Writing study: Reasoning with Sampling: Your Base Model is Smarter Than You Think

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← ICLR 2026 oral writing corpus

Aayush Karan, Yilun Du · 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) · Empirical analysis, diagnosis & auditing.

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

19 physical pages

Before references / appendix

≈ 9.81 page-equivalents

Main figures / tables

5 / 2

Attached appendix figures / tables

4 / 3

Attached appendix span

≈ 5.89 page-equivalents

Before references / appendix: ≈ 51.63%References / intervening material: ≈ 17.37%Attached appendix: ≈ 31%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	≈ 1.32 pp.	6.95%
2 RELATED WORKS	2	≈ 0.56 pp.	2.95%
3 PRELIMINARIES	3	≈ 0.23 pp.	1.21%
4 MCMC SAMPLING FOR POWER DISTRIBUTIONS	3	≈ 3.97 pp.	20.89%
5 EXPERIMENTS	7	≈ 2.92 pp.	15.37%
6 CONCLUSION	10	≈ 0.21 pp.	1.11%
7 ACKNOWLEDGEMENTS	10	≈ 0.07 pp.	0.37%
REFERENCES	10	≈ 3.29 pp.	17.32%
A APPENDIX	14	≈ 5.89 pp.	31%

All detected figure and table locations

Main text

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

Attached appendix

• Figure 6 · p. 15
• Figure 7 · p. 16
• Figure 8 · p. 17
• Figure 9 · p. 17
• Table 3 · p. 18
• Table 4 · p. 18
• Table 5 · p. 19

Argument and organization

1. Capability question and target distribution

   Turn an RL distribution-sharpening debate into a training-free inference hypothesis.

2. Power distribution, MH and blockwise sampler

   Explain why token temperature differs from sequence-level sharpening before deriving an approximate sampler.

3. Performance, likelihood and diversity

   Separate single-response accuracy from likelihood changes and multi-sample success.

Problem, claim and contribution

The introduction asks whether existing capabilities can be elicited by sampling rather than whether RL creates capabilities. This narrower intervention makes the experiments interpretable without resolving the entire philosophical debate.

Sections 1 and 4.1, pp. 1–4. · Main paper

Argument and section order

A small token example contrasts a sum of powers with a power of sums before the Metropolis–Hastings machinery is introduced. The mathematical distinction motivates the algorithm rather than appearing as an isolated theorem.

Proposition 1 and Example 1, pp. 4–5. · Main paper

Figures, captions and visual explanation

Figure 3 uses token boxes, a shaded resampled suffix and green/red acceptance outcomes to convey a stochastic transition. Algorithm 1 then supplies the blockwise mechanics that the schematic deliberately omits.

Figure 3, p. 5; Algorithm 1, p. 7. · Main paper

Tables, comparisons and evidence

Table 1 groups rows by model and preserves a low-temperature control, helping isolate the sampler from ordinary sharpening. Bold marks both focal methods rather than universally marking the best score, which the caption explains explicitly.

Table 1, p. 8. · Main paper

Appendix and reproducibility

Appendix A.3 quantifies the approximate 8.84× generated-token multiplier for the stated setting; A.4 reveals different HumanEval power settings and formatting-related failures. These details materially qualify the training-free headline.

Appendices A.3–A.4, pp. 15–16. · Main paper

What to reuse—and what not to infer

Transferable lesson: Explain the nearest plausible alternative with a minimal worked example, retain that alternative as an experimental control, and attach inference cost to a training-free claim.

Boundary: One final response is not one ordinary decoding pass: the sampler repeatedly regenerates suffixes. Finite-step MCMC is approximate, and the measured GRPO baselines do not establish that all RL adds no capabilities. The toy probabilities sum to 0.9 and pseudocode has an intermediate-distribution index ambiguity; neither should be copied uncritically.

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

Sections 1–7, pp. 1–10; references pp. 10–13.

Appendix / supplement

Appendix A.1–A.5, pp. 14–19: annealing literature, pivotal-token argument, hyperparameters/compute, additional pass@k plots and qualitative responses.

Visually inspected PDF pages

5, 8

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