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 ...