  We show that gauge-independent terms in the one-loop and multi-loops
$\beta$-functions of the Standard Model can be exactly computed from the
Wetterich functional renormalization of a matrix model. Our framework is
associated to the finite spectral triple underlying the computation of the
Standard Model Lagrangian from the spectral action of Noncommutative Geometry.
This matrix-Yukawa duality for the $\beta$-function is a first hint towards
understanding the renormalization of the Noncommutative Standard Model
conceptually, and provides a novel computational approach for multi-loop
$\beta$-functions of particle physics models.
