Related papers: Computing Multi-Eigenpairs of High-Dimensional Eig…

An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of…

The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure…

In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…

The computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose…

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte…

Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this…

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…

In this paper, we propose a novel tensor-based Dinkelbach--Type method for computing extremal tensor generalized eigenvalues. We show that the extremal tensor generalized eigenvalue can be reformulated as a critical subproblem of the…

In this paper, we present a nonnested augmented subspace algorithm and its multilevel correction method for solving eigenvalue problems with curved interfaces. The augmented subspace algorithm and the corresponding multilevel correction…

A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then we apply the indefinite Lanczos…

The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…

Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has…

Performance optimization of deep learning models is conducted either manually or through automatic architecture search, or a combination of both. On the other hand, their performance strongly depends on the target hardware and how…

Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…

High-performance tensor programs are crucial to guarantee efficient execution of deep neural networks. However, obtaining performant tensor programs for different operators on various hardware platforms is notoriously challenging.…

Monte Carlo Search gives excellent results in multiple difficult combinatorial problems. Using a prior to perform non uniform playouts during the search improves a lot the results compared to uniform playouts. Handmade heuristics tailored…

We present a novel approach for computing a variant of eigenvector centrality for multilayer networks with inter-layer constraints on node importance. Specifically, we consider a multilayer network defined by multiple edge-weighted,…

In this work, we study the approximation of expected values of functional quantities on the solution of a stochastic differential equation (SDE), where we replace the Monte Carlo estimation with the evaluation of a deep neural network. Once…