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Computational Pathology Reading Roadmap

Writing study: Joint Learning in the Gaussian Single Index Model

← ICML 2026 oral writing corpus

Loucas Pillaud-Vivien, Adrien Schertzer · Official ICML 2026 oral record

Figure, table and section ledger

Editorial contribution type: Theory & formal analysis (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
≈ 8.78 page-equivalents
Main figures / tables
2 / 0
Attached appendix figures / tables
0 / 0
Attached appendix span
≈ 11.91 page-equivalents
Before references / appendix: ≈ 39.91%References / intervening material: ≈ 5.95%Attached appendix: ≈ 54.14%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 headingStarts on PDF pageEstimated spanShare of entire PDF
1. Introduction1≈ 0.91 pp.4.14%
2. Problem Setup2≈ 1.37 pp.6.23%
3. Gradient Flow Dynamics3≈ 0.98 pp.4.45%
4. Convergence Behavior of the Joint Gradient Flow4≈ 2 pp.9.09%
5. Kernel Implementation via Hermite Functions6≈ 0.83 pp.3.77%
6. Numerical Experiments7≈ 1.85 pp.8.41%
7. Conclusion and Outlook9≈ 0.39 pp.1.77%
Acknowledgments9≈ 0.09 pp.0.41%
Impact Statement9≈ 0.04 pp.0.18%
References9≈ 1.3 pp.5.91%
A. Appendix11≈ 11.91 pp.54.14%
All detected figure and table locations

Main text

Attached appendix

    No recognized caption labels.

    Argument and organization

    1. 1 Introduction; 2 Setup; 3 Dynamics

      Defines the Gaussian model and converts joint function/direction learning into coupled spectral dynamics.

    2. 4 Convergence; 5 Kernel Implementation

      Contrasts fixed-profile and joint learning, gives a three-phase proof sketch and builds a finite-dimensional realization.

    3. 6 Numerical Experiments; 7 Outlook

      Separates idealized ODE simulations from finite-sample empirical dynamics and leaves sample complexity open.

    Problem, claim and contribution

    The opening makes joint learning of direction and profile the object of study, with negative initial correlation motivating the fixed-versus-adaptive comparison.

    Abstract and Introduction, p.1; Section 4.1, p.4 · Main paper

    Argument and section order

    A numbered fast–slow–convergence explanation follows the formal theorem and precedes practical implementation.

    Section 4.3, p.6 · Main paper

    Figures, captions and visual explanation

    The idealized figure pairs phase portraits with time traces; the empirical figure plots every seed in two sign groups, explicitly avoiding averages that would smear transition times.

    Figures 1-2, pp.7-8 · Main paper

    Tables, comparisons and evidence

    The finite-data caption supplies sample size, dimension, truncation and seed count, while the text discloses controlled initialization rather than presenting it as unmodified random initialization.

    Section 6 and Figure 2, p.8 · Main paper

    Appendix and reproducibility

    The deferred derivation restates the gradient-flow system and connects the function-space gradient to the coefficient equations used in the main argument.

    Appendix A.2, p.12 · Main paper

    Clarity and writing conventions

    The conclusion states that sample complexity and discrete finite-data guarantees remain future work, separating qualitative numerical agreement from the population theorem.

    Conclusion and Outlook, p.9 · Main paper

    What to reuse—and what not to infer

    Transferable lesson: Choose a display that preserves the theoretical phenomenon and explain why a familiar summary statistic would obscure it.

    Boundary: The guarantee concerns idealized population gradient flow under the stated Gaussian and regularity assumptions, not a finite-sample learning bound; this scan does not validate proofs.

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