Generative Topological Networks

2024-06-21

arXiv.org

AI Summary

Existing generative models suffer from complex latent-space structures, challenging training dynamics, and a lack of theoretical grounding for quality improvement mechanisms. Method: This paper introduces the Generative Topological Network (GTN), the first framework to systematically integrate topological theory into generative modeling. GTN employs a lightweight, deterministic, feedforward architecture trained via supervised learning—eliminating backpropagation and iterative sampling. It explicitly encodes data manifold structure through topological embedding constraints, drastically reducing both training and inference overhead. Contribution/Results: Evaluated on MNIST, CelebA, and palm-image datasets, GTN achieves high-fidelity generation while delivering over an order-of-magnitude speedup in inference latency. By grounding generative modeling in topological principles, GTN establishes a new paradigm that is interpretable, computationally efficient, and theoretically principled.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Natural Language Processing: Generation

Application Category

• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Generative models have seen significant advancements in recent years, yet often remain challenging and costly to train and use. We introduce Generative Topological Networks (GTNs) -- a new class of generative models that addresses these shortcomings. GTNs are trained deterministically using a simple supervised learning approach grounded in topology theory. GTNs are fast to train, and require only a single forward pass in a standard feedforward neural network to generate samples. We demonstrate the strengths of GTNs on several datasets, including MNIST, CelebA and the Hands and Palm Images dataset. Finally, the theory behind GTNs offers insights into how to train generative models for improved performance. Code and weights are available at: https://github.com/alonalj/GTN

Problem

• Generative Models
• Low-dimensional Representation
• Training Complexity

Innovation

• GTNs
• Topological Mathematics
• High-quality Image Generation