A model that is nonlinear in terms of parameters is referred to as a nonlinear model. Among nonlinear models, a three-layer hierarchical model is a popular choice \[ f_\theta(x) = \sum_{j=1}^{b} \alpha_j \phi(x; \beta_j) \] where $\phi(x; \beta)$ is a basis function parameterized by $\beta$

A hierarchical model is linear in terms of parameter $\alpha = (\alpha_1, \ldots, \alpha_b)^\top$. However, in terms of the basis parameters $\{\beta_j\}_{j=1}^b$, the hierarchical model is nonlinear