arXiv subjects

Agathe Herrou

Publications and source records attributed to Agathe Herrou.

3 recordsLinked to original sources

arXiv2024

Towards Fixed-Point Formats Determination for Faust Programs

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 programmer with the need to define each format, at every step of the computation. This article reviews existing methods to automatically determine fixed-point formats, then describes and evaluates the prototype implementation of automatic fixed-point format determination in the Faust compiler.

cs.PL↗

arXiv2022

Symmetrized semi-discrete optimal transport

Interpolating between measures supported by polygonal or polyhedral domains is a problem that has been recently addressed by the semi-discrete optimal transport framework. Within this framework, one of the domains is discretized with a set of samples, while the other one remains continuous. In this paper we present a method to introduce some symmetry into the solution using coupled power diagrams. This symmetry is key to capturing the discontinuities of the transport map reflected in the geometry of the power cells. We design our method as a fixed-point algorithm alternating between computations of semi-discrete transport maps and recentering of the sites. The resulting objects are coupled power diagrams with identical geometry, allowing us to approximate displacement interpolation through linear interpolation of the meshes vertices. Through these coupled power diagrams, we have a natural way of jointly sampling measures.

math.OC↗

arXiv2021

On Higher-Order Probabilistic Subrecursion

We study the expressive power of subrecursive probabilistic higher-order calculi. More specifically, we show that endowing a very expressive deterministic calculus like Gödel's $\mathbb{T}$ with various forms of probabilistic choice operators may result in calculi which are not equivalent as for the class of distributions they give rise to, although they all guarantee almost-sure termination. Along the way, we introduce a probabilistic variation of the classic reducibility technique, and we prove that the simplest form of probabilistic choice leaves the expressive power of $\mathbb{T}$ essentially unaltered. The paper ends with some observations about the functional expressive power: expectedly, all the considered calculi capture the functions which $\mathbb{T}$ itself represents, at least when standard notions of observations are considered.

cs.LO↗