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As we reach the limit of Moore's Law, researchers are exploring different paradigms to achieve unprecedented performance. Approximate Computing (AC), which relies on the ability of applications to tolerate some error in the results to…

Numerical Analysis · Mathematics 2023-04-14 Garima Singh , Baidyanath Kundu , Harshitha Menon , Alexander Penev , David J. Lange , Vassil Vassilev

In recent years fused-multiply-add (FMA) units with lower-precision multiplications and higher-precision accumulation have proven useful in machine learning/artificial intelligence applications, most notably in training deep neural networks…

Mathematical Software · Computer Science 2019-04-16 Greg Henry , Ping Tak Peter Tang , Alexander Heinecke

The acceleration of deep-learning kernels in hardware relies on matrix multiplications that are executed efficiently on Systolic Arrays (SA). To effectively trade off deep-learning training/inference quality with hardware cost, SA…

Hardware Architecture · Computer Science 2023-09-11 D. Filippas , C. Peltekis , G. Dimitrakopoulos , C. Nicopoulos

Recent renewed interest in optimizing and analyzing floating-point programs has lead to a diverse array of new tools for numerical programs. These tools are often complementary, each focusing on a distinct aspect of numerical programming.…

Programming Languages · Computer Science 2018-05-08 Heiko Becker , Pavel Pancheckha , Eva Darulova , Zachary Tatlock

We review the current state of automatic differentiation (AD) for array programming in machine learning (ML), including the different approaches such as operator overloading (OO) and source transformation (ST) used for AD, graph-based…

Machine Learning · Computer Science 2019-01-04 Bart van Merriënboer , Olivier Breuleux , Arnaud Bergeron , Pascal Lamblin

In problems of mathematical physics, to study the structures of spaces using the Cayley-Klein models in theoretical calculations, the use of generalized complex numbers is required. In the case of computational experiments, such tasks…

Mathematical Software · Computer Science 2020-07-21 Migran N. Gevorkyan , Anna V. Korolkova , Dmitry S. Kulyabov

Numerical data processing is a key task across different fields of computer technology use. However, even simple summation of values is not precise due to the floating point representation use. This paper presents a practical algorithm for…

Data Structures and Algorithms · Computer Science 2022-11-09 Vaclav Skala

Mixed integer sets have a strong modeling capacity to describe practical systems. Nevertheless, incorporating a mixed integer set often renders an optimization formulation drastically more challenging to compute. In this paper, we study how…

Optimization and Control · Mathematics 2023-12-22 Wei Wang , Bo Zeng

A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and implementation of the sensitivities can be quite laborious and error-prone, especially for non-trivial objectives, constraints and material…

Mathematical Software · Computer Science 2022-01-31 Aaditya Chandrasekhar , Saketh Sridhara , Krishnan Suresh

While Deep Neural Networks (DNNs) push the state-of-the-art in many machine learning applications, they often require millions of expensive floating-point operations for each input classification. This computation overhead limits the…

Neural and Evolutionary Computing · Computer Science 2017-05-12 Hokchhay Tann , Soheil Hashemi , Iris Bahar , Sherief Reda

The Rust programming language is an attractive choice for robotics and related fields, offering highly efficient and memory-safe code. However, a key limitation preventing its broader adoption in these domains is the lack of high-quality,…

Robotics · Computer Science 2025-04-23 Chen Liang , Qian Wang , Andy Xu , Daniel Rakita

Static analysis by abstract interpretation aims at automatically proving properties of computer programs. To do this, an over-approximation of program semantics, defined as the least fixpoint of a system of semantic equations, must be…

Programming Languages · Computer Science 2013-05-02 Olivier Bouissou , Yassamine Seladji , Alexandre Chapoutot

Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…

General Mathematics · Mathematics 2019-05-27 Nicolas Behr , Giuseppe Dattoli , Ambra Lattanzi , Silvia Licciardi

Applications in the smart industry domain, such as interaction with collaborative robots using vocal commands or machine vision systems often requires the deployment of deep learning algorithms on heterogeneous low power computing…

Artificial Intelligence · Computer Science 2021-02-03 Cristina Chesta , Luca Rinelli

The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…

Numerical Analysis · Computer Science 2015-03-13 Christoph Spandl

Data-flow analyses like points-to analysis can vastly improve the precision of other analyses, and help perform powerful code optimizations. However, whole-program points-to analysis of large programs tend to be expensive - both in terms of…

Programming Languages · Computer Science 2024-09-17 Shashin Halalingaiah , Vijay Sundaresan , Daryl Maier , V. Krishna Nandivada

Artificial intelligence (AI) has rapidly evolved into a critical technology; however, electrical hardware struggles to keep pace with the exponential growth of AI models. Free space optical hardware provides alternative approaches for…

Optics · Physics 2025-10-07 Xue Dong , Kai Lion , Fei Xia , YoonSeok Baek , Ziao Wang , Niao He , Sylvain Gigan

We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher-order language with algebraic data types and we characterise it as the unique structure-preserving macro given a…

Programming Languages · Computer Science 2026-05-07 Mathieu Huot , Sam Staton , Matthijs Vákár

Voice Activity Detection (VAD) and Overlapped Speech Detection (OSD) are key pre-processing tasks for speaker diarization. In the meeting context, it is often easier to capture speech with a distant device. This consideration however leads…

Audio and Speech Processing · Electrical Eng. & Systems 2024-02-14 Théo Mariotte , Anthony Larcher , Silvio Montrésor , Jean-Hugh Thomas

This paper investigates the possibility of approximating multiple mathematical operations in latent space for expression derivation. To this end, we introduce different multi-operational representation paradigms, modelling mathematical…

Machine Learning · Computer Science 2024-04-04 Marco Valentino , Jordan Meadows , Lan Zhang , André Freitas