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We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…

Computational Geometry · Computer Science 2009-09-29 M. H. van Emden , B. Moa

Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…

Numerical Analysis · Computer Science 2017-03-08 Michael Lass , Thomas D. Kühne , Christian Plessl

Deep neural networks (DNN) are powerful models for many pattern recognition tasks, yet their high computational complexity and memory requirement limit them to applications on high-performance computing platforms. In this paper, we propose…

Machine Learning · Computer Science 2018-10-24 Lukas Mauch , Bin Yang

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

Data efficiency, despite being an attractive characteristic, is often challenging to measure and optimize for in task-oriented semantic parsing; unlike exact match, it can require both model- and domain-specific setups, which have,…

Computation and Language · Computer Science 2021-07-13 Shrey Desai , Akshat Shrivastava , Justin Rill , Brian Moran , Safiyyah Saleem , Alexander Zotov , Ahmed Aly

Neural network algorithms simulated on standard computing platforms typically make use of high resolution weights, with floating-point notation. However, for dedicated hardware implementations of such algorithms, fixed-point synaptic…

Neural and Evolutionary Computing · Computer Science 2015-04-23 Lorenz K. Muller , Giacomo Indiveri

We analyze the forward error in the floating point summation of real numbers, for computations in low precision or extreme-scale problem dimensions that push the limits of the precision. We present a systematic recurrence for a martingale…

Numerical Analysis · Mathematics 2022-03-31 Eric Hallman , Ilse C. F. Ipsen

Nowadays, the number of emerging embedded systems rapidly grows in many application domains, due to recent advances in artificial intelligence and internet of things. The main inherent specification of these application-specific systems is…

Hardware Architecture · Computer Science 2024-03-26 Mohsen Faryabi , Amir Hossein Moradi

In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…

Symbolic Computation · Computer Science 2009-01-14 Jean-Guillaume Dumas , Pascal Giorgi , Clément Pernet

Continuously adapting pre-trained models to local data on resource constrained edge devices is the $\emph{last mile}$ for model deployment. However, as models increase in size and depth, backpropagation requires a large amount of memory,…

Machine Learning · Computer Science 2024-11-07 Chen Feng , Shaojie Zhuo , Xiaopeng Zhang , Ramchalam Kinattinkara Ramakrishnan , Zhaocong Yuan , Andrew Zou Li

Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less…

Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems…

Software Engineering · Computer Science 2007-05-23 Maurizio Pizzonia , Giuseppe Di Battista

With ever-increasing computational demand for deep learning, it is critical to investigate the implications of the numeric representation and precision of DNN model weights and activations on computational efficiency. In this work, we…

We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…

Machine Learning · Computer Science 2023-02-01 Eric J. Michaud , Ziming Liu , Max Tegmark

Mainstream math libraries for floating point (FP) do not produce correctly rounded results for all inputs. In contrast, CR-LIBM and RLIBM provide correctly rounded implementations for a specific FP representation with one rounding mode.…

Mathematical Software · Computer Science 2021-12-01 Jay P. Lim , Santosh Nagarakatte

Matrix multiplication is a fundamental operation in both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide it implemented in hardware. Due to the increased throughput…

Mathematical Software · Computer Science 2026-04-07 Faizan A. Khattak , Mantas Mikaitis

Unconstrained binary integer programming (UBIP) is a challenging optimization problem due to the presence of binary variables. To address the challenge, we introduce a novel class of functions named sharp-peak functions (SPFs), which…

Optimization and Control · Mathematics 2026-05-14 Shenglong Zhou , Shuai Li , Hui Zhang , Ziyan Luo

This paper presents the analysis of the impact of a floating-point number precision reduction on the quality of text classification. The precision reduction of the vectors representing the data (e.g. TF-IDF representation in our case)…

Computation and Language · Computer Science 2017-06-21 Krzysztof Wróbel , Maciej Wielgosz , Marcin Pietroń , Michał Karwatowski , Aleksander Smywiński-Pohl

In this paper, we present the High Energy Physics data format, processing toolset and analysis library a4, providing fast I/O of structured data using the Google protocol buffer library. The overall goal of a4 is to provide physicists with…

Data Analysis, Statistics and Probability · Physics 2013-02-14 Johannes Ebke , Peter Waller

Numerical accuracy of floating point computation is a well studied topic which has not made its way to the end-user in scientific computing. Yet, it has become a critical issue with the recent requirements for code modernization to harness…

Mathematical Software · Computer Science 2018-11-12 Christophe Denis , Pablo De Oliveira Castro , Eric Petit