Geometric origin of adversarial vulnerability in deep learning
Balancing training accuracy and adversarial robustness has beeen a challenge since the birth of deep learning. Here, we introduce a geometry-aware deep learning framework that leverages layer-wise local training to sculpt the internal representations of deep neural networks. This framework promotes intra-class compactness and inter-class separation in feature space, leading to manifold smoothness and adversarial robustness against white or black box attacks. The performance can be explained by \blue{data-dependent statistical mechanics of integrating out the network parameters}, \blue{supplemented by a phenomenological model} with Hebbian coupling between elements of the hidden representation. Based on the current geometry-aware learning framework, the deep network can assimilate new information into existing knowledge structures while reducing representation interference.