Related papers: Tensor calculus with open-source software: the Sag…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
We present the PSALTer software for efficiently computing the mass and energy of the particle spectrum for any (e.g. higher-rank) tensor field theory in the Wolfram Language. The user must provide a Lagrangian density which is expanded…
Manifold Learning is a class of algorithms seeking a low-dimensional non-linear representation of high-dimensional data. Thus manifold learning algorithms are, at least in theory, most applicable to high-dimensional data and sample sizes to…
Tensor algebra finds applications in various domains, and these applications, especially when accelerated on spatial hardware accelerators, can deliver high performance and low power. Spatial hardware accelerator exhibits complex design…
Trusted execution environments (TEEs) are being used in all the devices from embedded sensors to cloud servers and encompass a range of cost, power constraints, and security threat model choices. On the other hand, each of the current…
Yggdrasil Decision Forests is a library for the training, serving and interpretation of decision forest models, targeted both at research and production work, implemented in C++, and available in C++, command line interface, Python (under…
We argue for more widespread use of manifold-like polyfolds (M-polyfolds) as differential geometric objects. M-polyfolds possess a distinct advantage over differentiable manifolds, enabling a smooth and local change of dimension. To…
This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. We briefly overview the current state of tensor computations…
We present the tensor computer algebra package xTras, which provides functions and methods frequently needed when doing (classical) field theory. Amongst others, it can compute contractions, make Ans\"atze, and solve tensorial equations. It…
Classical functional calculus is primarily spectral, capturing eigenvalue information through resolvent methods while largely ignoring nilpotent structure. Building on the projector-nilpotent characterization developed in our companion…
Tensor networks are factorizations of high-dimensional tensors into networks of smaller tensors. They have applications in physics and mathematics, and recently have been proposed as promising machine learning architectures. To ease the…
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…
Genetic Programming (GP) is known to suffer from the burden of being computationally expensive by design. While, over the years, many techniques have been developed to mitigate this issue, data vectorization, in particular, is arguably…
The KeOps library provides a fast and memory-efficient GPU support for tensors whose entries are given by a mathematical formula, such as kernel and distance matrices. KeOps alleviates the major bottleneck of tensor-centric libraries for…
In this study, we present a new module built for users interested in a programming language similar to BUGS to fit a Bayesian model based on the piecewise exponential (PE) distribution. The module is an extension to the open-source program…
Any cutting-edge scientific research project requires a myriad of computational tools for data generation, management, analysis and visualization. Python is a flexible and extensible scientific programming platform that offered the perfect…
Distributed, large-scale quantum computing will need architectures that combine matter-based qubits with photonic links, but today's software stacks target either gate-based chips or linear-optical devices in isolation. We introduce Optyx,…
Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…
We introduce a learning-based framework to optimize tensor programs for deep learning workloads. Efficient implementations of tensor operators, such as matrix multiplication and high dimensional convolution, are key enablers of effective…
Spreadsheet engineering adapts the lessons of software engineering to spreadsheets, providing eight principles as a framework for organizing spreadsheet programming recommendations. Spreadsheets raise issues inadequately addressed by…