[1] Behnam Neyshabur, Ryota Tomioka, and Nathan Srebro. Norm-based capacity control in neural networks. In Peter Grünwald, Elad Hazan, and Satyen Kale, editors, Proceedings of The 28th Conference on Learning Theory, volume 40 of Proceedings of Machine Learning Research, pages 1376-1401, Paris, France, 03-06 Jul 2015. PMLR.
[2] Behnam Neyshabur, Russ R Salakhutdinov, and Nati Srebro. Path-sgd: Path-normalized optimization in deep neural networks. In C. Cortes, N. Lawrence, D. Lee, M. Sugiyama, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 28. Curran Associates, Inc., 2015.
[3] Tolga Ergen and Mert Pilanci. Convex geometry of two-layer relu networks: Implicit autoencoding and interpretable models. In Silvia Chiappa and Roberto Calandra, editors, Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, volume 108 of Proceedings of Machine Learning Research, pages 4024-4033, Online, 26-28 Aug 2020. PMLR.
[4] Tolga Ergen and Mert Pilanci. Convex geometry and duality of over-parameterized neural networks. Journal of Machine Learning Research, 22(212):1-63, 2021.
[5] T. Ergen and M. Pilanci. Convex optimization for shallow neural networks. In 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 79-83, 2019.
[6] Mert Pilanci and Tolga Ergen. Neural networks are convex regularizers: Exact polynomial-time convex optimization formulations for two-layer networks. In Hal Daumé III and Aarti Singh, editors, Proceedings of the 37th International Conference on Machine Learning, volume 119 of Proceedings of Machine Learning Research, pages 7695-7705. PMLR, 13-18 Jul 2020.
[7] Shai Shalev-Shwartz, Ohad Shamir, and Shaked Shammah. Failures of gradient-based deep learning. arXiv preprint arXiv:1703.07950, 2017.
[8] Ian Goodfellow, *Yoshua Bengio*, Aaron Courville, and *Yoshua Bengio. Deep learning*, volume 1. MIT press Cambridge, 2016.
[9] Rong Ge, Jason D. Lee, and Tengyu Ma. Learning one-hidden-layer neural networks with landscape design, 2017.
[10] Itay Safran and Ohad Shamir. Spurious local minima are common in two-layer relu neural networks. In International Conference on Machine Learning, pages 4433-4441. PMLR, 2018.
[11] Animashree Anandkumar and Rong Ge. Efficient approaches for escaping higher order saddle points in non-convex optimization. In Conference on learning theory, pages 81–102, 2016.
[12] Bhaskar DasGupta, Hava T Siegelmann, and Eduardo Sontag. On the complexity of training neural networks with continuous activation functions. IEEE Transactions on Neural Networks, 6(6):1490-1504, 1995.
[13] 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.
[14] Peter Bartlett and Shai Ben-David. Hardness results for neural network approximation problems. In European Conference on Computational Learning Theory, pages 50-62. Springer, 1999.
[15] Alon Brutzkus, Amir Globerson, Eran Malach, and Shai Shalev-Shwartz. SGD learns over-parameterized networks that provably generalize on linearly separable data. CoRR, abs/1710.10174, 2017.
[16] Simon S Du and Jason D Lee. On the power of over-parametrization in neural networks with quadratic activation. arXiv preprint arXiv:1803.01206, 2018.
[17] Sanjeev Arora, Nadav Cohen, and Elad Hazan. On the optimization of deep networks: Implicit acceleration by overparameterization. In 35th International Conference on Machine Learning, ICML 2018, pages 372-389. International Machine Learning Society (IMLS), 2018.
[18] Behnam Neyshabur, Zhiyuan Li, Srinadh Bhojanapalli, Yann LeCun, and Nathan Srebro. Towards understanding the role of over-parametrization in generalization of neural networks. arXiv preprint arXiv:1805.12076, 2018.
[19] Yifei Wang, Tolga Ergen, and Mert Pilanci. Parallel deep neural networks have zero duality gap. In The Eleventh International Conference on Learning Representations, 2023.