  We formulate conditions under which the asymptotically expanded spectral
action on an almost commutative manifold is renormalizable as a
higher-derivative gauge theory. These conditions are of graph theoretical
nature, involving the Krajewski diagrams that classify such manifolds. This
generalizes our previous result on (super)renormalizability of the
asymptotically expanded Yang-Mills spectral action to a more general class of
particle physics models that can be described geometrically in terms of a
noncommutative space. In particular, it shows that the asymptotically expanded
spectral action which at lowest order gives the Standard Model of elementary
particles is renormalizable.
