Writing study: Global Resolution: Optimal Multi-Draft Speculative Sampling via Convex Optimization

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← ICLR 2026 oral writing corpus

Rahul Thomas, Arka Pal · 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: Inference, algorithms & systems efficiency (primary) · Theory & formal foundations.

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

≈ 10.11 page-equivalents

Main figures / tables

1 / 2

Attached appendix figures / tables

4 / 3

Attached appendix span

≈ 20.89 page-equivalents

Before references / appendix: ≈ 29.74%References / intervening material: ≈ 8.82%Attached appendix: ≈ 61.44%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	≈ 1.08 pp.	3.18%
2 RELATED WORK	2	≈ 0.48 pp.	1.41%
3 BACKGROUND ON MULTI-DRAFT SPECULATIVE SAMPLING	3	≈ 0.67 pp.	1.97%
4 CANONICAL DECOMPOSITION BY RELAXED LP	3	≈ 0.49 pp.	1.44%
5 OPTIMAL MULTI-DRAFT SPECULATIVE SAMPLING BY MAX-FLOW	4	≈ 1.39 pp.	4.09%
6 NEAR-LINEAR SAMPLING VIA GLOBAL RESOLUTION	5	≈ 2.97 pp.	8.74%
7 EXPERIMENTS	8	≈ 1.99 pp.	5.85%
8 CONCLUSION	10	≈ 0.12 pp.	0.35%
REPRODUCIBILITY STATEMENT	10	≈ 0.32 pp.	0.94%
REFERENCES	11	≈ 3 pp.	8.82%
A REVIEW OF SINGLE-STEP SPECULATIVE SAMPLING	14	≈ 0.68 pp.	2%
B EQUIVALENCE OF CANONICAL DECOMPOSITION AND RELAXED LP	14	≈ 20.21 pp.	59.44%

All detected figure and table locations

Main text

• Figure 1 · p. 9
• Table 1 · p. 9
• Table 2 · p. 10

Attached appendix

• Figure 2 · p. 29
• Figure 3 · p. 29
• Table 3 · p. 30
• Figure 4 · p. 30
• Figure 5 · p. 31
• Table 4 · p. 32
• Table 5 · p. 33

Argument and organization

1. Equivalent formulations to an implementable solver

   Separates computing optimal acceptance from constructing the conditional sampling rule, then reduces the latter through flow, residual, and convex problems.

2. Runtime, success, and extensions

   Tests the solver with explicit error tolerances before studying end-to-end decoding and limits of generalization.

Problem, claim and contribution

The introduction identifies a precise gap: knowing the optimal objective value does not supply an efficient optimal transport sampler. This is more informative than a generic claim that prior decoding is slow.

Sections 1 and 3–5 · Main paper

Argument and section order

A three-step roadmap states which subproblem was previously solved and connects each new step to a theorem and the final algorithm.

Section 6, p. 6; Algorithm 1, p. 8 · Main paper

Figures, captions and visual explanation

The acceptance plots isolate vocabulary truncation and draft count with consistent colored curves for two model pairs, while the caption states the diminishing-return interpretation.

Figure 1, p. 9 · Main paper

Tables, comparisons and evidence

The runtime table prints solver success percentages beside milliseconds and colors runtime lower bounds rather than presenting them as completed measurements. A second table incorporates fallback cost under a time budget.

Tables 1–2, pp. 9–10 · Main paper

Appendix and reproducibility

The appendix separates derivation, numerical implementation, hardware/data, and end-to-end experiments. The final extension matrix explicitly labels immediate, possible, and obstructed generalizations.

Appendices B–S; Tables 4–5 · Main paper

Clarity and writing conventions

Exact-theory language and finite-tolerance implementation language need careful separation: the deployed approximation has an L1 error bound, can terminate early, and accumulates error across steps.

Section 6.3; Appendices K and R · Main paper

What to reuse—and what not to infer

Transferable lesson: For a numerical algorithm, report objective quality, computational cost, failure rate, fallback behavior, and approximation error together rather than letting one performance number stand for all five.

Boundary: The practical solver is approximate and specialized to i.i.d. drafts, with substantial failure rates in some settings. Algorithm 1 line 7 appears to use the wrong truncation domain relative to Theorem 6.4. The official program title says Optimization, while the PDF title says Minimization.

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

PDF pp. 1–10, Sections 1–8 and reproducibility statement.

Appendix / supplement

PDF pp. 14–34, Appendices A–S, including all proofs, solver details, temperature studies, multi-step experiments, and non-i.i.d. extension limits.

Visually inspected PDF pages

8, 9, 32

• ICLR 2026 official proceedings PDF, retrieved 2026-09-19 · 34 pages