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pro vyhledávání: '"Arnal, Charles"'
Autor:
Arnal, Charles
In this short note, we show that the distance function to any finite set $X\subset \mathbb{R}^n$ is a topological Morse function, regardless of whether $X$ is in general position. We also precisely characterize its topological critical points and the
Externí odkaz:
http://arxiv.org/abs/2407.15578
Large Language Models have recently been applied to text annotation tasks from social sciences, equalling or surpassing the performance of human workers at a fraction of the cost. However, no inquiry has yet been made on the impact of prompt selectio
Externí odkaz:
http://arxiv.org/abs/2407.10645
\v{C}ech Persistence diagrams (PDs) are topological descriptors routinely used to capture the geometry of complex datasets. They are commonly compared using the Wasserstein distances $OT_{p}$; however, the extent to which PDs are stable with respect
Externí odkaz:
http://arxiv.org/abs/2406.14919
Autor:
Cabannes, Vivien, Arnal, Charles, Bouaziz, Wassim, Yang, Alice, Charton, Francois, Kempe, Julia
Chain-of-Thought (CoT) reasoning is known to improve Large Language Models both empirically and in terms of theoretical approximation power. However, our understanding of the inner workings and conditions of apparition of CoT capabilities remains lim
Externí odkaz:
http://arxiv.org/abs/2406.02128
The combination of lightly supervised pre-training and online fine-tuning has played a key role in recent AI developments. These new learning pipelines call for new theoretical frameworks. In this paper, we formalize core aspects of weakly supervised
Externí odkaz:
http://arxiv.org/abs/2402.13079
In general, the critical points of the distance function $d_{\mathsf{M}}$ to a compact submanifold $\mathsf{M} \subset \mathbb{R}^D$ can be poorly behaved. In this article, we show that this is generically not the case by listing regularity condition
Externí odkaz:
http://arxiv.org/abs/2312.13147
Autor:
Cabannes, Vivien, Arnal, Charles
Publikováno v:
ICASSP, 2024
The number of sampling methods could be daunting for a practitioner looking to cast powerful machine learning methods to their specific problem. This paper takes a theoretical stance to review and organize many sampling approaches in the ``generative
Externí odkaz:
http://arxiv.org/abs/2311.13845
Autor:
Arnal, Charles, Hensel, Felix, Carrière, Mathieu, Lacombe, Théo, Kurihara, Hiroaki, Ike, Yuichi, Chazal, Frédéric
Despite their successful application to a variety of tasks, neural networks remain limited, like other machine learning methods, by their sensitivity to shifts in the data: their performance can be severely impacted by differences in distribution bet
Externí odkaz:
http://arxiv.org/abs/2305.13271
Autor:
Arnal, Charles, Garrigue, Louis
We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become singular because
Externí odkaz:
http://arxiv.org/abs/2305.09026
Autor:
Arnal, Charles
We call a real algebraic hypersurface in $(\mathbb{C}^*)^n$ simplicial if it is given by a real Laurent polynomial in $n$-variables that has exactly $n+1$ monomials with non-zero coefficients and such that the convex hull in $\mathbb{R}^n$ of the $n+
Externí odkaz:
http://arxiv.org/abs/2105.12100