Explore a 45-minute lecture on the approximation theory of deep learning from a dynamical perspective, delivered by Qianxiao Li from the National University of Singapore. Delve into the intersection of machine learning and dynamical systems, examining how composition in deep learning can be viewed as dynamics. Investigate supervised learning, the problem of approximation, and universal approximation by dynamics. Analyze sequence modeling applications, including deep learning architectures for sequence modeling and the approximation theory for sequence modeling. Examine recurrent neural network hypothesis spaces, their properties, and approximation guarantees. Gain insights into convolutional and encoder-decoder architectures, and discover how the analysis of recurrent neural networks can be extended to these structures.