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Better Representations via Adversarial Training in Pre-Training: A Theoretical Perspective

Yue Xing · Xiaofeng Lin · Qifan Song · Yi Xu · Belinda Zeng · Guang Cheng

MR1 & MR2 - Number 8
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Thu 2 May 8 a.m. PDT — 8:30 a.m. PDT


Pre-training is known to generate universal representations for downstream tasks in large-scale deep learning such as large language models. Existing literature, e.g., Kim et al. (2020), empirically observe that the downstream tasks can inherit the adversarial robustness of the pre-trained model. We provide theoretical justifications for this robustness inheritance phenomenon. Our theoretical results reveal that feature purification plays an important role in connecting the adversarial robustness of the pre-trained model and the downstream tasks in two-layer neural networks. Specifically, we show that (i) with adversarial training, each hidden node tends to pick only one (or a few) feature; (ii) without adversarial training, the hidden nodes can be vulnerable to attacks. This observation is valid for both supervised pre-training and contrastive learning. With purified nodes, it turns out that clean training is enough to achieve adversarial robustness in downstream tasks.

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