Writing study: A multi-scale information geometry reveals the structure of mutual information in neural populations
← NeurIPS 2026 oral writing corpus
Simone Azeglio, Steeve Laquitaine, Ulisse Ferrari, Matthew Chalk · Official NeurIPS 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
- ≈ 10.09 page-equivalents
- Main figures / tables
- 5 / 0
- Attached appendix figures / tables
- 1 / 1
- Attached appendix span
- ≈ 8.91 page-equivalents
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. Exclude inline prose “comparison in Fig. 4: any systematic” p.20; this is not an appendix Figure 4 caption.
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 | ≈ 0.73 pp. | 3.32% |
| 2 From Fisher information to a multi-scale geometry of neural coding | 2 | ≈ 1.28 pp. | 5.82% |
| 3 Deriving the geometry from coarse-graining | 3 | ≈ 1.84 pp. | 8.36% |
| 4 The geometry directly captures mutual information | 5 | ≈ 0.68 pp. | 3.09% |
| 5 Estimating the multi-scale geometry from diffusion models | 6 | ≈ 1.13 pp. | 5.14% |
| 6 Uncovering the multi-scale geometry of recorded visual neurons | 7 | ≈ 1.96 pp. | 8.91% |
| 7 Discussion | 9 | ≈ 1.65 pp. | 7.5% |
| References | 11 | ≈ 3 pp. | 13.64% |
| A Relation between geometry and mutual information | 14 | ≈ 1 pp. | 4.55% |
| B Estimating the geometry using diffusion models | 15 | ≈ 3.71 pp. | 16.86% |
| C Predictive neural models | 18 | ≈ 4.2 pp. | 19.09% |
All detected figure and table locations
Attached appendix
Argument and organization
- Problem and contribution
Shows why equal local Fisher information can conceal different global stimulus discriminability.
- Argument sequence
Moves from a one-dimensional counterexample to coarse-graining principles, the information relation, practical estimation and neural data.
- Evidence and verification
The robustness comparison separates predictive fit, eigenvector structure and within-/between-area alignment rather than relying on an attractive feature visualization alone.
Problem, claim and contribution
Shows why equal local Fisher information can conceal different global stimulus discriminability.
Introduction; Section 2 · Main paper
Argument and section order
Moves from a one-dimensional counterexample to coarse-graining principles, the information relation, practical estimation and neural data.
Sections 2–6 · Main paper
Figures, captions and visual explanation
The running example aligns tuning curves, scale-specific heatmaps and integrated geometry. A later multipanel figure compares encoding backbones before interpreting neural-area differences.
Figure 1, p. 3; Figure 4, p. 8 · Main paper
Tables, comparisons and evidence
The robustness comparison separates predictive fit, eigenvector structure and within-/between-area alignment rather than relying on an attractive feature visualization alone.
Figure 4; Section 6 · Main paper
Appendix and reproducibility
Proofs, diffusion-model estimation and neuronal encoding protocols are separated; additional geometry-distance comparisons test the main interpretation.
Appendices A–C · Main paper
Clarity and writing conventions
The discussion states that the geometry depends on a learned probabilistic encoding model and sufficient data.
Section 7 · Main paper
What to reuse—and what not to infer
Transferable lesson: Use a minimal counterexample to motivate a mathematical object, then test whether empirical conclusions survive the modeling choices used to estimate it.
Boundary: Backbone robustness is evidence within the tested encoders, not a guarantee that the estimated geometry is model-free.
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 distributed manuscript scan of Sections 1–7, pp. 1–10; reference region pp. 11–13: abstract/framing, section sequence, substantive text windows, captions, evidence organization and conclusion; not exhaustive technical verification.
- Appendix / supplement
- Writing-oriented scan of Appendices A–C, pp. 14–22; information relation, diffusion estimation and encoding-model details; code and experiments were not executed.
- Visually inspected PDF pages
- 3, 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.