| name | multi-scale-info-geometry-neural |
| description | Multi-scale information geometry framework revealing the structure of mutual information in neural populations. A unique Riemannian representational geometry emerges from coarse-graining, extending Fisher information metric to capture encoding structure from fine to coarse stimulus distinctions. Use when researching neural population coding, information geometry, Fisher information in neuroscience, or neural representational geometry. Based on arXiv:2605.06304. |
| arxiv_id | 2605.06304 |
| published | 2026-05-07T00:00:00.000Z |
| category | neuroscience |
| tags | ["neuroscience","information-geometry","neural-coding","multi-scale","mutual-information","fisher-information","riemannian-geometry","representational-geometry","neural-population-coding"] |
| related_skills | [] |
| activation | information geometry, neural population code, Fisher information metric, representational geometry, multi-scale encoding, neural coding theory, mutual information neural |
Multi-Scale Information Geometry for Neural Population Analysis
arXiv: 2605.06304 | Authors: Simone Azeglio, Steeve Laquitaine, Ulisse Ferrari, Matthew Chalk
Overview
This paper develops a principled framework connecting information geometry, mutual information, and neural population coding. The authors show that a unique Riemannian representational geometry emerges from first principles governing how distances contract as stimulus resolution is lost through coarse-graining.
Core Problem
Different constructions of representational distances (e.g., Fisher information, decoding-based) can lead to qualitatively different conclusions about the neural code. This ambiguity is resolved by deriving a unique geometry from first principles.
Key Contributions
1. Multi-Scale Fisher Information Metric
- Extends classic Fisher information metric to a multi-scale framework
- Captures encoding structure from fine stimulus details to coarse global distinctions
- Metric tensor can be estimated using diffusion models, making it practical for large neural populations
2. Exact Connection to Mutual Information
- The resulting geometry is exactly related to the mutual information encoded by the population
- Well-encoded stimulus directions → expanded in this geometry
- Poorly-encoded directions → contracted
- Provides an interpretable geometric visualization of neural information content
3. Diffusion Model Estimation
- Practical estimation method using diffusion models
- Scales to high-dimensional stimuli and large populations
- Applied to visual cortical responses to natural images
4. Interpretable Features
- Eigenvectors of the metric tensor identify stimulus variations contributing most to information transmission
- Robust to modelling choices
- Applied to visual cortex data revealing meaningful stimulus features
Theoretical Framework
Riemannian Geometry from Coarse-Graining
- Define distances in stimulus space based on how reliably stimuli are distinguished from neural activity
- As stimulus resolution is lost through coarse-graining, distances contract
- A unique geometry emerges from this contraction process — not dependent on arbitrary choices
Multi-Scale Extension
