Wakhloo Albert J, Sussman Tamara J, Chung SueYeon
Center for Computational Neuroscience, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA.
Department of Child and Adolescent Psychiatry, New York State Psychiatric Institute, 1051 Riverside Drive, New York, New York 10032, USA.
Phys Rev Lett. 2023 Jul 14;131(2):027301. doi: 10.1103/PhysRevLett.131.027301.
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.
理解神经活动的统计特性和几何特性如何与性能相关联是理论神经科学和深度学习中的一个关键问题。在这里，我们计算对象表示之间的相关性如何影响容量，这是一种线性可分性的度量。我们表明，对于球形对象流形，在质心之间引入相关性会有效地将球体推得更近，而在轴之间引入相关性会有效地缩小它们的半径，揭示了在分类问题上相关性和几何之间的对偶性。然后，我们应用我们的结果来准确估计深度网络数据的容量。
