Generative Topological Networks
This work addresses the challenge of improving generative model training and understanding for researchers and practitioners, though it appears incremental as it builds on existing latent-space methods with a new topological approach.
The authors tackled the problem of complex and difficult-to-train generative methods in latent spaces by introducing Generative Topological Networks (GTNs), a simple method based on topology theory that improves upon VAEs and converges quickly to generate realistic samples. They also provided insights into why lower-dimensional latent spaces benefit generative models, linking data intrinsic dimension to generation quality and explaining issues like out-of-distribution samples in diffusion models.
Generative methods have recently seen significant improvements by generating in a lower-dimensional latent representation of the data. However, many of the generative methods applied in the latent space remain complex and difficult to train. Further, it is not entirely clear why transitioning to a lower-dimensional latent space can improve generative quality. In this work, we introduce a new and simple generative method grounded in topology theory -- Generative Topological Networks (GTNs) -- which also provides insights into why lower-dimensional latent-space representations might be better-suited for data generation. GTNs are simple to train -- they employ a standard supervised learning approach and do not suffer from common generative pitfalls such as mode collapse, posterior collapse or the need to pose constraints on the neural network architecture. We demonstrate the use of GTNs on several datasets, including MNIST, CelebA, CIFAR-10 and the Hands and Palm Images dataset by training GTNs on a lower-dimensional latent representation of the data. We show that GTNs can improve upon VAEs and that they are quick to converge, generating realistic samples in early epochs. Further, we use the topological considerations behind the development of GTNs to offer insights into why generative models may benefit from operating on a lower-dimensional latent space, highlighting the important link between the intrinsic dimension of the data and the dimension in which the data is generated. Particularly, we demonstrate that generating in high dimensional ambient spaces may be a contributing factor to out-of-distribution samples generated by diffusion models. We also highlight other topological properties that are important to consider when using and designing generative models. Our code is available at: https://github.com/alonalj/GTN