Related papers: LAW: A Tool for Improved Productivity with High-Pe…
Processors with large numbers of cores are becoming commonplace. In order to take advantage of the available resources in these systems, the programming paradigm has to move towards increased parallelism. However, increasing the level of…
The resurgence of machine learning has increased the demand for high-performance basic linear algebra subroutines (BLAS), which have long depended on libraries to achieve peak performance on commodity hardware. High-performance BLAS…
One of the emerging use cases of AI in law is for code simplification: streamlining, distilling, and simplifying complex statutory or regulatory language. One U.S. state has claimed to eliminate one third of its state code using AI. Yet we…
The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research…
Porting applications to new hardware or programming models is a tedious and error prone process. Every help that eases these burdens is saving developer time that can then be invested into the advancement of the application itself instead…
A major driver behind the success of modern machine learning algorithms has been their ability to process ever-larger amounts of data. As a result, the use of distributed systems in both research and production has become increasingly…
Spatial (dataflow) computer architectures can mitigate the control and performance overhead of classical von Neumann architectures such as traditional CPUs. Driven by the popularity of Machine Learning (ML) workloads, spatial devices are…
We review strategies for differentiating matrix-based computations, and derive symbolic and algorithmic update rules for differentiating expressions containing the Cholesky decomposition. We recommend new `blocked' algorithms, based on…
Matrix factorizations are among the most important building blocks of scientific computing. State-of-the-art libraries, however, are not communication-optimal, underutilizing current parallel architectures. We present novel algorithms for…
The current computer architecture has moved towards the multi/many-core structure. However, the algorithms in the current sequential dense numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multi/many-core…
Analytics tasks manipulate structured data with variants of relational algebra (RA) and quantitative data with variants of linear algebra (LA). The two computational models have overlapping expressiveness, motivating a common programming…
Laplacian matrices of graphs arise in large-scale computational applications such as semi-supervised machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits;…
Mathematical problem solving is a fundamental benchmark for assessing the reasoning capabilities of artificial intelligence and a gateway to applications in education, science, and engineering where reliable symbolic reasoning is essential.…
The new and growing field of Quantitative Dependency Syntax has emerged at the crossroads between Dependency Syntax and Quantitative Linguistics. One of the main concerns in this field is the statistical patterns of syntactic dependency…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
It is well known that the behavior of dense linear algebra algorithms is greatly influenced by factors like target architecture, underlying libraries and even problem size; because of this, the accurate prediction of their performance is a…
Loop transformations are semantics-preserving optimization techniques, widely used to maximize objectives such as parallelism. Despite decades of research, applying the optimal composition of loop transformations remains challenging due to…
We present a code modularization approach to design efficient and massively parallel cubic and linear-scaling solvers for electronic structure calculations using atomic orbitals. The modular implementation of the orbital minimization…
Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also…
Models on logarithmic lattices have recently been proposed as an alternative approach to the study of multi-scale nonlinear physics. Here, we introduce LogLatt, an efficient MATLAB library for the calculus between functions on…