In the 2005 lecture 6
Alain Connes points out that although his framework predicts physical couplings that match $SU(5)$ unification, it achieves this without the addition of extra fields or supersymmetry arguments. Towards the end of the lecture he summarises the situation: the problem is to combine (1) the renormalisation theory (Hopf algebras, motivic Galois group) and (2) the geometric setup from NCG operator theory, in such a way that running geometries
(on different scales) are possible. Connes proposes a functional integral over geometries which is spectral in nature, and in fact looks like a matrix model
. The question is, what sort of constraints should be applied to geometries? It is made clear that this is a challenge to physicists: his spectral action principle is a statement about the nature of observables, but insufficient in itself to guide, as Connes puts it, the merging of motives and NCG
These lectures are highly recommended to physicists. Don't expect to understand all the mathematical gobbledygook, but try to take in the big picture, which is fantastically conveyed. Note that more recent work
removes much of the arbitrariness of the original NCG formulation of the SM, but still puts the number of generations in by hand.