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Explore the intersection of deep neural networks and manifold-structured data in this comprehensive lecture from the ICBS2024 conference. Delve into Rongjie Lai's research on how deep neural networks can effectively learn complex geometric information embedded in data. Discover the innovative Chart Auto-Encoder (CAE) approach, inspired by differential geometry, which utilizes a multi-chart latent space to enhance data representation. Learn about the universal approximation theorem established for CAE's representation capabilities and the statistical guarantees provided for generalization error in trained models. Examine the robustness of CAE to noise and its performance on data with complex geometry and topology through numerical experiments. Gain insights into this collaborative research effort that bridges the gap between deep learning and differential geometry, offering new perspectives on data representation and analysis.
