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Motivated by the recent emergence of category theory in machine learning, we teach a course on its philosophy, applications and outlook from the perspective of machine learning! See for more information: https://cats.for.ai/ In this third invited talk, David Spivak will discuss a generalization of gradient descent called "dynamic organizational systems", which includes ANNs, prediction markets, Hebbian learning, and strategic games. It is founded on the category Poly of polynomial functors, which generalizes Lens. I will review the relevant background on Poly and then explain dynamic organizational systems as coherent procedures by which a network of component systems can rewire its network structure in response to the data flowing through it. I'll explain the ANN case, and possibly the prediction market case, time permitting.