Related papers: BTAS: A Library for Tropical Algebra
Tropical circuits are circuits with Min and Plus, or Max and Plus operations as gates. Their importance stems from their intimate relation to dynamic programming algorithms. The power of tropical circuits lies somewhere between that of…
Choosing an appropriate programming paradigm for high-performance computing on low-power devices can be useful to speed up calculations. Many Android devices have an integrated GPU and - although not officially supported - the OpenCL…
Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input. The Fundamental Theorem of…
Matlab is very widely used in scientific computing, but Matlab computational efficiency is lower than C language program. In order to improve the computing speed, some toolbox can use GPU to accelerate the computation. This paper describes…
The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…
Spatial computing architectures pose an attractive alternative to mitigate control and data movement overheads typical of load-store architectures. In practice, these devices are rarely considered in the HPC community due to the steep…
Large-scale Bundle Adjustment (BA) requires massive memory and computation resources which are difficult to be fulfilled by existing BA libraries. In this paper, we propose MegBA, a GPU-based distributed BA library. MegBA can provide…
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral…
Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties…
We introduce a tropical version of the Fukaya algebra of a Lagrangian submanifold. Tropical graphs arise as large-scale behavior of pseudoholomorphic disks under a multiple cut operation on a symplectic manifold that produces a collection…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
Can algebraic geometry enhance the sharpness, robustness, and interpretability of modern neural reasoning models by equipping them with a mathematically grounded inductive bias? To answer this, we introduce Tropical Attention, an attention…
A universal analytic Gr{\"o}bner basis (UAGB) of an ideal of a Tate algebra is a set containing a local Gr{\"o}bner basis for all suitable convergence radii. In a previous article, the authors proved the existence of finite UAGB's for…
Learning an algorithm from examples is a fundamental problem that has been widely studied. Recently it has been addressed using neural networks, in particular by Neural Turing Machines (NTMs). These are fully differentiable computers that…
Using GPUs as general-purpose processors has revolutionized parallel computing by offering, for a large and growing set of algorithms, massive data-parallelization on desktop machines. An obstacle to widespread adoption, however, is the…
This work presents a heterogeneous communication library for clusters of processors and FPGAs. This library, Shoal, supports the Partitioned Global Address Space (PGAS) memory model for applications. PGAS is a shared memory model for…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
In the world of linear algebra computation, a well-established standard exists called BLAS(Basic Linear Algebra Subprograms). This standard has been crucial for the development of software using linear algebra operations. Its benefits…
Dense linear algebra libraries, such as BLAS and LAPACK, provide a relevant collection of numerical tools for many scientific and engineering applications. While there exist high performance implementations of the BLAS (and LAPACK)…
The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central…