[16] Alberto Bietti, Joan Bruna, Clayton Sanford, and Min Jae Song. Learning single-index models with shallow neural networks. arXiv preprint arXiv:2210.15651, 2022.
[17] Nicolas Boumal. An introduction to optimization on smooth manifolds. Cambridge University Press, 2023. doi: 10.1017/9781009166164. URL https://www.nicolasboumal.net/book.
[18] Alon Brutzkus and Amir Globerson. Globally optimal gradient descent for a convnet with gaussian inputs. arXiv preprint arXiv:1702.07966, 2017.
[19] Fan Chen, Zhenjie Ren, and Songbo Wang. Uniform-in-time propagation of chaos for mean field Langevin dynamics, 2023.
[20] Minshuo Chen, Yu Bai, Jason D Lee, Tuo Zhao, Huan Wang, Caiming Xiong, and Richard Socher. Towards understanding hierarchical learning: Benefits of neural representations. Neural Information Processing Systems (NeurIPS), 2020.
[21] 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.
[22] Lenaic Chizat and Francis Bach. A note on lazy training in supervised differentiable programming. arXiv preprint arXiv:1812.07956, 8, 2018.
[23] Alexandru Damian, Jason Lee, and Mahdi Soltanolkotabi. Neural networks can learn representations with gradient descent. In Conference on Learning Theory, pages 5413-5452. PMLR, 2022.
[24] Hadi Daneshmand, Jonas Kohler, Aurelien Lucchi, and Thomas Hofmann. Escaping saddles with stochastic gradients. In International Conference on Machine Learning, pages 1155-1164. PMLR, 2018.
[25] Amit Daniely and Eran Malach. Learning parities with neural networks. Advances in Neural Information Processing Systems, 33:20356-20365, 2020.
[26] Amit Daniely, Roy Frostig, and Yoram Singer. Toward deeper understanding of neural networks: The power of initialization and a dual view on expressivity. In Advances In Neural Information Processing Systems, pages 2253-2261, 2016.
[27] Kefan Dong and Tengyu Ma. Toward  $l_{\infty}$ -recovery of nonlinear functions: A polynomial sample complexity bound for gaussian random fields. arXiv preprint arXiv:2305.00322, 2023.
[28] Xialiang Dou and Tengyuan Liang. Training neural networks as learning data-adaptive kernels: Provable representation and approximation benefits. Journal of the American Statistical Association, 116(535):1507-1520, 2021.
[29] Simon S Du and Jason D Lee. On the power of over-parametrization in neural networks with quadratic activation. International Conference on Machine Learning (ICML), 2018.
[30] Simon S Du, Jason D Lee, Haochuan Li, Liwei Wang, and Xiyu Zhai. Gradient descent finds global minima of deep neural networks. arXiv preprint arXiv:1811.03804, pages 1675-1685, November 2018.
[31] Wolfgang Gabcke. New derivation and explicit remainder estimation of the Riemann-Siegel formula. PhD thesis, Georg-August-Universityität Göttingen, 1979.
[32] Rong Ge, Furong Huang, Chi Jin, and Yang Yuan. Escaping from saddle points—online stochastic gradient for tensor decomposition. In Conference on Learning Theory, COLT 2015, pages 797–842, 2015.
[33] Rong Ge, Jason D Lee, and Tengyu Ma. Learning one-hidden-layer neural networks with landscape design. arXiv preprint arXiv:1711.00501, 2017.
[34] Behrooz Ghorbani, Song Mei, Theodor Misiakiewicz, and Andrea Montanari. When do neural networks outperform kernel methods? Advances in Neural Information Processing Systems, 33: 14820-14830, 2020.