao, Jiancheng Lv · 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: Learning & optimization algorithms (primary) · Architecture & representation design.

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

24 physical pages

Before references / appendix

≈ 9.82 page-equivalents

Main figures / tables

5 / 7

Attached appendix figures / tables

2 / 3

Attached appendix span

≈ 7.89 page-equivalents

Before references / appendix: ≈ 40.92%References / intervening material: ≈ 26.21%Attached appendix: ≈ 32.88%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	≈ 1.05 pp.	4.38%
2 METHODOLOGY	2	≈ 3.88 pp.	16.17%
3 EXPERIMENT	6	≈ 3.92 pp.	16.33%
4 CONCLUSION	10	≈ 0.19 pp.	0.79%
ACKNOWLEDGMENTS	10	≈ 0.13 pp.	0.54%
REFERENCES	10	≈ 6.28 pp.	26.17%
A EXPECTATION-MAXIMIZATION ALGORITHM FOR GAUSSIAN MIXTURE	17	≈ 0.46 pp.	1.92%
B PROOFS	17	≈ 2.11 pp.	8.79%
C MORE DISCUSSIONS ON THE PROPOSED COCO	19	≈ 0.65 pp.	2.71%
D TRAINING PROCEDURE	20	≈ 0.3 pp.	1.25%
E COMPLEXITY ANALYSIS	20	≈ 0.52 pp.	2.17%
F DETAILS OF EXPERIMENTAL SETUP	21	≈ 0.36 pp.	1.5%
G ADDITIONAL MAIN EXPERIMENTAL RESULTS	21	≈ 0.67 pp.	2.79%
H ADDITIONAL RESULTS ON INFLUENCE OF CONSISTENCY LEARNING	22	≈ 0.43 pp.	1.79%
I ADDITIONAL SENSITIVITY ANALYSIS	22	≈ 0.26 pp.	1.08%
J GRAPH CONVOLUTIONAL FILTER v.s. GCN	22	≈ 0.76 pp.	3.17%
K RELATED WORK	23	≈ 1.37 pp.	5.71%

All detected figure and table locations

Main text

• Figure 1 · p. 3
• Table 1 · p. 6
• Figure 2 · p. 7
• Table 2 · p. 7
• Figure 3 · p. 8
• Figure 4 · p. 8
• Table 5 · p. 9
• Table 4 · p. 9
• Figure 5 · p. 9
• Table 3 · p. 9
• Table 6 · p. 9
• Table 7 · p. 10

Attached appendix

• Table 8 · p. 20
• Table 9 · p. 21
• Table 10 · p. 22
• Figure 6 · p. 23
• Figure 7 · p. 23

Argument and organization

1. Two representation deficiencies

   Pairs limited global context with noisy, redundant graph embeddings.

2. Local/global extraction, compactness and consistency

   Introduces complementary views, shared low-rank reconstruction and relational-distribution alignment.

3. Layered empirical audit

   Moves from clustering to ablations, noise, heterophily, efficiency and classification transfer.

Problem, claim and contribution

The two stated deficiencies map directly to the local/global views and compactness module, making the method’s organization predictable from the introduction.

Sections 1–2, pages 2–5. · Main paper

Argument and section order

The extensive evidence sequence is useful, but blanket superiority statements need checking against retained exceptions: Wisconsin NMI and Coauthor Physics accuracy do not favor CoCo.

Table 4, page 9; Table 7 and Section 3.9, page 10. · Main paper

Figures, captions and visual explanation

A three-stage architecture uses separate local/global colors, a nested EM cycle and anchor-similarity histograms. The caption is too terse to explain the stop-gradient reconstruction and residual path without consulting the equations.

Figure 1, page 3; Equation 5, page 5. · Main paper

Tables, comparisons and evidence

Small targeted tables accompany noise, heterophily and EM-iteration questions; an accuracy-versus-cost scatterplot communicates the efficiency tradeoff more directly than a runtime-only table.

Tables 3–6 and Figure 5, page 9. · Main paper

Appendix and reproducibility

The supplement separates statistical background, proofs, training steps, complexity and settings before additional results. This lets readers locate the procedure without navigating the long bibliography and proof details together.

Appendices A–F, pages 17–21. · Main paper

Clarity and writing conventions

The maximal-variation theorem is stronger than the EM argument supports: its displayed linear objective is unbounded under rank factorization alone. EM monotonicity also does not establish a globally optimal subspace or complete noise removal.

Theorem 2, page 5; Appendix B.3, pages 18–19. · Main paper

What to reuse—and what not to infer

Transferable lesson: Organize supplementary evidence around distinct failure modes, and pair an efficiency claim with an accuracy–cost plot rather than reporting speed in isolation.

Boundary: Low rank does not guarantee that discarded information is noise. The final residual representation is not itself constrained to the reconstruction’s rank, and relational consistency is not evidence of universal superiority over contrastive learning.

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 1–4; references through page 16.

Appendix / supplement

Pages 17–24, Appendices A–K, including GMM/EM derivations, pseudocode, complexity, all supplemental experiments and related work.

Visually inspected PDF pages

3, 9

• ICLR 2026 final proceedings · 24 pages