Robust Learning of Recurrent Neural Networks in Presence of Exogenous Noise

Recurrent Neural networks (RNN) have shown promising potential for learning dynamic features of sequential data. However, artificial neural networks are known to exhibit poor robustness in presence of noisy input, 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 noisy inputs. 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. Several theoretical upper bounds are also presented to show how the robustness measure depends on the trainable parameters. Our extensive simulations on benchmark problems reveal that our proposed methodology significantly improves robustness of recurrent neural networks in a systematic manner.