When I was learning about Trustworthy AI, I found there were limited systematic books on its mathematical foundations, so I put together my notes taken during the early phase of my self-learning. In these notes, I provide a rigorous mathematical examination of Trustworthy AI, exploring reliable machine learning through the lens of constrained optimization, statistical learning theory, and differential geometry. I bring together concepts to define the multidimensional requirements of AI systems, moving beyond heuristic approaches toward a grounded engineering discipline. The notes formalize critical properties such as adversarial robustness via Lipschitz continuity and dual norms, algorithmic fairness via group constraints and impossibility theorems, and causal inference via structural causal models. Through these, I aim to provide a useful systematic mathematical foundation for better understanding Trustworthy AI.
Download Full PDF@article{aiersilan2026mathematical,
title={Mathematical Foundations of Trustworthy AI},
author={Aiersilan, Aizierjiang},
year={2026}
}