Related papers: f4ncgb: High Performance Gr\"obner Basis Computati…
This is a brief introduction to the world of Noncommutative Algebra aimed at advanced undergraduate and beginning graduate students.
Gaussian process (GP) inference in Python is dominated by libraries such as GPyTorch and GPflow, which are built on deep-learning frameworks and inherit their dispatch overhead and dependency footprint. We present LightGP, a dependency-free…
Interval computation is widely used to certify computations that use floating point operations to avoid pitfalls related to rounding error introduced by inaccurate operations. Despite its popularity and practical benefits, support for…
In this paper, we start the investigation of a new natural approach to "unifying" noncommutative gauge field theories (NCGFT) based on approximately finite-dimensional ($AF$) $C^*$-algebras. The defining inductive sequence of an $AF$…
A major challenge in the deployment of scientific software solutions is the adaptation of research prototypes to production-grade code. While high-level languages like MATLAB are useful for rapid prototyping, they lack the resource…
We introduce a GUI fronted program that can compute combinatorial properties and topological invariants of recognisable and primitive symbolic substitutions on finite alphabets and their associated tiling spaces. We introduce theory from…
Graphic Processing Units (GPUs) have become ubiquitous in scientific computing. However, writing efficient GPU kernels can be challenging due to the need for careful code tuning. To automatically explore the kernel optimization space,…
This paper has a practical aim. For a long time, implementations of pseudorandom number generators in standard libraries of programming languages had poor quality. The situation started to improve only recently. Up to now, a large number of…
In this paper we briefly discuss \Rings --- an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gr\"obner bases are implemented with the use of modern asymptotically fast…
The paper presents a parallel math library, dMath, that demonstrates leading scaling when using intranode, internode, and hybrid-parallelism for deep learning (DL). dMath provides easy-to-use distributed primitives and a variety of…
This paper describes Nancy, a Network Calculus (NC) library that allows users to perform complex min-plus and max-plus algebra operations efficiently. To the best of our knowledge, Nancy is the only open-source library that implements…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
As the interest to Graph Neural Networks (GNNs) is growing, the importance of benchmarking and performance characterization studies of GNNs is increasing. So far, we have seen many studies that investigate and present the performance and…
We consider $\G$-graded commutative algebras, where $\G$ is an abelian group. Starting from a remarkable example of the classical algebra of quaternions and, more generally, an arbitrary Clifford algebra, we develop a general viewpoint on…
As optimization challenges continue to evolve, so too must our tools and understanding. To effectively assess, validate, and compare optimization algorithms, it is crucial to use a benchmark test suite that encompasses a diverse range of…
Recent studies have shown that Binary Graph Neural Networks (GNNs) are promising for saving computations of GNNs through binarized tensors. Prior work, however, mainly focused on algorithm designs or training techniques, leaving it open to…
Graph Neural Networks (GNNs) are based on repeated aggregations of information across nodes' neighbors in a graph. However, because common neighbors are shared between different nodes, this leads to repeated and inefficient computations. We…
Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a…
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in…
Driven by the powerful representation ability of Graph Neural Networks (GNNs), plentiful GNN models have been widely deployed in many real-world applications. Nevertheless, due to distribution disparities between different demographic…