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We propose SYNCE (synchronized step correlation enhancement), a new algorithm for coupling Markov chains within multilevel Markov chain Monte Carlo (ML-MCMC) estimators. We apply this algorithm to solve Bayesian inverse problems using…

Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…

Eigenvalue problems are among the most important topics in many scientific disciplines. With the recent surge and development of machine learning, neural eigenvalue methods have attracted significant attention as a forward pass of inference…

Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…

Single image super-resolution (SISR) is a challenging ill-posed problem that aims to up-sample a given low-resolution (LR) image to a high-resolution (HR) counterpart. Due to the difficulty in obtaining real LR-HR training pairs, recent…

Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…

In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution…

We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral clustering. First, the efficiency of the Chebyshev-Davidson algorithm relies on the prior…

This paper presents an architecture-friendly k-means clustering algorithm called SIVF for a large-scale and high-dimensional sparse data set. Algorithm efficiency on time is often measured by the number of costly operations such as…

Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…

Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…

Self-consistent field theory (SCFT) is one of the most widely-used framework in studying the equilibrium phase behaviors of inhomogenous polymers. For liquid crystalline polymeric systems, the main numerical challenges of solving SCFT…

With the success of self-supervised learning (SSL), it has become a mainstream paradigm to fine-tune from self-supervised pretrained models to boost the performance on downstream tasks. However, we find that current SSL models suffer severe…

In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the relaxed filtered Krylov subspace method for computing the eigenvalues with the largest real parts and the corresponding eigenvectors of non-symmetric…

Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large…

Compressed sensing (CS) is a promising tool for reducing sampling costs. Current deep neural network (NN)-based CS methods face the challenges of collecting labeled measurement-ground truth (GT) data and generalizing to real applications.…

A new numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other…

Aiming at improving performance of visual classification in a cost-effective manner, this paper proposes an incremental semi-supervised learning paradigm called Deep Co-Space (DCS). Unlike many conventional semi-supervised learning methods…

We present scalable hybrid-parallel algorithms for training large-scale 3D convolutional neural networks. Deep learning-based emerging scientific workflows often require model training with large, high-dimensional samples, which can make…

A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear…