The architecture of the cerebellar model articulation controller (CMAC) presents a rigid compromise between learning and generalization. In the presence of a sparse training dataset, this limitation manifestly causes overfitting, a drawback that is not overcome by current training algorithms. This paper proposes a novel training framework founded on the Tikhonov regularization, which relates to the minimization of the power of the sigma-order derivative. This smoothness criterion yields to an internal cell-interaction mechanism that increases the generalization beyond the degree hardcoded in the CMAC architecture while preserving the potential CMAC learning capabilities. The resulting training mechanism, which proves to be simple and computationally efficient, is deduced from a rigorous theoretical study. The performance of the new training framework is validated against comparative benchmarks from the DELVE environment.