Related papers: Floating-floating point: a highly accurate number …

Federated learning (FL) is a distributed learning paradigm that allows several clients to learn a global model without sharing their private data. In this paper, we generalize a primal dual fixed point (PDFP) \cite{PDFP} method to federated…

Counting integer points in large convex bodies with smooth boundaries containing isolated flat points is oftentimes an intermediate case between balls (or convex bodies with smooth boundaries having everywhere positive curvature) and cubes…

Modern programmable digital signal processing relies on floating-point numbers for their ease of use. Fixed-point number formats have the potential to save resources and improve execution time, but realising this potential burdens the…

Deep learning as a means to inferencing has proliferated thanks to its versatility and ability to approach or exceed human-level accuracy. These computational models have seemingly insatiable appetites for computational resources not only…

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.…

In numeric-intensive computations, it is well known that the execution of floating-point programs is imprecise as floating-point arithmetic incurs round-off errors. Although round-off errors are small for a single floating-point operation,…

The study on the expressive power of transformers shows that transformers are permutation equivariant, and they can approximate all permutation-equivariant continuous functions on a compact domain. However, these results are derived under…

Achieving high code coverage is essential in testing, which gives us confidence in code quality. Testing floating-point code usually requires painstaking efforts in handling floating-point constraints, e.g., in symbolic execution. This…

The posit number system is arguably the most promising and discussed topic in Arithmetic nowadays. The recent breakthroughs claimed by the format proposed by John L. Gustafson have put posits in the spotlight. In this work, we first…

Floating-point arithmetic plays a central role in science, engineering, and finance by enabling developers to approximate real arithmetic. To address numerical issues in large floating-point applications, developers must identify root…

Thanks to the computational power of modern cluster machines, numerical simulations can provide, with an unprecedented level of details, new insights into fluid mechanics. However, taking full advantage of this hardware remains challenging…

The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known…

Floating-point non-associativity makes fundamental deep learning operations, such as matrix multiplication (matmul) on GPUs, inherently non-deterministic. Despite this, the statistical structure of the resulting numerical error remains…

The upcoming IEEE-P3109 standard for low-precision floating-point arithmetic can become the foundation of future machine learning hardware and software. Unlike IEEE-754, P3109 introduces a parametric framework defined by bitwidth,…

We propose a federated methodology to learn low-dimensional representations from a dataset that is distributed among several clients. In particular, we move away from the commonly-used cross-entropy loss in federated learning, and seek to…

Fluid dynamics simulations with the lattice Boltzmann method (LBM) are very memory-intensive. Alongside reduction in memory footprint, significant performance benefits can be achieved by using FP32 (single) precision compared to FP64…

Neural networks have been criticized for their lack of easy interpretation, which undermines confidence in their use for important applications. Here, we introduce a novel technique, interpreting a trained neural network by investigating…

Finite-precision arithmetic computations face an inherent tradeoff between accuracy and efficiency. The points in this tradeoff space are determined, among other factors, by different data types but also evaluation orders. To put it simply,…

Researchers have developed neural network verification algorithms motivated by the need to characterize the robustness of deep neural networks. The verifiers aspire to answer whether a neural network guarantees certain properties with…

Debugging accumulation of floating-point errors is hard; ideally, computer should track it automatically. Here we consider twofold approximation of an exact real with value + error pair of floating-point numbers. Normally, value + error sum…