Related papers: A low-rank method for time-dependent transport cal…
The primary challenge in solving kinetic equations, such as the Vlasov equation, is the high-dimensional phase space. In this context, dynamical low-rank approximations have emerged as a promising way to reduce the high computational cost…
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…
Dose calculations in proton therapy require the fast and accurate solution of a high-dimensional transport equation for a large number of (pencil) beams with different energies and directions. Deterministically solving this transport…
Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. The main challenge of such computations is the high memory effort of classical solvers, which limits the accuracy of chosen discretizations.…
Low-rank pre-training and fine-tuning have recently emerged as promising techniques for reducing the computational and storage costs of large neural networks. Training low-rank parameterizations typically relies on conventional optimizers…
Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the…
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
We present an adaptation of two recent low-rank approximation technique proposed for first-order model reduction systems to the second-order systems. The resulting reduced order models are guaranteed to keep the second order structure which…
Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
The paper contains several theoretical results related to the weighted nonlinear least-squares problem for low-rank signal estimation, which can be considered as a Hankel structured low-rank approximation problem. A parameterization of the…
Kinetic equations are difficult to solve numerically due to their high dimensionality. A promising approach for reducing computational cost is the dynamical low-rank algorithm, which decouples the dimensions of the phase space by proposing…
We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a…
In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we establish a convergence theorem on manifolds for…
To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a…
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation.…