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