相关论文: BTAS: A Library for Tropical Algebra

In this paper, we investigate the computational complexity of the knapsack problem and subset sum problem for the following tropical algebraic structures. We consider the semigroup of square matrices of size $k \times k$ with non-negative…

Basic Linear Algebra Subprograms (BLAS) play key role in high performance and scientific computing applications. Experimentally, yesteryear multicore and General Purpose Graphics Processing Units (GPGPUs) are capable of achieving up to 15…

Les unit\'{e}s graphiques (Graphic Processing Units- GPU) sont d\'{e}sormais des processeurs puissants et flexibles. Les derni\`{e}res g\'{e}n\'{e}rations de GPU contiennent des unit\'{e}s programmables de traitement des sommets (vertex…

Tangled Program Graph (TPG) is a reinforcement learning technique based on genetic programming concepts. On state-of-the-art learning environments, TPGs have been shown to offer comparable competence with Deep Neural Networks (DNNs), for a…

A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…

A tropical (or min-plus) semiring is a set $\mathbb{Z}$ (or $\mathbb{Z \cup \{\infty\}}$) endowed with two operations: $\oplus$, which is just usual minimum, and $\odot$, which is usual addition. In tropical algebra the vector $x$ is a…

Sorting and scanning are two fundamental primitives for constructing highly parallel algorithms. A number of libraries now provide implementations of these primitives for GPUs, but there is relatively little information about the…

We present an approach for integrating the time evolution of quantum systems. We leverage the computation power of graphics processing units (GPUs) to perform the integration of all time steps in parallel. The performance boost is…

Extreme value statistics is the max analogue of classical statistics, while tropical geometry is the max analogue of classical geometry. In this paper, we review recent work where insights from tropical geometry were used to develop new,…

Future computing systems, from handhelds to supercomputers, will undoubtedly be more parallel and heterogeneous than todays systems to provide more performance and energy efficiency. Thus, GPUs are increasingly being used to accelerate…

Modeling data sharing in GPU programs is a challenging task because of the massive parallelism and complex data sharing patterns provided by GPU architectures. Better GPU caching efficiency can be achieved through careful task scheduling…

The open source ALPS (Algorithms and Libraries for Physics Simulations) project provides a collection of physics libraries and applications, with a focus on simulations of lattice models and strongly correlated electron systems. The…

Basic Linear Algebra Subprograms (BLAS) and Linear Algebra Package (LAPACK) form basic building blocks for several High Performance Computing (HPC) applications and hence dictate performance of the HPC applications. Performance in such…

To address the absence of a universal standard interface for tensor operations, we introduce the Tensor Algebra Processing Primitives (TAPP), a C-based interface designed to decouple the application layer from hardware-specific…

We introduce GPflux, a Python library for Bayesian deep learning with a strong emphasis on deep Gaussian processes (DGPs). Implementing DGPs is a challenging endeavour due to the various mathematical subtleties that arise when dealing with…

We use tropical algebras as platforms for a very efficient digital signature protocol. Security relies on computational hardness of factoring one-variable tropical polynomials; this problem is known to be NP-hard.

In the last decade, developments in tropical geometry have provided a number of uses directly applicable to problems in statistical learning. The TML package is the first R package which contains a comprehensive set of tools and methods…

Within scientific and real life problems, classification is a typical case of extremely complex tasks in data-driven scenarios, especially if approached with traditional techniques. Machine Learning supervised and unsupervised paradigms,…

In this paper we study the convergence of the max-consensus protocol. Tropical algebra is used to formulate the problem. Necessary and sufficient conditions for convergence of the max-consensus protocol over fixed as well as switching…

Maximizing the performance potential of the modern day GPU architecture requires judicious utilization of available parallel resources. Although dramatic reductions can often be obtained through straightforward mappings, further performance…