3-way factorization machines
I have recently started polylearn, a scikit-learn-contrib package for efficient implementation of factorization machines and polynomial networks, in Python with Cython. Polylearn currently coordinate descent solvers for 2nd and 3rd order factorization machines, and for arbitrary order polynomial networks, using the approach described in the papers cited on the polylearn website.

I'm currently working on an implementation of arbitrary higher order FMs using SG and CD style algorithms, using the approach from this recent paper, I should have it ready within a week.

Polylearn has not had a release yet, so I would love to hear any feedback on the API and functionality, in order to round things off before the 0.1 release!