[16] Boaz Barak, Benjamin L Edelman, Surbhi Goel, Sham M Kakade, Cyril Zhang, et al. Hidden progress in deep learning: Sgd learns parities near the computational limit. In Advances in Neural Information Processing Systems, 2022.
[17] Peter L Bartlett, Philip M Long, Gábor Lugosi, and Alexander Tsigler. Benign overfitting in linear regression. Proceedings of the National Academy of Sciences, 2020.
[18] Alberto Bietti, Joan Bruna, Clayton Sanford, and Min Jae Song. Learning single-index models with shallow neural networks. Advances in Neural Information Processing Systems, 2022.
[19] Avrim Blum and Ronald L Rivest. Training a 3-node neural network is np-complete. In Advances in neural information processing systems, pages 494-501, 1989.
[20] Yuan Cao and Quanquan Gu. Generalization bounds of stochastic gradient descent for wide and deep neural networks. Advances in Neural Information Processing Systems, 2019.
[21] Yuan Cao, Zhiying Fang, Yue Wu, Ding-Xuan Zhou, and Quanquan Gu. Towards understanding the spectral bias of deep learning, 2020.
[22] Yuan Cao, Zixiang Chen, Misha Belkin, and Quanquan Gu. Benign overfitting in two-layer convolutional neural networks. In Alice H. Oh, Alekh Agarwal, Danielle Belgrave, and Kyunghyun Cho, editors, Advances in Neural Information Processing Systems, 2022.
[23] Niladri S Chatterji, Philip M Long, and Peter L Bartlett. When does gradient descent with logistic loss find interpolating two-layer networks? Journal of Machine Learning Research, pages 1-48, 2021.
[24] Minshuo Chen, Haoming Jiang, Wenjing Liao, and Tuo Zhao. Efficient approximation of deep relu networks for functions on low dimensional manifolds. Advances in neural information processing systems, 32:8174-8184, 2019.
[25] Minshuo Chen, Haoming Jiang, Wenjing Liao, and Tuo Zhao. Nonparametric regression on low-dimensional manifolds using deep relu networks: Function approximation and statistical recovery. arXiv preprint arXiv:1908.01842, 2019.
[26] Minshuo Chen, Yu Bai, Jason D Lee, Tuo Zhao, Huan Wang, Caiming Xiong, and Richard Socher. Towards understanding hierarchical learning: Benefits of neural representations. arXiv preprint arXiv:2006.13436, 2020.
[27] Zhengdao Chen, Eric Vanden-Eijnden, and Joan Bruna. On feature learning in neural networks with global convergence guarantees. In International Conference on Learning Representations, 2022.
[28] Lenaic Chizat and Francis Bach. On the global convergence of gradient descent for overparameterized models using optimal transport. Advances in neural information processing systems, 31, 2018.
[29] Lenaic Chizat and Francis Bach. A note on lazy training in supervised differentiable programming. arXiv preprint arXiv:1812.07956, 2018.
[30] Lenaic Chizat and Francis Bach. Implicit bias of gradient descent for wide two-layer neural networks trained with the logistic loss. In Conference on Learning Theory. PMLR, 2020.
[31] Lenaic Chizat, Edouard Oyallon, and Francis Bach. On lazy training in differentiable programming. In Advances in Neural Information Processing Systems, 2019.
[32] Alexandru Damian, Jason Lee, and Mahdi Soltanolkotabi. Neural networks can learn representations with gradient descent. In Conference on Learning Theory. PMLR, 2022.
[33] Amit Daniely and Eran Malach. Learning parities with neural networks. Advances in Neural Information Processing Systems, 33, 2020.
[34] Amit Daniely and Gal Vardi. Hardness of learning neural networks with natural weights. Advances in Neural Information Processing Systems, 33:930-940, 2020.