Writing study: FlatLand: Personalized Graph Federated Learning via Tailored Lorentz Space

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← ICML 2026 oral writing corpus

Jiahong Liu, Ram Samarth B B, Xinyu Fu, Menglin Yang, Weixi Zhang, Zhitao Ying, Irwin King · 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: Architecture & representation (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

34 physical pages

Before references / appendix

≈ 9.19 page-equivalents

Main figures / tables

7 / 4

Attached appendix figures / tables

3 / 5

Attached appendix span

≈ 20.92 page-equivalents

Before references / appendix: ≈ 27.03%References / intervening material: ≈ 11.44%Attached appendix: ≈ 61.53%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Include the actual appendix cover/contents page in the attached supporting-material envelope, before its first lettered section. Contents entries are not counted as section starts. Newly detected unnumbered impact/singular-acknowledgment statements are retained from the size-aware source extraction; authored heading corrections are unchanged.

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	≈ 1.37 pp.	4.03%
2. Related Work	2	≈ 0.37 pp.	1.09%
3. Preliminaries	3	≈ 0.67 pp.	1.97%
4. Motivation and Insights	3	≈ 1.02 pp.	3%
5. The FlatLand Framework	4	≈ 1.11 pp.	3.26%
6. Analysis	5	≈ 1.28 pp.	3.76%
7. Experiments	7	≈ 2.55 pp.	7.5%
8. Conclusions	9	≈ 0.19 pp.	0.56%
Acknowledgments	9	≈ 0.15 pp.	0.44%
Impact Statement	10	≈ 0.14 pp.	0.41%
References	10	≈ 3.9 pp.	11.47%
Appendix — contents	14	≈ 1 pp.	2.94%
A. Related Work	15	≈ 1 pp.	2.94%
B. Preliminaries	16	≈ 3.44 pp.	10.12%
C. Methodology Supplementary	19	≈ 3.56 pp.	10.47%
D. Theoretical Analysis Supplementary	23	≈ 8 pp.	23.53%
E. Experimental Supplementary	31	≈ 3.91 pp.	11.5%

All detected figure and table locations

Main text

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

Attached appendix

• Figure 8 · p. 19
• Figure 9 · p. 19
• Table 5 · p. 31
• Table 6 · p. 31
• Table 7 · p. 31
• Table 8 · p. 33
• Table 9 · p. 33
• Figure 10 · p. 33

Argument and organization

1. 1 Introduction; 2 Related Work; 3 Preliminaries; 4 Motivation and Insights

   Links heterogeneous graph structure to a geometry hypothesis and introduces the required Lorentz quantities.

2. 5 The FlatLand Framework; 6 Analysis

   Specifies local/shared parameters and separately discusses representation validity, convergence and overhead.

3. 7 Experiments; 8 Conclusions

   Maps four research questions to performance, embedding dimension, participation and component ablations.

Problem, claim and contribution

A graph-curvature observation motivates tailored spaces, while the method explicitly treats curvature as learnable rather than as an exact graph statistic.

Sections 4–5.1, physical pp.3–5 · Main paper

Argument and section order

Four numbered research questions recur in experimental subsection headings, separating low-dimensional behavior, participation robustness and component necessity.

Sections 7.1–7.5, pp.7–9 · Main paper

Figures, captions and visual explanation

The framework distinguishes client-local parameters from the shared server path; the dimension plot and ablation trajectory answer separate questions on the same result page.

Figure 3, p.5; Figures 4–5, p.7 · Main paper

Tables, comparisons and evidence

Local Euclidean and local Lorentz baselines help distinguish geometry from federation. The appendix specifies disjoint graph partitions and reports accuracy averaged across clients.

Section 7.1, p.7; Appendix E.1–E.3, pp.31–32 · Main paper

Appendix and reproducibility

A unified ablation summary maps comparison variants to design choices; separate implementation details specify the bounded learnable Lorentz-scale parameter.

Appendix E.2–E.5, pp.31–32 · Main paper

Clarity and writing conventions

The conclusion calls the framework exploratory and acknowledges that negative curvature is not optimal for every client graph.

Section 8 limitations, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: Make ownership of parameters visible in a federated method diagram, and use local-model controls plus question-linked ablations to separate representation and collaboration gains.

Boundary: Simulated client partitions are not a deployment privacy guarantee. Geometry/heterogeneity theorems and convergence were not independently verified, and graph curvature does not itself establish that all heterogeneity lies in one coordinate. Keep backbone and local/shared parameter choices explicit when interpreting gains.

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 scan across physical PDF pp.1–9, covering framing, section progression, definitions, method/evidence explanations, captions and scope. Physical pages extracted individually to avoid form-feed pagination errors. Selected full-page rasters inspected; not exhaustive line-by-line technical verification or experimental reproduction.

Appendix / supplement

Appendix heading inventory A–E checked; selected reading of datasets, client partitions, learnable-curvature parameterization, training details, baseline rationale and ablation map E.1–E.5 (pp.31–32). The formal geometry/convergence proofs and complete extra results were not independently verified.

Visually inspected PDF pages

5, 7

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 proceedings PDF, PMLR volume 306, retrieved 2026-10-07 · 34 pages