Writing study: Fractional State Space Transition for Long Sequence Modeling

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← NeurIPS 2026 oral writing corpus

Ivan Kobyzev, Abbas Ghaddar, Ali Nasiri-Sarvi, Lifeng Shang, Yufei CUI · Official NeurIPS 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: Architecture & representation (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

28 physical pages

Before references / appendix

≈ 9.21 page-equivalents

Main figures / tables

4 / 4

Attached appendix figures / tables

0 / 6

Attached appendix span

≈ 11.91 page-equivalents

Before references / appendix: ≈ 32.89%References / intervening material: ≈ 24.57%Attached appendix: ≈ 42.54%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Top-level heading and reference/appendix boundaries checked against source PDF text. Bibliography titles/author initials, numbered contribution/property bullets, diagram steps, equations and TOC entries are not substantive headings. Section spans are page-coordinate estimates, not ink area or prose-only length. This is an author manuscript mirror, not a verified accepted-version template. Source layout uses physical single-column y/page-height, including equation-heavy pages.

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	≈ 0.72 pp.	2.57%
2 Preliminaries	2	≈ 2.43 pp.	8.68%
3 Method	4	≈ 2.07 pp.	7.39%
4 Experiments	6	≈ 2.46 pp.	8.79%
5 Related Work	9	≈ 0.85 pp.	3.04%
6 Conclusion	10	≈ 0.12 pp.	0.43%
References	10	≈ 6.88 pp.	24.57%
A Discussion of Theorem 1	17	≈ 0.71 pp.	2.54%
B Proof of Theorem 2	17	≈ 2.29 pp.	8.18%
C Proof of Proposition 3	20	≈ 1.1 pp.	3.93%
D Frac State Transition Algorithm	21	≈ 0.63 pp.	2.25%
E Experimental Setting	21	≈ 3.5 pp.	12.5%
F FracMixer Efficient Implementation	25	≈ 1.1 pp.	3.93%
G FRAC Ablation	26	≈ 1.11 pp.	3.96%
H Limitations and Broader Impact	27	≈ 1.46 pp.	5.21%

All detected figure and table locations

Main text

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

Attached appendix

• Table 5 · p. 22
• Table 6 · p. 22
• Table 7 · p. 24
• Table 8 · p. 25
• Table 9 · p. 26
• Table 10 · p. 27

Argument and organization

1. Problem and contribution

   Locates the contribution in the memory law of a bounded-state model, distinguishing exponential forgetting from a practical finite approximation to long-memory dynamics.

2. Argument sequence

   Mathematical preliminaries introduce the kernel and approximation before the selective recurrence, then experiments move from controlled memory probes to language and DNA tasks.

3. Evidence and verification

   The long-context claim is accompanied by short-context and recall-retrieval results where FRAC is not the best model; throughput is separated into prefill lengths, decode and training.

Problem, claim and contribution

Locates the contribution in the memory law of a bounded-state model, distinguishing exponential forgetting from a practical finite approximation to long-memory dynamics.

Sections 1–2, pp. 1–4 · Main paper

Argument and section order

Mathematical preliminaries introduce the kernel and approximation before the selective recurrence, then experiments move from controlled memory probes to language and DNA tasks.

Sections 2–4, pp. 2–9 · Main paper

Figures, captions and visual explanation

Figure 3 uses three matched passkey-retrieval panels with the same context-length axis; the adjacent tables group LongBench task families and distinguish perplexity-down from accuracy-up metrics. Figure 2 plots the synthetic extrapolation task over context length, with point markers and a shared accuracy axis; the prose states the 512-token training length and matched model size. Table 1 separately reports the MADLab tasks and five-run variation, so the extrapolation curve and task-suite averages are not treated as one experiment.

Figure 3 and Tables 2–4, p. 8 (render inspected); Figure 2 and Table 1, p. 7 (additional rendered inspection) · Main paper

Tables, comparisons and evidence

The long-context claim is accompanied by short-context and recall-retrieval results where FRAC is not the best model; throughput is separated into prefill lengths, decode and training.

Tables 2–4, p. 8; Table 8, p. 25 · Main paper

Appendix and reproducibility

An explicit remark distinguishes the exact zero-order-hold coefficient from the modeling choice used in pseudocode, keeping mathematical derivation and implementation from being conflated.

Appendix D, p. 21; Appendix F, pp. 25–26 · Main paper

Clarity and writing conventions

The result discussion uses competitive rather than best when the model trails on short-context averages, and the limitations acknowledge the finite-state approximation.

Section 4.2, p. 8; Appendix H, pp. 27–28 · Main paper

What to reuse—and what not to infer

Transferable lesson: Bridge a mathematical prior to an implementable recurrence, then test the targeted capability alongside capabilities that might regress.

Boundary: The source's practical recurrence is not identical to every coefficient in the continuous derivation. Preserve that distinction and the non-winning short-context results.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-10-02

Reading status

Writing-focused manuscript scan + selected visuals inspected

Main text

Writing-oriented scan across manuscript framing, section sequence, figure/table captions, selected argument/evaluation prose and conclusion; not exhaustive technical or proof verification. Sections 1–6, pp. 1–10; references pp. 10–15 Source is the exact public author version listed below, not a verified accepted/camera-ready revision.

Appendix / supplement

Writing-oriented appendix/documentation scan: Appendices A–H, pp. 16–28: theorem discussion/proofs, recurrence pseudocode, full protocols, implementation throughput, ablation and limitations. Source code, data, model outputs and external video assets were not executed or independently validated.

Visually inspected PDF pages

7, 8

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.

• Public author arXiv manuscript 2609.36314v1; not verified identical to the accepted or camera-ready OpenReview revision · 28 pages