Writing study: Skip a Layer or Loop It? Learning Program-of-Layers in LLMs

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← ICML 2026 oral writing corpus

Ziyue Li, Yang Li, Tianyi Zhou · 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: Efficiency, inference & systems (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

22 physical pages

Before references / appendix

≈ 10.04 page-equivalents

Main figures / tables

8 / 4

Attached appendix figures / tables

0 / 7

Attached appendix span

≈ 9.91 page-equivalents

Before references / appendix: ≈ 45.64%References / intervening material: ≈ 9.32%Attached appendix: ≈ 45.05%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	≈ 1.21 pp.	5.5%
2. Dynamic Inference as a Program-of-Layers (POLAR) in Large Language Models	2	≈ 3.09 pp.	14.05%
3. Learning Program-of-Layers (POLAR) in Large Language Models	5	≈ 1.64 pp.	7.45%
4. Experiments	7	≈ 1.96 pp.	8.91%
5. Related Works	9	≈ 0.54 pp.	2.45%
6. Conclusion	9	≈ 0.25 pp.	1.14%
Impact Statement	10	≈ 1 pp.	4.55%
References	11	≈ 2.04 pp.	9.27%
A. Related Work	13	≈ 1 pp.	4.55%
B. Searching the Execution Program Space	14	≈ 2 pp.	9.09%
C. Experimental Results	16	≈ 5 pp.	22.73%
D. Empirical Details	21	≈ 1.91 pp.	8.68%

All detected figure and table locations

Main text

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

Attached appendix

• Table 5 · p. 17
• Table 6 · p. 18
• Table 7 · p. 19
• Table 8 · p. 19
• Table 9 · p. 20
• Table 10 · p. 20
• Table 11 · p. 21

Argument and organization

1. 1 Introduction; 2 Dynamic Inference

   Uses offline search to characterize alternative valid layer executions.

2. 3 Learning POLAR

   Converts observed structural regularities into a restricted program representation and supervised predictor.

3. 4 Experiments; 5 Related Work; 6 Conclusion

   Separates held-out prediction, transfer and measured inference overhead from search-based discovery.

Problem, claim and contribution

The abstract challenges fixed execution depth, but the practical method trains a separate predictor while keeping the base LLM frozen.

Abstract, p.1; Section 3.2, p.6 · Main paper

Argument and section order

Four diagnostic findings motivate the compact program vocabulary before the learned prediction network is defined.

Section 2 through Section 3.1, pp.3-5 · Main paper

Figures, captions and visual explanation

The search tree and direct-prediction schematic contrast two computational stages; a later table separately accounts for encoder, predictor and beam-search overhead.

Figure 2, p.3; Table 4, p.9 · Main paper

Tables, comparisons and evidence

Pass-at-k means predicted execution programs for POLAR but stochastic output samples for the baseline, and the paper explicitly defines both.

Experimental Setup, p.7 · Main paper

Appendix and reproducibility

The split protocol deduplicates questions, enumerates train/validation/test sizes and specifies direct-answer prompting without elicited chain of thought.

Appendix D, p.21 · Main paper

Clarity and writing conventions

Cross-domain explanations are labeled conjectures, while repeated training-free language must be read as referring to frozen base-model weights rather than the entire workflow.

Section 4.3, p.9; predictor training, p.6 · Main paper

What to reuse—and what not to infer

Transferable lesson: Separate offline discovery, learned selection and online execution costs, and define candidate counting whenever pass-at-k compares different search mechanisms.

Boundary: Search-found accuracy is not practical predictor accuracy; the pipeline includes offline supervision and an external embedding model, and its direct-answer setting differs from long-chain reasoning.

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, 5, 6, 7, 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, 21. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

3, 9

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 · 22 pages