How Does Cross-Layer Correlation in Deep Neural Networks Influence Generalization and Adversarial Robustness?
Keywords: Deep Neural Network, Generalization, Adversarial Robustness
TL;DR: Addressing the problem of the impact of weight correlation across layers to the generalization and adversarial robustness for Deep Neural Networks.
Abstract: \textit{Generalization} and \textit{adversarial robustness} are two critical concepts in machine learning. Understanding the key factors that affect the trade-off between these concepts is essential for guiding architectural design and developing training strategies, such as adversarial training, especially for deep neural networks. In this paper, we investigate the impact of cross-layer correlations in weight matrices on both generalization and adversarial robustness. We provide a theoretical analysis demonstrating that increasing cross-layer correlations leads to a monotonic increase in the generalization gap. Furthermore, we establish a connection between adversarial risk and natural risk. Leveraging this connection, we show that in linear models, higher cross-layer correlations also degrade adversarial robustness. Finally, we validate our theoretical findings through experiments conducted on MLPs.
Primary Area: learning theory
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Submission Number: 2650
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