Writing study: Modeling Hierarchical Thinking in Large Reasoning Models

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G M Shahariar, Erfan Shayegani, Ali Nazari, Nael Abu-Ghazaleh · 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: Empirical analysis, diagnosis & auditing (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

26 physical pages

Before references / appendix

≈ 9.33 page-equivalents

Main figures / tables

3 / 2

Attached appendix figures / tables

2 / 7

Attached appendix span

≈ 13.91 page-equivalents

Before references / appendix: ≈ 35.88%References / intervening material: ≈ 10.62%Attached appendix: ≈ 53.5%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	≈ 1.01 pp.	3.88%
2. Finite State Abstraction of LLM Reasoning	2	≈ 2.15 pp.	8.27%
3. Controlling Reasoning Trajectories as an FSM Application	4	≈ 1.97 pp.	7.58%
4. Experimental Setup	6	≈ 0.67 pp.	2.58%
5. Experimental Results	7	≈ 1.77 pp.	6.81%
6. Related Work	9	≈ 0.65 pp.	2.5%
7. Conclusion	9	≈ 0.22 pp.	0.85%
Impact Statement	10	≈ 0.29 pp.	1.12%
References	10	≈ 2.76 pp.	10.62%
Appendix	13	≈ 0.03 pp.	0.12%
A. Description of FSM States	13	≈ 0.97 pp.	3.73%
B. Value-based Policy: Deterministic MDP Reduction	14	≈ 1 pp.	3.85%
C. Empirical Validation of Markov Assumption	15	≈ 1 pp.	3.85%
D. Prompt-based Steering	16	≈ 1.2 pp.	4.62%
E. Limitations and Future Work	17	≈ 0.8 pp.	3.08%
F. Diversity and Fluency Evaluation	18	≈ 0.25 pp.	0.96%
G. Additional Results	18	≈ 0.38 pp.	1.46%
H. Intervention Effectiveness	18	≈ 0.69 pp.	2.65%
I. Failure Analysis	19	≈ 0.35 pp.	1.35%
J. Hyper-parameter Sensitivity	19	≈ 0.6 pp.	2.31%
K. Annotation Prompts	20	≈ 0.97 pp.	3.73%
L. Prompt-Based Steering Templates	21	≈ 1.19 pp.	4.58%
M. Example of Annotated CoT Reasoning	22	≈ 2.54 pp.	9.77%
N. Transition Advantage Matrices	25	≈ 1.96 pp.	7.54%

All detected figure and table locations

Main text

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

Attached appendix

• Table 3 · p. 15
• Table 4 · p. 15
• Table 5 · p. 16
• Table 6 · p. 18
• Table 7 · p. 18
• Table 8 · p. 19
• Table 9 · p. 20
• Figure 4 · p. 25
• Figure 5 · p. 26

Argument and organization

1. 1 Introduction; 2 Finite State Abstraction

   Defines sentence labels and outcome-conditioned transition statistics.

2. 3 Controlling Reasoning Trajectories

   Separates vector extraction, state prediction, transition selection and activation injection.

3. 4 Setup; 5 Results; 6 Related Work; 7 Conclusion

   Reports accuracy, generated tokens and intervention counts before transfer and related work.

Problem, claim and contribution

The abstract introduces an approximation of reasoning dynamics, a useful qualification that should survive stronger cognitive and optimal-control language later in the paper.

Abstract, p.1; Section 3.3, p.6 · Main paper

Argument and section order

The control method is divided into when, where and how to intervene, making annotation, classifier training and inference roles separately inspectable.

Sections 3.1-3.4, pp.4-6 · Main paper

Figures, captions and visual explanation

The two-tier overview separates abstraction from control and shows classifier training explicitly; the main table reports accuracy, length and intervention frequency in parallel groups.

Figure 2, p.4; Table 1, p.7 · Main paper

Tables, comparisons and evidence

The paper reports a fixed seed and a limited human annotation audit, while some steering variants lose accuracy and fewer interventions do not always shorten generation.

Annotation and Hyper-parameter Settings; Table 1, p.7 · Main paper

Appendix and reproducibility

Second-order alternatives test the Markov approximation, and failure analysis quantifies false punctuation boundaries rather than merely acknowledging segmentation noise.

Appendix C, p.15; Appendix I, p.19 · Main paper

Clarity and writing conventions

Training-free describes the base-model intervention, not the trained state encoder and classifiers; the method itself also states that its empirical Q-values do not guarantee global optimality.

Section 3.2, p.5; Section 3.3, p.6 · Main paper

What to reuse—and what not to infer

Transferable lesson: Expose the distinction between descriptive state abstraction, learned intervention machinery and the separate costs of tokens and interventions.

Boundary: Six labels are an approximation, not verified cognitive states; the held-out extraction protocol can use test-set subsets, so independent evaluation separation needs explicit checking.

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, 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, 15, 19. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

4, 7

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 · 26 pages