Geometric origin of adversarial vulnerability in deep learning

Yixiong Ren; Wenkang Du; Jianhui Zhou; Haiping Huang

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arXiv · 2509.01235

Geometric origin of adversarial vulnerability in deep learning

Yixiong Ren·Wenkang Du·Jianhui Zhou·Haiping Huang

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Abstract

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.

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Yixiong Ren, Wenkang Du, Jianhui Zhou, Haiping Huang. 2026-07-20. Geometric origin of adversarial vulnerability in deep learning. https://arxiv.org/abs/2509.01235

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