The past decade has witnessed a remarkable surge in breakthroughs in artificial intelligence (AI), with the potential to profoundly impact various aspects of our lives. However, the fundamental mathematical principles underlying the success of deep learning, the core technology behind these breakthroughs, is still far from well-understood. In this presentation, I will share some interesting connections between the theory of deep learning and harmonic analysis. The first half provides a gentle introduction to machine learning and deep learning. The second half focuses on two technical topics: An uncertainty principle between space and frequency and its significance in overcoming the curse of dimensionality. The multi-scale Marchenko-Pastur law and its interplay with the multiple-descent learning curve phenomenon.

Speaker’s website: https://sites.google.com/site/lechaoxiao/