Ran Levi - Bedlewo: Topological Analysis of Neural Networks
Explore topological analysis techniques applied to neural networks in this conference talk by Ran Levi. Delve into the challenges of obtaining connectivity data from biological brains and how artificial neural networks provide partial solutions. Learn about an ongoing collaborative project applying topological methods to study the brain, motivated by the Blue Brain Project's digital reconstruction of rat cortex. Discover how directed structural connectivity graphs are extracted and analyzed using novel ideas and basic algebraic topology. Examine the Flag Complex, abstract ordered simplicial complexes, and the directed flag complex of directed graphs. Investigate reciprocal connections and the Transmission-Response method for analyzing neural activity. Compare point vs. circle experiments and explore highway graphs and their relations through line digraphs. Gain insights into the intersection of topology, neuroscience, and artificial intelligence in this comprehensive presentation.