Linear Classification of Neural Manifolds with Correlated Variability

Albert J. Wakhloo, Tamara J. Sussman, Sueyeon Chung

Research output: Contribution to journalArticlepeer-review


Understanding how the statistical and geometric properties of neural activity relate to performance is a key problem in theoretical neuroscience and deep learning. Here, we calculate how correlations between object representations affect the capacity, a measure of linear separability. We show that for spherical object manifolds, introducing correlations between centroids effectively pushes the spheres closer together, while introducing correlations between the axes effectively shrinks their radii, revealing a duality between correlations and geometry with respect to the problem of classification. We then apply our results to accurately estimate the capacity of deep network data.

Original languageEnglish (US)
Article number027301
JournalPhysical Review Letters
Issue number2
StatePublished - Jul 14 2023

ASJC Scopus subject areas

  • General Physics and Astronomy


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