For n unit vectors, the smallest eigenvalue of the average ReLU feature Gram matrix is at least a constant times Delta/sqrt(log n), and the paper claims this rate is tight.
Bounds for the smallest eigenvalue of the NTK for arbitrary spherical data of arbitrary dimension
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Tight Worst-Case Bounds for the Smallest Eigenvalue of ReLU NTK Gram Matrices
For n unit vectors, the smallest eigenvalue of the average ReLU feature Gram matrix is at least a constant times Delta/sqrt(log n), and the paper claims this rate is tight.