Zobrazeno 1 - 10
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pro vyhledávání: '"Arnal P"'
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the curse of dime
Externí odkaz:
http://arxiv.org/abs/2411.01375
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
Missing values are a major challenge in most data science projects working on real data. To avoid losing valuable information, imputation methods are used to fill in missing values with estimates, allowing the preservation of samples or variables tha
Externí odkaz:
http://arxiv.org/abs/2407.11767
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
Autor:
Antoni-Micollier, Laura, Arnal, Maxime, Gautier, Romain, Janvier, Camille, Ménoret, Vincent, Richard, Jérémie, Vermeulen, Pierre, Rosenbusch, Peter, Majek, Cédric, Desruelle, Bruno
Gravity measurements provide valuable information on the mass distribution below the earth surface relevant to various areas of geosciences such as hydrology, geodesy, geophysics, volcanology, and natural resources management. During the past decades
Externí odkaz:
http://arxiv.org/abs/2405.10844
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
Autor:
Arnal, A., Monterde, J.
The affine space of all tensor product B\'ezier patches of degree nxn with prescribed main diagonal curves is determined. First, the pair of B\'ezier curves which can be diagonals of a B\'ezier patch is characterized. Besides prescribing the diagonal
Externí odkaz:
http://arxiv.org/abs/2402.03892
We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet--Magnus expansion for periodic systems, the quantum averagin
Externí odkaz:
http://arxiv.org/abs/2401.12955