Topological Neural Network

Topological neural networks (TNNs) aim to improve upon traditional graph neural networks by incorporating higher-order relationships and topological information within data, leading to richer representations. Current research focuses on developing novel architectures like equivariant TNNs and transformer-based models (e.g., Cellular Transformers, PersFormers) that efficiently handle complex data structures such as simplicial complexes and cell complexes, often leveraging persistent homology for feature extraction. This approach shows promise for enhancing performance in diverse applications, including molecular property prediction, air pollution modeling, and combinatorial optimization, by capturing long-range dependencies and multi-way interactions that are often missed by simpler models.