Linear Classification of Neural Manifolds with Correlated Variability
Albert J. Wakhloo, Tamara J. Sussman, SueYeon Chung
Abstract
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.
Topics & Concepts
CentroidDuality (order theory)Artificial neural networkMeasure (data warehouse)Object (grammar)Artificial intelligencePhysicsSPHERESPattern recognition (psychology)Computer scienceStatistical physicsGeometryMathematicsPure mathematicsData miningAstronomyCell Image Analysis TechniquesMachine Learning in Materials ScienceNeural dynamics and brain function