Related papers: Simultaneous diagonalization: the asymmetric, low-…

A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…

Deep learning has revolutionized neuroimage analysis by delivering unprecedented speed and accuracy. However, the narrow scope of many training datasets constrains model robustness and generalizability. This challenge is particularly acute…

In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications -- the singular value decomposition…

We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in Exact Diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of…

Deep metric learning maps visually similar images onto nearby locations and visually dissimilar images apart from each other in an embedding manifold. The learning process is mainly based on the supplied image negative and positive training…

We propose a categorical semantics for machine learning algorithms in terms of lenses, parametric maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of…

We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…

Distributed Computation has been a recent trend in engineering research. Parallel Computation is widely used in different areas of Data Mining, Image Processing, Simulating Models, Aerodynamics and so forth. One of the major usage of…

We provide an overview of high dimensional dynamical systems driven by random matrices, focusing on applications to simple models of learning and generalization in machine learning theory. Using both cavity method arguments and path…

Harnessing parallelism in seemingly sequential models is a central challenge for modern machine learning. Several approaches have been proposed for evaluating sequential processes in parallel using iterative fixed-point methods, like…

Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…

Several key questions remain unanswered regarding overparameterized learning models. It is unclear how (stochastic) gradient descent finds solutions that generalize well, and in particular the role of small random initializations. Matrix…

In this article, we focus on extending the notion of lattice linearity to self-stabilizing programs. Lattice linearity allows a node to execute its actions with old information about the state of other nodes and still preserve correctness.…

Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…

Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD)…

Following the success of deep learning in a wide range of applications, neural network-based machine learning techniques have received interest as a means of accelerating magnetic resonance imaging (MRI). A number of ideas inspired by deep…

This paper presents a general method for applying hierarchical matrix skeletonization factorizations to the numerical solution of boundary integral equations with possibly rank-deficient integral operators. Rank-deficient operators arise in…

Shared resource interference is observed by applications as dynamic performance asymmetry. Prior art has developed approaches to reduce the impact of performance asymmetry mainly at the operating system and architectural levels. In this…

Approximate Simultaneous Diagonalization (ASD) is a problem to find a common similarity transformation which approximately diagonalizes a given square-matrix tuple. Many data science problems have been reduced into ASD through ingenious…

Hybrid parallelism techniques are essential for efficiently training large language models (LLMs). Nevertheless, current automatic parallel planning frameworks often overlook the simultaneous consideration of node heterogeneity and dynamic…