Equivalence among dynamic neural networks by transdimensional changes of coordinates

We present conditions under which two classes of dynamic neural networks have equivalent (input-)output behavior. We achieve this result by proving a general result on trans-dimensional changes of coordinates in dynamic networks. As a corollary, we show that a single-hidden-layer dynamic perception can be equivalently simulated by a dynamic perceptron with no hidden layer but having an output map. This result is of interest because dynamic perceptions without hidden layer are more amenable to analytical studies.