Explore the application of rank-based persistence in comparing neural network architectures in this 49-minute conference talk. Delve into a generalized persistence framework that characterizes data representations at each layer of artificial neural networks. Learn about the theoretical approach, including generalized categories, fiberwise rank functions, and categorical persistence. Discover how persistence diagrams, multicolor persistence, and levelpoint clouds fit into this generalized framework. Examine practical applications, focusing on data distribution, weighted graphs, and optimal agent group actions. Gain insights into the results of comparing different neural architectures using this innovative approach, bridging the gap between artificial neural networks and topological persistence.