Abstract: This paper proposes a new approach to accelerate spectral norm estimation for a kernel matrix of n data points. Our key intuition is that, by applying the seminal random feature technique, ...

PolarGrad (Polar Gradient methods; Lau et al., 2025) is a class of matrix-gradient optimizers based on the concept of gradient-anisotropy preconditioning in optimization. It has close relation to Muon ...

The proofs are based on a combination of the moment method and geometric functional analysis techniques. As an application, we show that our bounds immediately yield the correct phase transition ...

Aiming to make inferences about the spectral distribution of the population covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral ...