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Creating A Novel Geometric Hypergraph Neural Network
Introduction
In the dynamic landscape of machine learning, two of the most promising avenues are graph theory and geometric deep learning, this morning I had an idea on how to combine these two processes to make a more solid network. This article explores the architecture and implementation of a Geometric Hypergraph Neural Network (GHNN), which extends traditional graph neural networks to model more complex relationships using hypergraphs and geometric embeddings.
Introduction to Hypergraphs and Geometric Deep Learning
Understanding Hypergraphs
Introduction to Geometric Deep Learning
Geometric Deep Learning involves applying principles from differential geometry and Riemannian optimization to neural networks. By embedding data onto geometric spaces, such as hyperbolic or spherical manifolds, these networks can capture complex relational structures more effectively than traditional Euclidean spaces.
In hyperbolic space, distances grow exponentially with radius, which naturally accommodates hierarchical structures. A common representation of hyperbolic space is the Poincare Ball Model, defined as:
