Basically , Theorem 5 says that the Gram matrix G ∞ should have high chance of having large smallest eigenvalue if the training data are uniformly distributed . Intuitively , we would expect the smallest eigenvalue to be very small if all x i are similar to each other . Therefore , some notion of diversity of the training inputs is needed . We conjecture that the smallest eigenvalue would still be large if the data are δ - separable ( i.e. , x i − x j 2 ≥ δ for any pair i , j ∈ [ n ] ) , an assumption adopted by Li and Liang [ 2018 ] , Allen - Zhu et al . [ 2018 ] , Zou et al . [ 2018 ] .