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We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…

Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…

Cross-view geolocalization (CVGL) systems, while effective at retrieving a list of relevant candidates (high Recall@k), often fail to identify the single best match (low Top-1 accuracy). This work investigates the use of zero-shot…

Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…

In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive…

Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible…

Existing Zero-Shot Composed Image Retrieval (ZS-CIR) methods typically train adapters that convert reference images into pseudo-text tokens, which are concatenated with the modifying text and processed by frozen text encoders in pretrained…

Large Language Models (LLMs) are very demanding in terms of their computational resources. Low-rank decompositions of LLM weights, e.g. via Singular Value Decomposition (SVD), is a promising approach for LLM compression, but presents…

The architecture of multimodal large language models (MLLMs) commonly connects a vision encoder, often based on CLIP-ViT, to a large language model. While CLIP-ViT works well for capturing global image features, it struggles to model local…

While Large Vision-Language Models (LVLMs) have rapidly advanced in recent years, the prevalent issue known as the `hallucination' problem has emerged as a significant bottleneck, hindering their real-world deployments. Existing methods…

In this paper we develop a new Bayesian inference method for low rank matrix reconstruction. We call the new method the Relevance Singular Vector Machine (RSVM) where appropriate priors are defined on the singular vectors of the underlying…

Large pre-trained models (LPMs) have demonstrated exceptional performance in diverse natural language processing and computer vision tasks. However, fully fine-tuning these models poses substantial memory challenges, particularly in…

Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and…

Truncated singular value decomposition (SVD), also known as the best low-rank matrix approximation, has been successfully applied to many domains such as biology, healthcare, and others, where high-dimensional datasets are prevalent. To…

Recently, label consistent k-svd (LC-KSVD) algorithm has been successfully applied in image classification. The objective function of LC-KSVD is consisted of reconstruction error, classification error and discriminative sparse codes error…

For a datastream, the change over a short interval is often of low rank. For high throughput information arranged in matrix format, recomputing an optimal SVD approximation after each step is typically prohibitive. Instead, incremental and…

In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using…

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…

We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework. We show the t-SVD is a…

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…