Noisy Recurrent Neural Networks
This work provides theoretical insights into the implicit regularization effects of noise injection in RNNs, which is significant for researchers and practitioners aiming to improve the robustness and stability of RNN models.
This paper investigates recurrent neural networks (RNNs) trained with noise injected into hidden states, viewing them as discretizations of stochastic differential equations. The study reveals that this implicit regularization promotes flatter minima, more stable dynamics, and larger classification margins in classification tasks.
We provide a general framework for studying recurrent neural networks (RNNs) trained by injecting noise into hidden states. Specifically, we consider RNNs that can be viewed as discretizations of stochastic differential equations driven by input data. This framework allows us to study the implicit regularization effect of general noise injection schemes by deriving an approximate explicit regularizer in the small noise regime. We find that, under reasonable assumptions, this implicit regularization promotes flatter minima; it biases towards models with more stable dynamics; and, in classification tasks, it favors models with larger classification margin. Sufficient conditions for global stability are obtained, highlighting the phenomenon of stochastic stabilization, where noise injection can improve stability during training. Our theory is supported by empirical results which demonstrate that the RNNs have improved robustness with respect to various input perturbations.