  Recurrent Neural networks (RNN) have shown promising potential for learning
dynamics of sequential data. However, artificial neural networks are known to
exhibit poor robustness in presence of input noise, where the sequential
architecture of RNNs exacerbates the problem. In this paper, we will use ideas
from control and estimation theories to propose a tractable robustness analysis
for RNN models that are subject to input noise. The variance of the output of
the noisy system is adopted as a robustness measure to quantify the impact of
noise on learning. It is shown that the robustness measure can be estimated
efficiently using linearization techniques. Using these results, we proposed a
learning method to enhance robustness of a RNN with respect to exogenous
Gaussian noise with known statistics. Our extensive simulations on benchmark
problems reveal that our proposed methodology significantly improves robustness
of recurrent neural networks.
