Related papers: Preconditioning via Randomized Range Deflation (Ra…
Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices are efficient, but in our tests the algorithms have…
Recent advancements in deep learning-based image compression are notable. However, prevalent schemes that employ a serial context-adaptive entropy model to enhance rate-distortion (R-D) performance are markedly slow. Furthermore, the…
In this study, we propose a novel deep learning-based method to predict an optimized structure for a given boundary condition and optimization setting without using any iterative scheme. For this purpose, first, using open-source topology…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a…
We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…
This paper introduces a novel method of Progressive Low Rank Decomposition (PLRD) tailored for the compression of large language models. Our approach leverages a pre-trained model, which is then incrementally decompressed to smaller sizes…
Strong correlations between explanatory variables are problematic for high-dimensional regularized regression methods. Due to the violation of the Irrepresentable Condition, the popular LASSO method may suffer from false inclusions of…
We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the…
Guessing random additive noise decoding (GRAND) is a noise-centric decoding method, which is suitable for ultra-reliable low-latency communications, as it supports high-rate error correction codes that generate short-length codewords. GRAND…
Guessing Random Additive Noise Decoding (GRAND) is a family of universal decoding algorithms suitable for decoding any moderate redundancy code of any length. We establish that, through the use of list decoding, soft-input variants of GRAND…
Modern applications are driving demand for ultra-reliable low-latency communications, rekindling interest in the performance of short, high-rate error correcting codes. To that end, here we introduce a soft-detection variant of Guessing…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
Latent traversal is a popular approach to visualize the disentangled latent representations. Given a bunch of variations in a single unit of the latent representation, it is expected that there is a change in a single factor of variation of…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…
Low Rank Decomposition of matrix - splitting a large matrix into a product of two smaller matrix offers a means for compression that reduces the parameters of a model without sparsification, and hence delivering more speedup on modern…
Sampling methods, as important inference and learning techniques, are typically designed for unconstrained domains. However, constraints are ubiquitous in machine learning problems, such as those on safety, fairness, robustness, and many…
This paper introduces the Nystr\"om PCG algorithm for solving a symmetric positive-definite linear system. The algorithm applies the randomized Nystr\"om method to form a low-rank approximation of the matrix, which leads to an efficient…