If asked, what mathematical tools are mostly used in machine learning, one would probably name statistics, probability, or combinatorics. So it is especially pleasing when some other tools, considered rather exotic in this area, find natural applications to ML problems. In this talk, I will speak about an application of (a variant of) topological Radon theorem to an old open problem in theoretical machine learning regarding the existence of the so-called sample compression schemes.

The talk is based on the joint work with Zachary Chase, Steve Hanneke, Shay Moran, and Amir Yehudayoff.