Evaluating Generative Models via Cubical Homology based Persistent Entropy

Topological tools have become popular in improving and evaluating the performance of generative models by exploring the connection between their representation power and topological properties.This has led to the development of various measures that can assess the diversity and quality of generated data.However, existing methods are impractical in higher dimensions and large-scale datasets/models.To address this, we propose a scalable framework based on persistent entropy.We first establish a theoretical relation between the homological complexity of the underlying topology and the persistent entropy.We then empirically study the topological transformation during training of the generated data manifold using cubical homology.The proposed method is domain & modelagnostic and scales well for various neural architectures at different depths.