Numerous studies have addressed nonlinear functional approximation by multilayer perceptrons (MLPs) and RBF networks as a special case of the more general mapping problem. The performance of both these supervised network models intimately depends on the efficiency of their learning process. This paper presents an unsupervised recurrent neural network, based on the recurrent Mean Field Theory (MFT) network model, that finds a least-squares approximation to an arbitrary L2 function, given a set of Gaussian radially symmetric basis functions (RBFs). Essential is the reformulation of RBF approximation as a problem of constrained optimisation. A new concept of adiabatic network organisation is introduced. Together with an adaptive mechanism of temperature control this allows the network to build a hierarchical multiresolution approximation with preservation of the global optimisation characteristics. A revised problem mapping results in a position invariant local interconnectivity pattern, which makes the network attractive for electronic implementation. The dynamics and performance of the network are illustrated by numerical simulation.