Writing study: How Do Transformers Learn to Associate Tokens: Gradient Leading Terms Bring Mechanistic Interpretability

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← ICLR 2026 oral writing corpus

Shawn Im, Changdae Oh, Zhen Fang, Sharon Li · 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: Theory & formal foundations (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

39 physical pages

Before references / appendix

≈ 10.62 page-equivalents

Main figures / tables

7 / 1

Attached appendix figures / tables

1 / 2

Attached appendix span

≈ 24.89 page-equivalents

Before references / appendix: ≈ 27.23%References / intervening material: ≈ 8.95%Attached appendix: ≈ 63.82%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	≈ 1.57 pp.	4.03%
2 RELATED WORKS	3	≈ 0.4 pp.	1.03%
3 PRELIMINARY	3	≈ 1.22 pp.	3.13%
4 THEORETICAL ANALYSIS	4	≈ 3.34 pp.	8.56%
5 EXPERIMENTS	8	≈ 2.62 pp.	6.72%
6 CONCLUSION	10	≈ 0.38 pp.	0.97%
ETHICS STATEMENT	11	≈ 0.18 pp.	0.46%
REPRODUCIBILITY STATEMENT	11	≈ 0.12 pp.	0.31%
ACKNOWLEDGMENTS	11	≈ 0.21 pp.	0.54%
REFERENCES	11	≈ 3.48 pp.	8.92%
A DETAILED DESCRIPTION ON WEIGHT CHARACTERIZATION	15	≈ 0.73 pp.	1.87%
B ADDITIONAL EXPERIMENTS	15	≈ 1.27 pp.	3.26%
C EXPERIMENTAL DETAILS	17	≈ 0.24 pp.	0.62%
D PROOFS	17	≈ 22.65 pp.	58.08%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 5
• Figure 3 · p. 6
• Table 1 · p. 8
• Figure 4 · p. 8
• Figure 5 · p. 8
• Figure 6 · p. 9
• Figure 7 · p. 10

Attached appendix

• Table 2 · p. 16
• Table 3 · p. 16
• Figure 8 · p. 16

Argument and organization

1. Semantic association as the question

   Defines an interpretable target before introducing the training-dynamics approximation.

2. Theorem and interpretation

   Separates approximation bounds from their decomposition into corpus-statistic mappings.

3. Controlled and practical-model experiments

   Tests the exact setting before exploring corresponding statistics in Pythia.

Problem, claim and contribution

Concrete token relationships introduce the abstract target, while the research question is isolated before notation. This helps readers understand why a matrix characterization is useful.

Sections 1 and 3.1, pages 1–3. · Main paper

Argument and section order

A theorem is followed by three named basis mappings, their composition into four parameter classes, and their joint forward computation. The progression translates algebra into an argument rather than leaving interpretation implicit.

Sections 4.1–4.2.3, pages 5–7. · Main paper

Figures, captions and visual explanation

The conceptual diagram uses shared token colors and distinct arrow styles for local and long-range dependencies. It places output, value and query–key constructions in separate framed panels next to the theorem.

Figure 2, page 5. · Main paper

Tables, comparisons and evidence

A small minimum-similarity table, training trajectory and selected token lists offer complementary numerical, temporal and semantic views. The selected top-30 examples are illustrative, not a comprehensive semantic evaluation.

Table 1 and Figures 4–5, page 8. · Main paper

The Pythia analysis explicitly changes to token-covariance comparisons because real-model matrices are not directly comparable. That methodological bridge should remain visible whenever the practical results are summarized.

Section 5.2, pages 9–10. · Main paper

Appendix and reproducibility

Definitions, BPE and intervention tests precede the long proof sequence, which grows from initial gradient steps to multilayer and small-Gaussian cases. The intervention table provides a behavioral check beyond similarity.

Appendices A–D, pages 15–39; Table 3, page 16. · Main paper

What to reuse—and what not to infer

Transferable lesson: After a formal result, explain its basis objects, compose them into individual components, and finally show how the components cooperate in the full computation.

Boundary: The theorem assumes an attention-only, vocabulary-space model with full-batch gradient descent and restrictive early-time initialization conditions. Pythia covariance agreement is supporting empirical evidence, not a proof of equivalent learned mechanisms or downstream reasoning.

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

Pages 1–11, Sections 1–6 plus ethics/reproducibility; references through page 14.

Appendix / supplement

Pages 15–39, Appendices A–D: construction, supplementary experiments, setup, and all single-layer, multilayer and Gaussian-initialization derivations.

Visually inspected PDF pages

5, 8

• ICLR 2026 final proceedings · 39 pages