相关论文: Collect, Commit, Expand: Efficient CPQR-Based Colu…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
Certain classes of CUR algorithms, also referred to as cross or pseudoskeleton algorithms, are widely used for low-rank matrix approximation when direct access to all matrix entries is costly. Their key advantage lies in constructing a…
In this work, we develop a fast hierarchical solver for solving large, sparse least squares problems. We build upon the algorithm, spaQR (sparsified QR), that was developed by the authors to solve large sparse linear systems. Our algorithm…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
QR factorisation plays an important role in matrix computations. Within the context of optimisation and of automatic differentiation of such computations, we need to compute the derivative of this factorisation. For tall matrices, however,…
Compactness in deep learning can be critical to a model's viability in low-resource applications, and a common approach to extreme model compression is quantization. We consider Iterative Product Quantization (iPQ) with Quant-Noise to be…
Parameter quantization for Large Language Models (LLMs) has attracted increasing attentions recently in reducing memory costs and improving computational efficiency. Early approaches have been widely adopted. However, the existing methods…
CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for…
We present two new algorithms for Householder QR factorization of Block Low-Rank (BLR) matrices: one that performs block-column-wise QR, and another that is based on tiled QR. We show how the block-column-wise algorithm exploits BLR…
This paper describes a new QR factorization algorithm which is especially designed for massively parallel platforms combining parallel distributed multi-core nodes. These platforms make the present and the foreseeable future of…
The selection of most informative and discriminative features from high-dimensional data has been noticed as an important topic in machine learning and data engineering. Using matrix factorization-based techniques such as nonnegative matrix…
Matrix completion and approximation are popular tools to capture a user's preferences for recommendation and to approximate missing data. Instead of using low-rank factorization we take a drastically different approach, based on the simple…
In this note we describe two modifications of the ScaLAPACK subroutines PxGEQPF for computing the QR factorization with the Businger-Golub column pivoting. First, we resolve a subtle numerical instability in the same way as we have done it…
Query reformulation is a well-known problem in Information Retrieval (IR) aimed at enhancing single search successful completion rate by automatically modifying user's input query. Recent methods leverage Large Language Models (LLMs) to…
Quantum computing has become a promising computing approach because of its capability to solve certain problems, exponentially faster than classical computers. A $n$-qubit quantum system is capable of providing $2^{n}$ computational space…
Recent advances in large language model (LLM) pretraining have led to high-quality LLMs with impressive abilities. By compressing such LLMs via quantization to 3-4 bits per parameter, they can fit into memory-limited devices such as laptops…
Coded computation techniques provide robustness against straggling workers in distributed computing. However, most of the existing schemes require exact provisioning of the straggling behaviour and ignore the computations carried out by…
Near-term quantum machine learning must balance expressivity, optimization, and hardware constraints. We study quantum re-uploading units (QRUs) as compact circuits and compare them, at matched parameter count, to a standard mono-encoded…
Gibbs sampling from continuous real-valued functions is a challenging problem of interest in machine learning. Here we leverage quantum Fourier transforms to build a quantum algorithm for this task when the function is periodic. We use the…
While uniform sampling has been widely studied in the matrix completion literature, CUR sampling approximates a low-rank matrix via row and column samples. Unfortunately, both sampling models lack flexibility for various circumstances in…