Learning Manifold-Structured Data Using Deep Neural Networks - Theory and Applications
Offered By: BIMSA via YouTube
Course Description
Overview
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.
Syllabus
Rongjie Lai: Learning Manifold-Structured Data using Deep Neural Networks: Theory... #ICBS2024
Taught by
BIMSA
Related Courses
From Reinforcement Learning to Spin Glasses - The Many Surprises in Quantum State PreparationAPS Physics via YouTube Mathematical Frameworks for Signal and Image Analysis - Diffusion Methods in Manifold and Fibre Bundle Learning
Joint Mathematics Meetings via YouTube Quantifying the Topology of Coma
Institute for Pure & Applied Mathematics (IPAM) via YouTube Reconstructing Manifolds by Weighted L_1-Norm Minimization
Applied Algebraic Topology Network via YouTube Demystifying Latschev's Theorem for Manifold Reconstruction
Applied Algebraic Topology Network via YouTube