Mathematical Foundation

Mathematical foundations underpin numerous scientific and technological advancements, focusing on rigorous frameworks for existing methods and developing new ones. Current research emphasizes strengthening the theoretical basis of machine learning algorithms (like diffusion models and neural networks), improving the accuracy and efficiency of statistical inference techniques (including Bayesian methods and graph-based approaches), and clarifying the mathematical principles behind diverse applications such as signal processing, head pose estimation, and even musical instrument design. This work is crucial for enhancing the reliability, interpretability, and applicability of these methods across various fields.