Research Projects

This project aims to uncover the latent space of generative models through mathematical modeling, addressing the weakness of many models in the generative space due to a lack of topological understanding. The project will provide extensive theoretical and mathematical proofs for modeling the latent space of a generative model based on model architecture and parameters. The use of computational topology, particularly Persistent Homology, will be employed to understand the topology of the latent space and infer mathematically how it came to be. This project could potentially solve some of the biggest problems in AGI and deep generative modelling. References to previous research include Wu et al.'s work on learning a probabilistic latent space of object shapes via 3D generative-adversarial modeling and Goodfellow's work ongenerative adversarial networks.This project might yield solutions to some of the biggest problems in AGI and deep generative modelling. References: [1] J. Wu, C. Zhang, T. Xue, W. T. Freeman, and J. B. Tenenbaum, “Learning a probabilistic latent space of object shapes via 3d generative-adversarial modeling,” 2017. [2] I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial networks,” Communications of the ACM, vol. 63, no. 11, pp. 139–144, 2020.