Writing study: Learning to Segment for Vehicle Routing Problems

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← ICLR 2026 oral writing corpus

Wenbin Ouyang, Sirui Li, Yining Ma, Cathy Wu · 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

37 physical pages

Before references / appendix

≈ 10.37 page-equivalents

Main figures / tables

7 / 5

Attached appendix figures / tables

5 / 11

Attached appendix span

≈ 22.89 page-equivalents

Before references / appendix: ≈ 28.03%References / intervening material: ≈ 10.11%Attached appendix: ≈ 61.86%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: L2Seg: Figure 11 is a real hyperparameter-analysis caption at the extreme bottom of physical page 33. Its label yMin is 748.157357 on a 792-point page, below the extractor's 94% body cutoff. Visually checked page 33, including the caption below the printed page number; restore it rather than treating the source as missing Figure 11.

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	≈ 1.11 pp.	3%
2 RELATED WORKS	2	≈ 0.95 pp.	2.57%
3 FIRST-SEGMENT-THEN-AGGREGATE (FSTA)	3	≈ 1.7 pp.	4.59%
4 LEARNING TO SEGMENT (L2SEG)	5	≈ 2.39 pp.	6.46%
5 EXPERIMENT	7	≈ 3.04 pp.	8.22%
6 CONCLUSION	10	≈ 0.53 pp.	1.43%
REPRODUCIBILITY STATEMENT	11	≈ 0.11 pp.	0.3%
REFERENCES	11	≈ 3.74 pp.	10.11%
APPENDICES	15	≈ 1 pp.	2.7%
A SUPPLEMENTARY DEFINITIONS	16	≈ 0.48 pp.	1.3%
B DETAILS OF FIRST-SEGMENT-THEN-AGGREGATE (FSTA)	16	≈ 9.98 pp.	26.97%
C L2SEG DETAILS	26	≈ 2.21 pp.	5.97%
D EXPERIMENTAL AND IMPLEMENTATION DETAILS	28	≈ 5 pp.	13.51%
E ADDITIONAL EXPERIMENTS AND ANALYSIS	33	≈ 3.08 pp.	8.32%
F BROADER IMPACTS	36	≈ 0.45 pp.	1.22%
G LARGE LANGUAGE MODELS USAGE	37	≈ 0.69 pp.	1.86%

All detected figure and table locations

Main text

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

Attached appendix

• Table 6 · p. 17
• Figure 8 · p. 17
• Figure 9 · p. 18
• Table 7 · p. 21
• Figure 10 · p. 23
• Table 8 · p. 28
• Table 9 · p. 32
• Table 10 · p. 33
• Figure 11 · p. 33
• Table 11 · p. 34
• Table 12 · p. 34
• Table 13 · p. 35
• Figure 12 · p. 35
• Table 14 · p. 36
• Table 15 · p. 36
• Table 16 · p. 37

Argument and organization

1. Empirical stability motivates a decomposition theorem

   Connects redundant edge searches to segment aggregation, then separates feasibility guarantees from learned prediction.

2. Complementary decoders and practical validation

   Introduces shared encoding, NAR/AR alternatives and their synergy, followed by solver comparisons and prediction diagnostics.

Problem, claim and contribution

An observable inefficiency—many route edges do not change—provides a concrete motivation before architecture details.

Introduction and Figure 1, pp. 1–3. · Main paper

Argument and section order

The mathematical aggregation framework precedes the predictor. This distinguishes what is guaranteed for a chosen segmentation from whether the network chooses useful segments.

Sections 3–4, pp. 3–7. · Main paper

Figures, captions and visual explanation

The overview uses a common top-row pipeline and color-coded lower branches for NAR, AR and synergy, letting readers compare variants without three disconnected diagrams.

Figure 2, p. 4. · Main paper

Tables, comparisons and evidence

A fixed-budget objective table sits beside objective-versus-time curves: the former shows final quality while the latter explains the reported time-to-quality speedups.

Table 1 and Figure 5, p. 8. · Main paper

Appendix and reproducibility

Formal variant-specific proofs, executable-style algorithms, feature tables and timing breakdowns support independent reconstruction of the method.

Appendices B–E, pp. 16–37. · Main paper

Clarity and writing conventions

Question-led analysis headings connect recall/true-negative tradeoffs to search quality, but broad claims need the exceptions visible in the tables.

Section 5.4, pp. 9–10; Table 2, p. 9. · Main paper

What to reuse—and what not to infer

Transferable lesson: Separate the correctness of a transformation from the quality of its learned controller, and pair endpoint scores with time-to-quality curves when claiming acceleration.

Boundary: The 2–7× figure is not a universal runtime reduction. Some baselines use reported timings, and CVRP1k has stronger objective values than the best proposed variant. The route-interior/boundary explanation changes between the introduction and Appendix B; avoid repeating it as a universal rule.

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 reproducibility statement.

Appendix / supplement

Pages 16–37, Appendices A–G, including aggregation proofs, algorithms, all experimental tables and disclosures.

Visually inspected PDF pages

4, 8

• ICLR 2026 official proceedings PDF, retrieved 2026-09-19 · 37 pages