Understanding how the statistical and geometric properties of neural activations relate to network performance is a key problem in theoretical neuroscience and deep learning. In this letter, 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 spheres' axes effectively shrinks their radii, revealing a duality between neural correlations and geometry. We then show that our results can be used to accurately estimate the capacity with real neural data.

翻译：理解神经激活的统计和几何特性与网络性能的关系是理论神经科学和深层学习中的一个关键问题。 在本信中,我们计算了天体表达方式如何影响能力,即线性分离的度量。我们显示,对于球形物体的方体,引入中央机器人之间的关联有效地将球体拉近,同时引入球体轴之间的关联有效地缩小了它们的弧度,揭示了神经相关性和几何学之间的双重性。然后我们表明,我们的结果可以用实际神经数据来准确估计能力。