Noise Sensitivity and Stability of Deep Neural Networks for Binary Classification
This work addresses the non-robustness problem in DNN classifiers for researchers in machine learning theory, but it is incremental as it takes a first step without providing concrete results or numbers.
The paper investigates the noise sensitivity and stability of deep neural networks for binary classification by analyzing Boolean function sequences in common DNN models, extending these concepts to annealed and quenched versions due to inherent randomness.
A first step is taken towards understanding often observed non-robustness phenomena of deep neural net (DNN) classifiers. This is done from the perspective of Boolean functions by asking if certain sequences of Boolean functions represented by common DNN models are noise sensitive or noise stable, concepts defined in the Boolean function literature. Due to the natural randomness in DNN models, these concepts are extended to annealed and quenched versions. Here we sort out the relation between these definitions and investigate the properties of two standard DNN architectures, the fully connected and convolutional models, when initiated with Gaussian weights.