Networks that Adapt to Intrinsic Dimensionality Beyond the Domain

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

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Subjects

Data Science