  A set of renormalization invariants is constructed using approximate,
two-flavor, analytic solutions for RGEs. These invariants exhibit explicitly
the correlation between quark flavor mixings and mass ratios in the context of
the SM, DHM and MSSM of electroweak interaction. The well known empirical
relations $\theta_{23}\propto m_s /m_b $, $\theta_{13}\propto m_d /m_b$ can
thus be understood as the result of renormalization evolution toward the
infrared point. The validity of this approximation is evaluated by comparing
the numerical solutions with the analytical approach. It is found that the
scale dependence of these quantities for general three flavoring mixing follows
closely these invariants up to the GUT scale.
