learning. arXiv preprint arXiv:2001.04413, 2020a.

Zeyuan Allen-Zhu and Yuanzhi Li. Feature puriﬁcation: How adversarial training performs robust

deep learning. arXiv preprint arXiv:2005.10190, 2020b.

Zeyuan Allen-Zhu, Yuanzhi Li, and Zhao Song. A convergence theory for deep learning via over-
parameterization. In ICML, 2019. Full version available at http://arxiv.org/abs/1811.
03962.

Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. Layer normalization, 2016.
LORA