Is there an energy (norm) preserving neural network architecture? • r/MachineLearning

A neural network passes an input vector through a series of "matrix (rotations / scaling / translation) operations followed by a non-linearity". The output vector of the neural network may or may not have the same norm as the input vector. Could you please point me to a / some neural network architecture/s that is / are able to preserve the norm of the input vector? If we consider the norm as a measure of the energy of the input vector / signal, what I am looking for is a neural net that can preserve the energy of the input signal. Is there any other metric that is analogous to the energy of the input signal?