Writing study: Markov Chain Monte Carlo without Evaluating the Target: an Auxiliary Variable Approach

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← ICML 2026 oral writing corpus

Wei Yuan, Guanyang Wang · 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: Theory & formal analysis (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

35 physical pages

Before references / appendix

≈ 9.06 page-equivalents

Main figures / tables

2 / 3

Attached appendix figures / tables

11 / 4

Attached appendix span

≈ 23.91 page-equivalents

Before references / appendix: ≈ 25.89%References / intervening material: ≈ 5.8%Attached appendix: ≈ 68.31%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Join wrapped printed heading text using adjacent source lines; original heading start coordinates 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	≈ 1.45 pp.	4.14%
2. A Common Procedure of Existing Algorithms	2	≈ 0.46 pp.	1.31%
3. A New Framework with (Two) Auxiliary Variables	3	≈ 3.01 pp.	8.6%
4. Theory	6	≈ 1.09 pp.	3.11%
5. Numerical Experiments	7	≈ 2.29 pp.	6.54%
6. Future Directions	9	≈ 0.21 pp.	0.6%
Acknowledgement	9	≈ 0.07 pp.	0.2%
Impact Statement	9	≈ 0.14 pp.	0.4%
References	10	≈ 2.03 pp.	5.8%
A. Details of Exchange algorithm, PoissonMH, TunaMH	12	≈ 1.31 pp.	3.74%
B. Additional Proofs	13	≈ 10.03 pp.	28.66%
C. Implementation Details of Poisson Minibatching	23	≈ 1.21 pp.	3.46%
D. Implementation Details of Locally Balanced PoissonMH	24	≈ 1.7 pp.	4.86%
E. Additional Comment on Algorithm 5 and 6	26	≈ 0.24 pp.	0.69%
F. Further Details of Experiments in Section 5	26	≈ 1.15 pp.	3.29%
G. Additional Experiments	27	≈ 8.26 pp.	23.6%

All detected figure and table locations

Main text

• Table 1 · p. 8
• Figure 1 · p. 8
• Table 2 · p. 8
• Figure 2 · p. 9
• Table 3 · p. 9

Attached appendix

• Figure 3 · p. 28
• Table 4 · p. 28
• Figure 4 · p. 28
• Figure 5 · p. 29
• Table 5 · p. 29
• Figure 6 · p. 29
• Table 6 · p. 30
• Figure 7 · p. 30
• Figure 8 · p. 30
• Table 7 · p. 31
• Figure 9 · p. 31
• Figure 10 · p. 33
• Figure 11 · p. 34
• Figure 12 · p. 34
• Figure 13 · p. 35

Argument and organization

1. 1 Introduction; 2 Common Procedure

   Separates expensive likelihood normalization from expensive full-data evaluation and unifies existing samplers.

2. 3 Two-Auxiliary-Variable Framework; 4 Theory

   Defines proposal and acceptance auxiliaries, constructs algorithms and compares ideal and implemented chains.

3. 5 Numerical Experiments; 6 Future Directions

   Reports time-aware sampling diagnostics and explicit correctness checks before practical restrictions.

Problem, claim and contribution

Without evaluating the target means cancellation within a computable auxiliary acceptance ratio, not sampling with no model access, gradients or precomputed bounds.

Section 3.1, p.3; limitations, p.9 · Main paper

Argument and section order

Three auxiliary-variable cases link the general algorithm to prior methods; the paper explicitly locates the validity argument within involutive MCMC.

Section 3.1 and Algorithm 1, p.4 · Main paper

Figures, captions and visual explanation

The central pseudocode keeps both auxiliary draws and reverse-proposal factors visible; result captions identify coordinate-wise ESS summaries, best-over-tuning selection and one-hundred-run averaging.

Algorithm 1, p.4; Tables 1-2 and Figure 1, p.8 · Main paper

Tables, comparisons and evidence

Posterior MSE and ESS per second are complemented by a matched-budget reference-sampling KS check; fixed-step SGLD bias is distinguished from exact stationary-target methods.

Sections 5.1-5.4, pp.7-9 · Main paper

Appendix and reproducibility

The implementation explicitly separates one-time alias-table construction from per-iteration Poisson minibatch cost and credits that existing subsampling mechanism.

Appendix C, pp.23-24 · Main paper

Clarity and writing conventions

The conclusion admits that useful bounds may be unavailable and that the source of large empirical speedups remains incompletely explained.

Future Directions, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: Use a unifying algorithm to expose shared assumptions, then validate sampling quality separately from task accuracy and throughput.

Boundary: Reversibility does not guarantee rapid finite-budget mixing; reported speedups depend on tuning, tempering, parameter constraints and setup costs, and the current algorithms assume independent-data likelihoods.

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-oriented scan of the main argument through physical p.9, with focused physical-page text inspection on 1, 3, 4, 5, 6, 7, 8, 9. Framing, section progression, mechanism/proof explanation, displays, comparison conditions and conclusions were inspected. This is not exhaustive technical reading, proof verification or reproduction.

Appendix / supplement

Appendix organization and main-text pointers were checked; focused text inspection of physical pages 13, 20, 23, 24. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

4, 8

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 · 35 pages