Related papers: Compression of animated 3D models using HO-SVD
Singular Value Decomposition (SVD) has become an important technique for reducing the computational burden of Vision Language Models (VLMs), which play a central role in tasks such as image captioning and visual question answering. Although…
The higher-order generalized singular value decomposition (HO-GSVD) is a matrix factorization technique that extends the GSVD to $N \ge 2$ data matrices, and can be used to identify shared subspaces in multiple large-scale datasets with…
Under certain conditions, an element of a tensor product space can be identified with a compact operator and the singular value decomposition (SVD) applies to the latter. These conditions are not fulfilled in Sobolev spaces. In the previous…
First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon (e-ph) interactions being a prime example. However, these techniques use large matrices encoding the…
Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…
In the era of big data, effectively compressing large datasets while performing complex mathematical operations is crucial. Tensor-based decomposition methods have shown superior compression capabilities with minimal loss of accuracy…
This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…
We study neural image compression based on the Sparse Visual Representation (SVR), where images are embedded into a discrete latent space spanned by learned visual codebooks. By sharing codebooks with the decoder, the encoder transfers…
The pursuit of higher compression efficiency continuously drives the advances of video coding technologies. Fundamentally, we wish to find better "predictions" or "priors" that are reconstructed previously to remove the signal dependency…
This paper considers a way of generalizing the t-SVD of third-order tensors (regarded as tubal matrices) to tensors of arbitrary order N (which can be similarly regarded as tubal tensors of order (N-1)). \color{black}Such a generalization…
The tensor Singular Value Decomposition (t-SVD) for third order tensors that was proposed by Kilmer and Martin~\cite{2011kilmer} has been applied successfully in many fields, such as computed tomography, facial recognition, and video…
Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and…
Variational Autoencoder (VAE), compressing videos into latent representations, is a crucial preceding component of Latent Video Diffusion Models (LVDMs). With the same reconstruction quality, the more sufficient the VAE's compression for…
We devise and evaluate numerically a Hybrid High-Order (HHO) method for incremental associative plasticity with small deformations. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton,…
The Nystr\"{o}m method is routinely used for out-of-sample extension of kernel matrices. We describe how this method can be applied to find the singular value decomposition (SVD) of general matrices and the eigenvalue decomposition (EVD) of…
This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD).…
Tensor decompositions are powerful tools for analyzing multi-dimensional data in their original format. Besides tensor decompositions like Tucker and CP, Tensor SVD (t-SVD) which is based on the t-product of tensors is another extension of…
The deployment of Large Language Models is constrained by the memory and bandwidth demands of static weights and dynamic Key-Value cache. SVD-based compression provides a hardware-friendly solution to reduce these costs. However, existing…
Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…
We propose a compression based continual task learning method that can dynamically grow a neural network. Inspired from the recent model compression techniques, we employ compression-aware training and perform low-rank weight approximations…