  Ascertaining whether a classical model can efficiently replace a given
quantum model -- dequantization -- is crucial in assessing the true potential
of quantum algorithms. In this work, we introduced the dequantizability of the
function class of variational quantum-machine-learning~(VQML) models by
employing the tensor network formalism, effectively identifying every VQML
model as a subclass of matrix product state (MPS) model characterized by
constrained coefficient MPS and tensor product-based feature maps. From this
formalism, we identify the conditions for which a VQML model's function class
is dequantizable or not. Furthermore, we introduce an efficient quantum
kernel-induced classical kernel which is as expressive as given any quantum
kernel, hinting at a possible way to dequantize quantum kernel methods. This
presents a thorough analysis of VQML models and demonstrates the versatility of
our tensor-network formalism to properly distinguish VQML models according to
their genuine quantum characteristics, thereby unifying classical and quantum
machine-learning models within a single framework.
