Mathematical Challenges in Deep Learning Theory

Research in deep learning theory spans a wide range of fundamental questions, from formulating appropriate prediction problems to understanding the generalization capabilities of complex models. This talk provides an overview of key challenges and open problems that arise in the theoretical analysis of deep neural networks. We highlight how even the precise formulation of the prediction task can significantly influence the resulting analysis. Furthermore, we discuss the expressive power of neural networks and examine the persistent gap between statistical guarantees and optimization-based results. Finally, we outline emerging directions and recent advances aimed at bridging these gaps and developing a more unified theoretical framework for deep learning.