Topology-Driven Insights into Naturalistic Behavior from Neuromechanical Agent Modeling
We like to talk about and quantify things in Euclidean space, that's where our intuition works the best. However, most of the times it might be complicated trying to find the correct "metric" of understanding things in here. Under such nice and structured space, we sometimes don't know how to talk about complex, yet interesting, data. However, as a “coordinate-free” method, computational topology may provide us a new way to understand the shape of data in a more abstract but comprehensive way.
Video in curtesy of Donald R. Sheehy's group: illustration of topological filtration.
I am currently using computational topological data analysis with advising from professor Yusu Wang and in collaboration with the VNL team in Talmo's Lab in to try to understand what's truely happening inside the representation space of neural network when they are training upon specific tasks. Particularly, I am interested in seeing how the intention created by deep reinforcement learning in the VNL system may be interpreted from an computational topology perspective. We believe that there exist certain hidden space within the ambient space of the intention, that the organization of it is meaningful yet noisy and a topological lens may help to discover the signals from the noises.