Related papers: Wanted: Floating-Point Add Round-off Error instruc…
State-of-the-art static analysis tools for verifying finite-precision code compute worst-case absolute error bounds on numerical errors. These are, however, often not a good estimate of accuracy as they do not take into account the…
Federated Learning (FL) has attracted much interest due to the significant advantages it brings to training deep neural network (DNN) models. However, since communications and computation resources are limited, training DNN models in FL…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
Servo error pre-compensation and feedrate optimization are often performed independently to improve the accuracy and speed of manufacturing machines. However, this independent approach leads to unnecessary trade-offs between productivity…
The advent of foundation models have revolutionized various fields, enabling unprecedented task accuracy and flexibility in computational linguistics, computer vision and other domains. Attention mechanism has become an essential component…
Can we assure math computations by automatic verifying floating-point accuracy? We define fast arithmetic (based on Dekker [1971]) over twofold approximations $z\approx z_0+z_1$, such that $z_0$ is standard result and $z_1$ assesses…
Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded…
As safety-critical applications increasingly rely on data-parallel floating-point computations, there is an increasing need for flexible and configurable fault tolerance in parallel floating-point accelerators such as tensor engines. While…
To obtain accurate results in numerical computation, high-precision arithmetic is a straightforward approach. However, most processors lack hardware support for floating-point formats beyond double precision (FP64). Double-word arithmetic…
In boundary element methods (BEM) in $\mathbb{R}^3$, matrix elements and right hand sides are typically computed via analytical or numerical quadrature of the layer potential multiplied by some function over line, triangle and tetrahedral…
Quantum computers require quantum processors. An important part of the processor of any computer is the arithmetic unit, which performs binary addition, subtraction, division and multiplication, however multiplication can be performed using…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
Although quantization for linear layers has been widely used, its application to accelerate the attention process remains limited. To further enhance the efficiency of attention computation compared to SageAttention while maintaining…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
We accelerated an {\it ab-initio} QMC electronic structure calculation by using GPGPU. The bottleneck of the calculation for extended solid systems is replaced by CUDA-GPGPU subroutine kernels which build up spline basis set expansions of…
It is well known that the computation of accurate trajectories of the Lorenz system is a difficult problem. Computed solutions are very sensitive to the discretization error determined by the time step size and polynomial order of the…
This paper discusses a simple and effective method for the summation of long sequences of floating point numbers. The method comprises two phases: an accumulation phase where the mantissas of the floating point numbers are added to…
Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices which are used to represent dense data in an optimized form by applying low-rank…
The heavy burdens of computation and off-chip traffic impede deploying the large scale convolution neural network on embedded platforms. As CNN is attributed to the strong endurance to computation errors, employing block floating point…
Parameter-efficient fine-tuning (PEFT) methods have emerged as a practical solution for adapting large foundation models to downstream tasks, reducing computational and memory costs by updating only a small subset of parameters. Among them,…