Les fondements statistiques et probabilistes des modèles d’Intelligence Artificielle Générative

The statistical and probabilistic foundations of Generative Artificial Intelligence models

Moussa Keita

MPRA Paper from University Library of Munich, Germany

Abstract: In the context of the recent disruption of generative artificial intelligence and Large Language Models (LLMs), a critical epistemological gap persists in treating them as opaque 'magical boxes' rather than rigorous systems of mathematical statistics. This book addresses how to bridge this gap, demonstrating that generative AI fundamentally relies on high-dimensional probability density estimation and cost function optimization. Bridging classical statistical methods (Markov chains, Maximum Likelihood, information theory) with modern continuous architectures (VAEs, GANs, and Transformers), this book provides a comprehensive tri-prism framework (probabilistic, geometric-informational, and algorithmic) to elucidate generative mechanics. It systematically tackles the curse of dimensionality, autoregressive modeling, scaling laws, and model alignment. The book demonstrates the timeless relevance of statistics and probability in the technological advancements of generative artificial intelligence observed in recent years.

Keywords: Generative Artificial Intelligence; Statistical Learning Theory; Probability Density Estimation; Large Language Models; Transformer Architecture; Information Theory; Latent Spaces; algorithms. (search for similar items in EconPapers)
JEL-codes: C80 C81 C82 (search for similar items in EconPapers)
Date: 2026-11
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