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Starts 2 June 2025 14:35

Ends 2 June 2025

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Networks that Adapt to Intrinsic Dimensionality Beyond the Domain

Explore neural networks' ability to adapt to intrinsic dimensionality, focusing on ReLU networks approximating functions with dimensionality-reducing feature maps. Gain insights into manifold learning and data analysis.
Inside Livermore Lab via YouTube

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Overview

Explore neural networks' ability to adapt to intrinsic dimensionality, focusing on ReLU networks approximating functions with dimensionality-reducing feature maps. Gain insights into manifold learning and data analysis.

Syllabus

  • Introduction to Neural Networks and Intrinsic Dimensionality
  • Overview of Neural Networks
    Concept of Intrinsic Dimensionality
    Importance in Deep Learning
  • ReLU Networks and Function Approximation
  • Understanding Rectified Linear Units (ReLU)
    Function Approximation using ReLU Networks
    Dimensionality Reduction Techniques
  • Feature Maps and Dimensionality Reduction
  • Definition and Role of Feature Maps
    Techniques for Dimensionality Reduction in Neural Networks
    Application of Feature Maps in ReLU Networks
  • Manifold Learning
  • Basics of Manifold Learning
    Manifold Hypothesis in Data Analysis
    Techniques and Algorithms for Learning Manifolds
  • Adaptive Network Architectures
  • Design Principles of Adaptive Networks
    Network Architectures Responding to Intrinsic Dimensionality
    Case Studies in Adaptive Network Design
  • Advanced Topics in Manifold Learning
  • Exploring Geometric and Topological Structures
    Recent Advances in Manifold-Based Methods
    Theoretical Foundations and Practical Implementations
  • Practicals and Hands-on Sessions
  • Implementing ReLU Networks for Dimensionality Reduction
    Tools and Libraries for Manifold Learning
    Project: Building an Adaptive Neural Network for Real-world Data
  • Conclusion and Future Directions
  • Summary of Key Concepts
    Current Trends and Research Directions
    Open Problems and Opportunities in Adaptive Network Design

Subjects

Data Science