Related papers: Efficient algorithms for discrete Gabor transforms…
Data-parallel SGD is the de facto algorithm for distributed optimization, especially for large scale machine learning. Despite its merits, communication bottleneck is one of its persistent issues. Most compression schemes to alleviate this…
Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration,…
Deep generative models (DGMs) for graphs achieve impressively high expressive power thanks to very efficient and scalable neural networks. However, these networks contain non-linearities that prevent analytical computation of many standard…
The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards -- such as JPEG and HEVC -- adopt the DCT as a…
The increasing use of microfluidics in industrial, biomedical, and clinical applications requires a more and more precise control of the microfluidic flows and suspended particles or cells. This leads to higher demands in three-dimensional…
Lattice QCD calculations require significant computational effort, with the dominant fraction of resources typically spent in the numerical inversion of the Dirac operator. One of the simplest methods to solve such large and sparse linear…
Graph Transformers (GTs) have emerged as powerful architectures for graph-structured data, yet remain constrained by rigid designs and lack quantifiable interpretability. Current state-of-the-art GTs commit to fixed GNN types across all…
This paper proposes a distributed dual gradient tracking algorithm (DDGT) to solve resource allocation problems over an unbalanced network, where each node in the network holds a private cost function and computes the optimal resource by…
We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save…
Continuous-time dynamic graphs (CTDGs) are essential for modeling interconnected, evolving systems. Traditional methods for extracting knowledge from these graphs often depend on feature engineering or deep learning. Feature engineering is…
With an increasing influx of classical signal processing methodologies into the field of graph signal processing, approaches grounded in discrete linear canonical transform have found application in graph signals. In this paper, we…
We present and analyze a stochastic distributed method (S-NEAR-DGD) that can tolerate inexact computation and inaccurate information exchange to alleviate the problems of costly gradient evaluations and bandwidth-limited communication in…
Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a high computational burden. A lot of work has been done to reduce the complexity of computations used in…
The article describes a system for image recognition using deep convolutional neural networks. Modified network architecture is proposed that focuses on improving convergence and reducing training complexity. The filters in the first layer…
Discrete transforms, such as the discrete Fourier transform, are widely used in machine learning to improve model performance by extracting meaningful features. However, with numerous transforms available, selecting an appropriate one often…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…
We study lattice fermions from the viewpoint of spectral graph theory (SGT). We find that a fermion defined on a certain lattice is identified as a spectral graph. SGT helps us investigate the number of zero eigenvalues of lattice Dirac…
The discontinuous Galerkin (DG) algorithm is a representative high order method in Computational Fluid Dynamics (CFD) area which possesses considerable mathematical advantages such as high resolution, low dissipation, and dispersion.…
We present a multi-task learning formulation for Deep Gaussian processes (DGPs), through non-linear mixtures of latent processes. The latent space is composed of private processes that capture within-task information and shared processes…