Sunghee Yun (He/Him)

Co-founder & CTO @ Erudio Bio, Inc., Chief Business Development Officer @ WeStory.ai, Advisor & Evangelist @ CryptoLab, Inc., KFAS-Salzburg Global Leadership Initiative Fellow @ Salzburg Global Seminar, Adjunct Professor @ Sogang University, Advisory Professor @ DGIST, Global Advisory Board Member @ Innovative Future Brain-Inspired Intelligence System Semiconductor of Sogang University, Network Expert @ Gerson Lehrman Group

Abstract

This lecture provides a rigorous mathematical foundation for understanding artificial intelligence, bridging the gap between theoretical concepts and practical machine learning implementations. Building upon the architectural insights from the previous session on modern AI systems, this presentation delves into the essential mathematical prerequisites that underpin all contemporary AI developments. The lecture systematically covers linear algebra fundamentals including matrix operations and transformations, calculus concepts focusing on multivariate functions and chain rule applications crucial for neural network training, and statistical foundations encompassing probability theory, random variables, and Bayesian inference. These mathematical building blocks are then directly connected to core machine learning concepts, demonstrating how optimal estimation theory, bias-variance tradeoffs, and maximum likelihood estimation form the theoretical backbone of modern AI systems.

The technical core of the presentation focuses on the mathematical formulations that drive machine learning algorithms, progressing from fundamental estimation problems to the complex optimization challenges inherent in deep neural networks. Through detailed mathematical exposition, the lecture explains how machine learning reduces to numerical optimization of loss functions, explores the equivalence between maximum likelihood estimation and mean square error minimization, and demonstrates the statistical foundations underlying supervised, unsupervised, and reinforcement learning paradigms. Special emphasis is placed on the mathematical mechanics of deep neural network training, including the rigorous derivation of backpropagation using chain rule calculus, stochastic gradient descent formulations, and the matrix-vector operations that enable efficient computation of gradients across multiple network layers.

The presentation culminates with mathematical perspectives on large language models and generative AI, showing how probability theory and optimization principles scale to the massive parameter spaces characteristic of modern transformers. By examining the mathematical formulations behind sequence-to-sequence models, attention mechanisms, and generative modeling approaches including VAEs and GANs, attendees gain insight into how relatively simple mathematical concepts enable the sophisticated behaviors observed in contemporary AI systems. This mathematical grounding provides practitioners with the theoretical understanding necessary to effectively implement, debug, and innovate within the rapidly evolving AI landscape, ensuring they can navigate both current applications and future developments with confidence rooted in fundamental mathematical principles.