87 citations · 349 across the 33 of their papers we have counts for
38 papers
Quantum-compatible Riemannian conjugate gradient for ground-state preparation
Andres Arcia-Lopez, Marek Gluza, Yudai Suzuki +1
Riemannian optimization provides a natural geometric framework for designing quantum algorithms for ground-state preparation, most notably through quantum imaginary-time evolution.…
Optimization over covariance matrices with a parameterized metric
Yibang Li, Bamdev Mishra, Pratik Jawanpuria +1
The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices. Euclidean, Bures-Wasserstein and affine-invariant me…
Universality of kernels on Riemannian symmetric spaces
Salem Said, Nathaël Da Costa, Franziskus Steinert +1
We investigate universality properties of continuous, positive-definite invariant kernels on Riemannian symmetric spaces, providing a unified harmonic-analytic characterization acr…
Wrench-Based Bayesian Pose Estimation via Matrix--Fisher Gaussian Inference
Jianyu Chen, Lin Yang, Yibang Li +2
In this paper, a residual-safeguarded local Matrix Fisher--Gaussian (MFG) inference method is developed for wrench-based pose estimation on . The…
Horospherical Depth and Busemann Median on Hadamard Manifolds
Yangdi Jiang, Xiaotian Chang, Cyrus Mostajeran
\We introduce the horospherical depth, an intrinsic notion of statistical depth on Hadamard manifolds, and define the Busemann median as the set of its maximizers. The construction…
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…
Geometric Renyi Differential Privacy: Ricci Curvature Characterized by Heat Diffusion Mechanisms
Xiaotian Chang, Yangdi Jiang, Cyrus Mostajeran +1
In this paper, we develop a novel privacy mechanism for Riemannian manifold-valued data. Our key contribution lies in uncovering unexpected connections among geometric analysis, he…
Min-Max Grassmannian Optimization for Online Subspace Tracking
Shreyas Bharadwaj, Bamdev Mishra, Cyrus Mostajeran +3
We propose GeRoST (Geometrically Robust Subspace Tracking), an online subspace tracking algorithm that models uncertainty in a subspace using a Grassmannian ball. We derive an exac…
Geometrically robust least squares through manifold optimization
Jeremy Coulson, Alberto Padoan, Cyrus Mostajeran
This paper presents a methodology for solving a geometrically robust least squares problem, which arises in various applications where the model is subject to geometric constraints…
Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach
Shreyas Bharadwaj, Bamdev Mishra, Cyrus Mostajeran +3
The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturb…
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…
Geometric statistics with subspace structure preservation for SPD matrices
Cyrus Mostajeran, Nathaël Da Costa, Graham Van Goffrier +1
We present a geometric framework for the processing of SPD-valued data that preserves subspace structures and is based on the efficient computation of extreme generalized eigenvalu…
Programming evolution of geometry in shape-morphing sheets via spatiotemporal activation
Daniel Duffy, Itay Griniasty, John Biggins +1
Shape-programmed sheets morph from one surface into another upon activation by stimuli such as illumination, and have attracted much interest for their potential engineering applic…
Invariant kernels on the space of complex covariance matrices
Salem Said, Franziskus Steinert, Cyrus Mostajeran
The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{…
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…
Determinantal expressions of certain integrals on symmetric spaces
Salem Said, Cyrus Mostajeran
The integral of a function defined on a symmetric space may be expressed in the form of a determinant (or Pfaffian), when is -invariant and, in a certain…
Differential geometry with extreme eigenvalues in the positive semidefinite cone
Cyrus Mostajeran, Nathaël Da Costa, Graham Van Goffrier +1
Differential geometric approaches to the analysis and processing of data in the form of symmetric positive definite (SPD) matrices have had notable successful applications to numer…
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…
Discontinuous metric programming in liquid crystalline elastomers
Tayler S. Hebner, Riley G. A. Bowman, Daniel Duffy +6
Liquid crystalline elastomers (LCEs) are shape-changing materials that exhibit large deformations in response to applied stimuli. Local control of the orientation of LCEs spatially…
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…
Affine-Invariant Midrange Statistics
Cyrus Mostajeran, Christian Grussler, Rodolphe Sepulchre
We formulate and discuss the affine-invariant matrix midrange problem on the cone of positive definite Hermitian matrices , which is based on the Thompso…
Riemannian statistics meets random matrix theory: towards learning from high-dimensional covariance matrices
Salem Said, Simon Heuveline, Cyrus Mostajeran
Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of…
Node-wise monotone barrier coupling law for formation control
Jin Gyu Lee, Cyrus Mostajeran, Graham Van Goffrier
We study a node-wise monotone barrier coupling law, motivated by the synaptic coupling of neural central pattern generators. It is illustrated that this coupling imitates the desir…