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The SiMul team at the University of Lorraine is offering a fully funded PhD position on the theoretical foundations of self-supervised learning, focusing on representation stability, interpretability, and efficiency. Despite their success, self-supervised approaches and foundation models still lack a thorough theoretical understanding. This project aims to bridge that gap by exploring connections between AI models and low-rank tensor decompositions, providing a rigorous mathematical framework to address key questions: When are learned representations interpretable and stable? How do models perform on heterogeneous data (e.g., federated or personalized learning)? Can smaller, energy-efficient models achieve strong performance on specialized tasks?