Writing study: Quantitative Bounds for Length Generalization in Transformers

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← ICLR 2026 oral writing corpus

Zachary Izzo, Eshaan Nichani, Jason Lee · 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).

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

≈ 9.54 page-equivalents

Main figures / tables

4 / 0

Attached appendix figures / tables

0 / 0

Attached appendix span

≈ 26.89 page-equivalents

Before references / appendix: ≈ 24.46%References / intervening material: ≈ 6.59%Attached appendix: ≈ 68.95%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	≈ 0.9 pp.	2.31%
2 RELATED WORK	2	≈ 0.69 pp.	1.77%
3 PROBLEM FORMULATION	3	≈ 2.47 pp.	6.33%
4 LENGTH GENERALIZATION WITH FINITE PRECISION	5	≈ 1.24 pp.	3.18%
5 SOFT ATTENTION TRANSFORMERS WITH INFINITE PRECISION	6	≈ 1.89 pp.	4.85%
6 EXPERIMENTS	8	≈ 1.34 pp.	3.44%
7 CONCLUSION	10	≈ 0.24 pp.	0.62%
ETHICS STATEMENT	10	≈ 0.13 pp.	0.33%
REPRODUCIBILITY STATEMENT	10	≈ 0.07 pp.	0.18%
REFERENCES	10	≈ 2.57 pp.	6.59%
A OMITTED PROOFS FROM SECTION 4	13	≈ 12.65 pp.	32.44%
B OMITTED PROOFS FROM SECTION 5	25	≈ 12.77 pp.	32.74%
C EXPERIMENTAL METHODOLOGY	38	≈ 1.47 pp.	3.77%

All detected figure and table locations

Main text

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

Attached appendix

No recognized caption labels.

Argument and organization

1. Precision and error regimes

   Separate finite-precision hard attention from modified infinite-precision soft attention before presenting bounds.

2. Simulation lemmas and qualitative experiments

   A common short-string simulation idea links different theorems; synthetic tasks vary corresponding complexity factors.

Problem, claim and contribution

The introduction identifies an exact gap between eventual identifiability and quantitative training-length bounds, then states agreement of two limit transformers as the actual object of study.

Section 1, pages 1–2 · Main paper

Argument and section order

Finite- and infinite-precision assumptions receive separate subsections, including the rounding rule and changed positional-logit scaling. This prevents the two analyses from appearing to concern an identical implemented architecture.

Sections 3.2–3.3, pages 3–5 · Main paper

Figures, captions and visual explanation

Paired plots separate extrapolation length from training length; captions explicitly tell readers which quantity is fixed and which varies. Small legends and dense rainbow curves weaken readability at reduced scale.

Figures 1–2, page 8; Figure 4, page 9 · Main paper

Tables, comparisons and evidence

Synthetic tasks isolate frequency, positional period, vocabulary and local context, offering qualitative support rather than a numerical verification of loose worst-case bounds or an optimization guarantee.

Section 6, pages 8–9 · Main paper

Appendix and reproducibility

Proofs are organized by theorem with reusable helper lemmas; the final appendix separately lists data generators, model widths, stopping rules and seed counts, making mathematical and empirical reproducibility independently navigable.

Appendices A–C, pages 13–39 · Main paper

Clarity and writing conventions

Theorem, proof sketch and remarks form a reusable sequence: the sketch supplies the simulation intuition, while remarks explain parameter dependence and what remains unresolved.

Theorems 4.1–4.2 and 5.2, pages 5–8 · Main paper

What to reuse—and what not to infer

Transferable lesson: State the precise comparison problem before the theorem, expose architectural assumptions, and pair each complexity factor with an experiment that actually varies it.

Boundary: Bounds assume agreement on short strings or specified mixture-distribution error and restricted one-/two-layer limit transformers; they do not show ordinary LLM training reaches that agreement. Full proofs were read for presentation and scope, not independently certified.

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 1–10, Sections 1–7 and statements

Appendix / supplement

Pages 13–39, all proofs in Appendices A–B and experimental methodology/constructions in C

Visually inspected PDF pages

7, 8

• ICLR 2026 final proceedings · 39 pages