Related papers: A robust collision source method for rank adaptive…

We study the diffusion of $N$ particles in one dimension interacting via a drift proportional to their rank. In the attractive case (self-gravitating gas) a mapping to the Lieb Liniger quantum model allows to obtain stationary time…

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally…

Weighted low-rank approximation (WLRA), a dimensionality reduction technique for data analysis, has been successfully used in several applications, such as in collaborative filtering to design recommender systems or in computer vision to…

This paper focuses on the identification of graphical autoregressive models with dynamical latent variables. The dynamical structure of latent variables is described by a matrix polynomial transfer function. Taking account of the sparse…

We present a data-adaptive method for parameter-efficient fine-tuning of large neural networks. Standard low-rank adaptation methods improve efficiency by restricting each layer update to a fixed low-rank form, but this static…

Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights, dramatically reducing trainable parameters and memory. In this work, we address the gap between training with full steps with low-rank…

A central aim in computational neuroscience is to relate the activity of large populations of neurons to an underlying dynamical system. Models of these neural dynamics should ideally be both interpretable and fit the observed data well.…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

Dynamical low-rank approximation, as has been demonstrated recently, can be extremely efficient in solving kinetic equations. However, a major deficiency is that they do not preserve the structure of the underlying physical problem. For…

We propose a new representation of visual data that disentangles object position from appearance. Our method, termed Deep Latent Particles (DLP), decomposes the visual input into low-dimensional latent ``particles'', where each particle is…

Low-Rank Factorization (LRF) is a widely adopted technique for compressing deep neural networks (DNNs). However, it faces several challenges, including optimal rank selection, a vast design space, long fine-tuning times, and limited…

Parameter-Efficient Fine-Tuning (PEFT) of text-to-image models has become an increasingly popular technique with many applications. Among the various PEFT methods, Low-Rank Adaptation (LoRA) and its variants have gained significant…

This paper proposes low tensor-train (TT) rank and low multilinear (ML) rank approximations for de-speckling and compression of 3D optical coherence tomography (OCT) images for a given compression ratio (CR). To this end, we derive the…

Training and fine-tuning large language models (LLMs) come with challenges related to memory and computational requirements due to the increasing size of the model weights and the optimizer states. Various techniques have been developed to…

The main aim of this paper is to develop a new algorithm for computing nonnegative low rank tensor approximation for nonnegative tensors that arise in many multi-dimensional imaging applications. Nonnegativity is one of the important…

MDPs with low-rank transitions -- that is, the transition matrix can be factored into the product of two matrices, left and right -- is a highly representative structure that enables tractable learning. The left matrix enables expressive…

Fluid-structure interaction models are used to study how a material interacts with different fluids at different Reynolds numbers. Examining the same model not only for different fluids but also for different solids allows to optimize the…

The Vlasov--Maxwell equations are used for the kinetic description of magnetized plasmas. As they are posed in an up to 3+3 dimensional phase space, solving this problem is extremely expensive from a computational point of view. In this…

In this letter, we propose a novel low-rank quaternion approximation (LRQA) model by directly constraining the quaternion rank prior for effectively removing the noise in color images. The LRQA model treats the color image holistically…

Deep Click-Through Rate (CTR) prediction models play an important role in modern industrial recommendation scenarios. However, high memory overhead and computational costs limit their deployment in resource-constrained environments.…