Related papers: Rieoptax: Riemannian Optimization in JAX
Zernike polynomials serve as an orthogonal basis on the unit disc, and have proven to be effective in optics simulations, astrophysics, and more recently in plasma simulations. Unlike Bessel functions, Zernike polynomials are inherently…
Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…
We introduce geomstats, a python package that performs computations on manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive definite matrices and Lie groups of transformations. We provide efficient and extensively…
Since the popularization of the Stiefel manifold for numerical applications in 1998 in a seminal paper from Edelman et al., it has been exhibited to be a key to solve many problems from optimization, statistics and machine learning. In…
Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…
This paper exploits a basic connection between sequential quadratic programming and Riemannian gradient optimization to address the general question of selecting a metric in Riemannian optimization, in particular when the Riemannian…
This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…
We consider the proximal gradient method on Riemannian manifolds for functions that are possibly not geodesically convex. Starting from the forward-backward-splitting, we define an intrinsic variant of the proximal gradient method that uses…
This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets,…
Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…
PARyOpt is a python based implementation of the Bayesian optimization routine designed for remote and asynchronous function evaluations. Bayesian optimization is especially attractive for computational optimization due to its low cost…
Various tasks in scientific computing can be modeled as an optimization problem on the indefinite Stiefel manifold. We address this using the Riemannian approach, which basically consists of equipping the feasible set with a Riemannian…
We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement…
Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank…
Distributed, large-scale quantum computing will need architectures that combine matter-based qubits with photonic links, but today's software stacks target either gate-based chips or linear-optical devices in isolation. We introduce Optyx,…
We develop new algorithms for Riemannian bilevel optimization. We focus in particular on batch and stochastic gradient-based methods, with the explicit goal of avoiding second-order information such as Riemannian hyper-gradients. We propose…
Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational science they arise in symmetric (generalized) eigenvalue problems, in nonlinear…
This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…
A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and implementation of the sensitivities can be quite laborious and error-prone, especially for non-trivial objectives, constraints and material…
Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn…