Mathematical underpinning of adaptive capability of recurrent neural network with fixed weights

A recurrent neural network with fixed weights is known to be able to adapt an uncertain environmental process. Such a network is called an accommodative neural network to differentiate it from an adaptive neural network, which needs to be adjusted online for adaptation. This paper provides mathematical underpinning of the adaptive capability of accommodative networks, showing that they are capable of adapting to observable environmental processes as well as constant but not necessarily observable environmental processes.