Linear Classification of Neural Manifolds with Correlated Variability
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.
Code (0)
등록된 구현이 없습니다.
Tasks
ClassificationObjectSimilar Papers 제목 키워드 기반
Statistical Mechanics of Neural Processing of Object Manifolds
Invariant object recognition is one of the most fundamental cognitive tasks performed by the brain. In the neural state space, different objects with stimulus variabilities are represented as different manifolds. In this…
ObjectObject RecognitionSoft-margin classification of object manifolds
A neural population responding to multiple appearances of a single object defines a manifold in the neural response space. The ability to classify such manifolds is of interest, as object recognition and other computatio…
ClassificationObjectObject RecognitionClassification and Geometry of General Perceptual Manifolds
Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual …
ClassificationGeneral ClassificationObjectObject RecognitionThe correlated variability control problem: a dominant approach
Given a population of interconnected input-output agents repeatedly exposed to independent random inputs, we talk of correlated variability when agents' outputs are variable (i.e., they change randomly at each input repe…
Convolutional Neural Networks Regularized by Correlated Noise
Neurons in the visual cortex are correlated in their variability. The presence of correlation impacts cortical processing because noise cannot be averaged out over many neurons. In an effort to understand the functional …