Related papers: Cubic NK-SVD: An Algorithm for Designing Parametri…

Randomized methods, such as the randomized SVD (singular value decomposition) and Nystr\"om approximation, are an effective way to compute low-rank approximations of large matrices. Motivated by applications to operator learning, Boull\'e…

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…

In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for…

The massive size of modern neural networks has motivated substantial recent interest in neural network quantization. We introduce Stochastic Markov Gradient Descent (SMGD), a discrete optimization method applicable to training quantized…

Anomaly detection is a critical problem in data analysis and pattern recognition, finding applications in various domains. We introduce quantum support vector data description (QSVDD), an unsupervised learning algorithm designed for anomaly…

A new variational mode decomposition (VMD) based deep learning approach is proposed in this paper for time series forecasting problem. Firstly, VMD is adopted to decompose the original time series into several sub-signals. Then, a…

We present two new remarkably simple stochastic second-order methods for minimizing the average of a very large number of sufficiently smooth and strongly convex functions. The first is a stochastic variant of Newton's method (SN), and the…

As the size and complexity of models and datasets grow, so does the need for communication-efficient variants of stochastic gradient descent that can be deployed to perform parallel model training. One popular communication-compression…

As the size and complexity of models and datasets grow, so does the need for communication-efficient variants of stochastic gradient descent that can be deployed to perform parallel model training. One popular communication-compression…

We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…

An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…

We present a simple yet novel parameterized form of linear mapping to achieves remarkable network compression performance: a pseudo SVD called Ternary SVD (TSVD). Unlike vanilla SVD, TSVD limits the $U$ and $V$ matrices in SVD to ternary…

Very deep convolutional neural networks (CNNs) have been firmly established as the primary methods for many computer vision tasks. However, most state-of-the-art CNNs are large, which results in high inference latency. Recently, depth-wise…

Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has…

We develop a scalable algorithmic framework for sparse convex quantile regression (SCQR), addressing key computational challenges in the literature. Enhancing the classical CQR model, we introduce L2-norm regularization and an…

Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on…

To address the communication bottleneck challenge in distributed learning, our work introduces a novel two-stage quantization strategy designed to enhance the communication efficiency of distributed Stochastic Gradient Descent (SGD). The…

This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel…

Although deep learning (DL) methods are powerful for solving inverse problems, their reliance on high-quality training data is a major hurdle. This is significant in high-dimensional (dynamic/volumetric) magnetic resonance imaging (MRI),…

The Key-Value (KV) cache is central to the efficiency of transformer-based large language models (LLMs), storing previously computed vectors to accelerate inference. Yet, as sequence length and batch size grow, the cache becomes a major…