5 papers
Mixed precision Newton's method for optimization
Nicolas Brisebarre, Giuseppe Carrino, Theo Mary +1
Second-order optimization methods, such as Newton's algorithm, achieve fast local convergence and high accuracy, but their practical use is often limited by high computational cost…
Multiword matrix multiplication over large finite fields in floating-point arithmetic
Jérémy Berthomieu, Stef Graillat, Dimitri Lesnoff +1
This article is concerned with the efficient computation of modular matrix multiplication C=AB mod p, a key kernel in computer algebra. We focus on floating-point arithmetic, which…
Mixed precision accumulation for neural network inference guided by componentwise forward error analysis
El-Mehdi El Arar, Silviu-Ioan Filip, Theo Mary +1
This work proposes a mathematically founded mixed precision accumulation strategy for the inference of neural networks. Our strategy is based on a new componentwise forward error a…
3D Modeling of Solar Oscillations with Hybridizable Discontinuous Galerkin Method
Florian Faucher, Ha Pham, Damien Fournier +5
With increasing quantity and quality of solar observations, it becomes essential to account for three-dimensional heterogeneities in wave modeling for seismic data interpretation.…
Frugality in second-order optimization: floating-point approximations for Newton's method
Giuseppe Carrino, Elena Loli Piccolomini, Elisa Riccietti +1
Minimizing loss functions is central to machine-learning training. Although first-order methods dominate practical applications, higher-order techniques such as Newton's method can…