相关论文: Spectral Ergodicity in Deep Learning Architectures…

When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different…

Orthogonal group synchronization aims to recover orthogonal group elements from their noisy pairwise measurements. It has found numerous applications including computer vision, imaging science, and community detection. Due to the orthogonal…

Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…

In synchronization problems, the goal is to estimate elements of a group from noisy measurements of their ratios. A popular estimation method for synchronization is the spectral method. It extracts the group elements from eigenvectors of a…

In this work, we study some statistical properties of the extreme eigenstates of the randomly-weighted adjacency matrices of random graphs. We focus on two random graph models: Erd\H{o}s-R\'{e}nyi (ER) graphs and random geometric graphs…

Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…

Deep neural network ensembles hold the potential of improving generalization performance for complex learning tasks. This paper presents formal analysis and empirical evaluation to show that heterogeneous deep ensembles with high ensemble…

We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization. Our self-supervised models adapt to input operators using coarse spectral…

A probabilistic approach of computing geometric rate of convergence of stochastic processes is introduced in this paper. The goal is to quantitatively compute both upper and lower bounds of the exponential rate of convergence to the…

While symmetry has been exploited to analyze synchronization patterns in complex networks, the identification of symmetries in large-size network remains as a challenge. We present in the present work a new method, namely the method of…

Purpose:To develop a method that enhances the accuracy of spectral analysis in the presence of static magnetic field B0 inhomogeneity. Methods:The authors proposed a new spectral analysis method utilizing a deep learning model trained on…

Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…

Learning similarity functions between image pairs with deep neural networks yields highly correlated activations of embeddings. In this work, we show how to improve the robustness of such embeddings by exploiting the independence within…

Exponential random graph models, or ERGMs, are a flexible and general class of models for modeling dependent data. While the early literature has shown them to be powerful in capturing many network features of interest, recent work…

Scientists at the Berkeley SETI Research Center are Searching for Extraterrestrial Intelligence (SETI) by a new signal detection method that converts radio signals into spectrograms through Fourier transforms and classifies signals…

While several feature embedding models have been developed in the literature, comparisons of these embeddings have largely focused on their numerical performance in classification-related downstream applications. However, an interpretable…

We consider the uniform approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix by that of a smaller counterpart obtained through projections. The projection subspaces are constructed iteratively by means of…

The Intelligent Fault Diagnosis of rotating machinery currently proposes some captivating challenges. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open…

We compute exact asymptotic of the statistical density of random matrices belonging to invariant random matrices ensemble (RMT) orthogonal, unitary and symplectic ensembles, where all its eigenvalues lie within the interval $[\sigma,…

Ensembles of neural networks achieve superior performance compared to stand-alone networks in terms of accuracy, uncertainty calibration and robustness to dataset shift. \emph{Deep ensembles}, a state-of-the-art method for uncertainty…