87 citations · 349 across the 33 of their papers we have counts for
8 papers · 1 filter
Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds
Yibang Li, Bihari Lal Pandey, Ravi Sah +4
Muon and related norm-constrained matrix optimizers have become central to large-scale learning problems. They are formulated as a linear maximization oracle (LMO) over an ambient…
Universal kernels via harmonic analysis on Riemannian symmetric spaces
Franziskus Steinert, Salem Said, Cyrus Mostajeran
The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental import…
Invariant kernels on Riemannian symmetric spaces: a harmonic-analytic approach
Nathael Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega +1
This work aims to prove that the classical Gaussian kernel, when defined on a non-Euclidean symmetric space, is never positive-definite for any choice of parameter. To achieve this…
Geometric Learning with Positively Decomposable Kernels
Nathael Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega +1
Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces…
The Gaussian kernel on the circle and spaces that admit isometric embeddings of the circle
Nathaël Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega
On Euclidean spaces, the Gaussian kernel is one of the most widely used kernels in applications. It has also been used on non-Euclidean spaces, where it is known that there may be…
Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm
Berlin Chen, Cyrus Mostajeran, Salem Said
We present a novel algorithm for learning the parameters of hidden Markov models (HMMs) in a geometric setting where the observations take values in Riemannian manifolds. In partic…
Online learning of Riemannian hidden Markov models in homogeneous Hadamard spaces
Quinten Tupker, Salem Said, Cyrus Mostajeran
Hidden Markov models with observations in a Euclidean space play an important role in signal and image processing. Previous work extending to models where observations lie in Riema…
Inductive Geometric Matrix Midranges
Graham W. Van Goffrier, Cyrus Mostajeran, Rodolphe Sepulchre
Covariance data as represented by symmetric positive definite (SPD) matrices are ubiquitous throughout technical study as efficient descriptors of interdependent systems. Euclidean…