A lot of secure FL papers quietly stop at “we can sum gradients,” because once clustering or routing needs argmin/argmax, the crypto bill gets ugly fast. So pushing the server-side EM update down to additive sufficient statistics is the real trick here, since it keeps the whole thing inside the part of Paillier or secure aggregation that people can actually run without turning the round into a science project.
Additive sufficient stats is the useful bit, sure. But EM doesn’t make clustering cheap, it mostly just moves the ugly part into metadata, and that can still leak more than people want.
Came for the encryption-compatible part, had to read the title twice because the actual result is buried under a pretty heroic amount of metadata and expectation-maximization jargon.