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Artificial Neural Networks (ANNs) are prevalent machine learning models that are applied across various real-world classification tasks. However, training ANNs is time-consuming and the resulting models take a lot of memory to deploy. In…

Two program packages are presented for evaluating one-loop amplitudes. They can work either in dimensional regularization or in constrained differential renormalization. The latter method is found at the one-loop level to be equivalent to…

Randomized Numerical Linear Algebra (RandNLA) is a powerful class of methods, widely used in High Performance Computing (HPC). RandNLA provides approximate solutions to linear algebra functions applied to large signals, at reduced…

PixelCNNs are a recently proposed class of powerful generative models with tractable likelihood. Here we discuss our implementation of PixelCNNs which we make available at https://github.com/openai/pixel-cnn. Our implementation contains a…

We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The…

We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to…

We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the…

In this paper the C++ version of FIRE is presented - a powerful program performing Feynman integral reduction to master integrals. All previous versions used only Wolfram Mathematica, the current version mostly uses Wolfram Mathematica as a…

The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…

Generalized log-sine functions appear in higher order epsilon-expansion of different Feynman diagrams. We present an algorithm for numerical evaluation of these functions of real argument. This algorithm is implemented as C++ library with…

Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines learning methods on solver heuristics has shown potential to overcome this issue allowing for applications…

The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in…

This paper presents alpaqa, an open-source C++ implementation of an augmented Lagrangian method for nonconvex constrained numerical optimization, using the first-order PANOC algorithm as inner solver. The implementation is packaged as an…

Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…

In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…

We report on recent progress in numerical evaluation of one loop tensor integrals. A public C++ package PJFry implementing algorithms from arXiv:1009.4436 and its extension to hexagons up to rank 6 are presented.

In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method…

We present a suite of packages in R, Python, Julia, and C++ that efficiently solve the Sorted L-One Penalized Estimation (SLOPE) problem. The packages feature a highly efficient hybrid coordinate descent algorithm that fits generalized…

We discuss an algorithm for the numerical evaluation of NLO multiparton processes. We focus hereby on the virtual part of the NLO calculation, i.e. on evaluating the one-loop integration numerically. We employ and extend the ideas of the…

High-fidelity binaural audio synthesis is crucial for immersive listening, but existing methods require extensive computational resources, limiting their edge-device application. To address this, we propose the Lightweight Implicit Neural…