Title: Non-Euclidean Neural Network Architectures for Generative Modeling

Abstract

This paper investigates the potential of non-Euclidean neural network architectures for enhanced generative modeling. Traditional neural networks, predicated on linear transformations and gradient descent, often struggle to capture the intricate patterns and high-dimensional space inherent in data. We propose a novel set of architectural designs that explicitly leverage concepts from manifold learning and graph theory to create networks with inherent diversity and adaptability. The core claim is that these architectures, by fostering emergent structures driven by geometry, can produce more expressive and robust generative models than standard approaches. The study focuses on developing novel network topologies and training strategies to encourage the formation of diverse manifolds and graph structures, ultimately leading to improved generative performance. This work addresses a significant gap in generative modeling by moving beyond simple linear transformations to explore more complex and flexible representations.