  We introduce Noise Injection Node Regularization (NINR), a method of
injecting structured noise into Deep Neural Networks (DNN) during the training
stage, resulting in an emergent regularizing effect. We present theoretical and
empirical evidence for substantial improvement in robustness against various
test data perturbations for feed-forward DNNs when trained under NINR. The
novelty in our approach comes from the interplay of adaptive noise injection
and initialization conditions such that noise is the dominant driver of
dynamics at the start of training. As it simply requires the addition of
external nodes without altering the existing network structure or optimization
algorithms, this method can be easily incorporated into many standard problem
specifications. We find improved stability against a number of data
perturbations, including domain shifts, with the most dramatic improvement
obtained for unstructured noise, where our technique outperforms other existing
methods such as Dropout or $L_2$ regularization, in some cases. We further show
that desirable generalization properties on clean data are generally
maintained.

Machine Learning;Disordered Systems and Neural Networks;Statistical Mechanics;Artificial Intelligence;Machine Learning