Beijing Institute of Mathematical Sciences and Applications

Large foundation models have achieved remarkable success across various domains, including general applications like Natural Language Processing, image, speech, and video, as well as scientific fields such as materials science, molecular biology, and protein engineering. While the underlying techniques are firmly rooted in applied mathematics, their development has often been driven by empirical engineering practices, leading to significant practical breakthroughs. Diffusion models serve as a prime example, demonstrating both substantial engineering benefits and profound mathematical underpinnings.

This lecture series aims to bridge the gap between foundation models and their mathematical foundations, fostering interdisciplinary discussions, particularly between mathematics and machine learning.

Prerequisites:
-- For participants from a machine learning background, a solid understanding of Calculus and graduate-level Probability is required. While knowledge of stochastic processes is not strictly necessary, a basic understanding will significantly enhance comprehension.
-- For those from a mathematics background, prior knowledge of neural networks is essential. If you lack this prerequisite, please refer to the first three chapters of 'Neural Networks and Deep Learning' (http://neuralnetworksanddeeplearning.com).

Course Content:
The course will primarily cover autoregressive models, diffusion models, and discrete diffusion models, including their underlying mathematics and algorithms. We will explore their diverse applications across various domains, with a particular focus on multi-modalities.