This tutorial provides an in-depth exploration into the realm of hyperbolic learning, a burgeoning field within machine learning that leverages the mathematical properties of hyperbolic geometry to model and analyze data. Particularly, it is well-suited for representing hierarchical structures and has demonstrated superior performance in various domains such as computer vision, natural language processing, and graph analysis.
- Pengxiang Li
- Peilin Yu
- Yangkai Xue
- Yuwei Wu
- Zhi Gao
School of Computer Science & Technology
Beijing Institute of Technology, China
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Introduction to Hyperbolic Geometry
- Motivation for using hyperbolic spaces
- Riemannian manifolds and their relevance
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Basic Concepts and Operations
- Hyperbolic models and their properties
- Basic operations in hyperbolic space (Exponential map, Logarithmic map, Möbius addition, etc.)
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The Five Isometric Models
- Lorentz Model
- Poincaré Model
- Klein Model
- Poincaré Half Model
- Hemisphere Model
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Applications of Hyperbolic Learning
- Embedding
- Distribution
- Dimension Reduction
- Clustering
- Metric Learning
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Theoretical Foundations
- Shallow and Deep Learning Theories
- Hyperbolic Neural Networks (HNN)
- Hyperbolic Graph Neural Networks (HGNN)
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Optimization Techniques
- Addressing the vanishing gradient problem
- Geodesically convex optimization
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Challenges and Future Directions
- Current limitations and practical implementation challenges
- Opportunities for future research and development
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Q & A Session
- Interactive session to address queries and discussions
- Basic understanding of machine learning and geometric concepts
- Familiarity with neural network architectures
- Knowledge of differential geometry is a plus
This tutorial is provided under the Creative Commons Attribution 4.0 International License.
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