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Updated: Jul 21, 2025
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Linear Classification of Neural Manifolds with Correlated Variability
Albert J Wakhloo1,2, Tamara J Sussman2,3, SueYeon Chung1,4
1Center for Computational Neuroscience, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA.
Physical Review Letters
|July 28, 2023
Summary
Correlations in neural activity impact classification performance by altering the geometry of object representations. This study reveals a geometric duality linking correlations to linear separability in deep learning models.
Area of Science:
- Theoretical neuroscience
- Deep learning
- Computational neuroscience
Background:
- Understanding neural activity's statistical and geometric properties is crucial for performance in neuroscience and deep learning.
- Linear separability, measured by capacity, is a key metric for evaluating classification performance.
Purpose of the Study:
- To investigate how correlations between object representations influence the capacity of neural networks.
- To reveal the relationship between correlation, geometry, and classification performance.
Main Methods:
- Calculating the effect of correlations on the capacity of spherical object manifolds.
- Analyzing how correlations between centroids and axes modify geometric properties.
Main Results:
- Correlations between centroids push object representations closer, reducing capacity.
- Correlations between axes effectively shrink representation radii, also reducing capacity.
- A geometric duality exists between correlations and classification capacity.
Conclusions:
- The study provides a framework for understanding how neural activity correlations affect linear separability.
- Results can be applied to accurately estimate the capacity of deep network data.
- Findings offer insights into the geometric underpinnings of classification in neural systems.
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