Related papers: EigenKernel - A middleware for parallel generalize…

We present a mixed-precision benchmark called HPL-MxP that uses both a lower-precision LU factorization with a non-stationary iterative refinement based on GMRES. We evaluate the numerical stability of one of the methods of generating the…

Scientific communities are increasingly adopting machine learning and deep learning models in their applications to accelerate scientific insights. High performance computing systems are pushing the frontiers of performance with a rich…

The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference…

The level of abstraction at which application experts reason about linear algebra computations and the level of abstraction used by developers of high-performance numerical linear algebra libraries do not match. The former is conveniently…

Large Transformer networks are increasingly used in settings where low inference latency can improve the end-user experience and enable new applications. However, autoregressive inference is resource intensive and requires parallelism for…

Kernel matrix-vector product is ubiquitous in many science and engineering applications. However, a naive method requires $O(N^2)$ operations, which becomes prohibitive for large-scale problems. We introduce a parallel method that provably…

Today, many scientific and engineering areas require high performance computing to perform computationally intensive experiments. For example, many advances in transport phenomena, thermodynamics, material properties, computational…

Numerical models of complex real-world phenomena often necessitate High Performance Computing (HPC). Uncertainties increase problem dimensionality further and pose even greater challenges. We present a parallelization strategy for…

The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approaches that aim to maximize the classical Rayleigh quotient…

The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…

Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…

Eigenvalue interlacing is a versatile technique for deriving results in algebraic combinatorics. In particular, it has been successfully used for proving a number of results about the relation between the (adjacency matrix or Laplacian)…

Next generation computer architectures will include order of magnitude more intra-node parallelism; however, many application programmers have a difficult time keeping their codes current with the state-of-the-art machines. In this context,…

A key hurdle is demonstrating compute resource capability with limited benchmarks. We propose workflow templates as a solution, offering adaptable designs for specific scientific applications. Our paper identifies common usage patterns for…

A new neural network architecture (PSCNN) is developed to improve performance and speed of such networks. The architecture has all the advantages of the previous models such as self-organization and possesses some other superior…

Elliptic partial differential equations must be solved numerically for many problems in numerical relativity, such as initial data for every simulation of merging black holes and neutron stars. Existing elliptic solvers can take multiple…

McKernel introduces a framework to use kernel approximates in the mini-batch setting with Stochastic Gradient Descent (SGD) as an alternative to Deep Learning. Based on Random Kitchen Sinks [Rahimi and Recht 2007], we provide a C++ library…

Many important computational problems require utilization of high performance computing (HPC) systems that consist of multi-level structures combining higher and higher numbers of devices with various characteristics. Utilizing full power…

Differential evolution (DE) is an effective global evolutionary optimization algorithm using to solve global optimization problems mainly in a continuous domain. In this field, researchers pay more attention to improving the capability of…

The emerging edge computing paradigm promises to provide low latency and ubiquitous computation to numerous mobile and Internet of Things (IoT) devices at the network edge. How to efficiently allocate geographically distributed…