  We provide an empirical study of the stability of recurrent neural networks
trained to recognize regular languages. When a small amount of noise is
introduced into the activation function, the neurons in the recurrent layer
tend to saturate in order to compensate the variability. In this saturated
regime, analysis of the network activation shows a set of clusters that
resemble discrete states in a finite state machine. We show that transitions
between these states in response to input symbols are deterministic and stable.
The networks display a stable behavior for arbitrarily long strings, and when
random perturbations are applied to any of the states, they are able to recover
and their evolution converges to the original clusters. This observation
reinforces the interpretation of the networks as finite automata, with neurons
or groups of neurons coding specific and meaningful input patterns.
