Reviews: Higher-Order Factorization Machines

It is an interesting, reasoned and promising approach. But there a few issues which I would like to have clarified in the rebuttal to accept the paper. The idea of the paper seems to strongly rely on the paper "Polynomial Networks and Factorization Machines: New Insights and Efficient Training Algorithms" by Blondel et al., where ANOVA kernels have already been used. Can you explain in more detail the difference and contributions in comparison to this paper? I'm wondering why such approaches cannot be applied to the given problem or why it is not better to adapt them to HOFMs.