CZS Summer School, day 3: Deep Sets

Today was day 3 of the CZS Summer School, in which I am helping mentor a group of students working on equivariant methods on point clouds. In our working session today, Soledad Villar (JHU) (who is the main mentor for this group of students) gave a short, spontaneous explanation of the main Deep Sets result in machine learning: (Almost) any permutation-invariant function of a set of objects x_i can be written in an amazingly simple form: h(Σ_ig(x_i)), where h and g are potentially nonlinear functions. That result is super-strong, and super-useful!