[21] K. Leino, Z. Wang, and M. Fredrikson. Globally-robust neural networks. In International Conference on Machine Learning, 2021.
[22] M. Li, Y. Wang, and Z. Lin. Cerdeq: Certifiable deep equilibrium model. In International Conference on Machine Learning, pages 12998-13013. PMLR, 2022.
[23] M. Li, Y. Wang, X. Xie, and Z. Lin. Optimization inspired multi-branch equilibrium models. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=nbC8iTTXIrk.
[24] Q. Li, S. Haque, C. Anil, J. Lucas, R. B. Grosse, and J.-H. Jacobsen. Preventing gradient attenuation in Lipschitz constrained convolutional networks. In Advances in Neural Information Processing Systems, 2019.
[25] Z. Ling, X. Xie, Q. Wang, Z. Zhang, and Z. Lin. Global convergence of over-parameterized deep equilibrium models. In International Conference on Artificial Intelligence and Statistics, pages 767-787. PMLR, 2023.
[26] A. Megretski and A. Rantzer. System analysis via integral quadratic constraints. IEEE Transactions on Automatic Control, 42(6):819-830, 1997.
[27] L. Meunier, B. Delattre, A. Araujo, and A. Allauzen. A dynamical system perspective for Lipschitz neural networks. In International Conference on Machine Learning, 2022.
[28] P. Micaelli, A. Vahdat, H. Yin, J. Kautz, and P. Molchanov. Recurrence without recurrence: Stable video landmark detection with deep equilibrium models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22814-22825, 2023.
[29] T. Miyato, T. Kataoka, M. Koyama, and Y. Yoshida. Spectral normalization for generative adversarial networks. In International Conference on Learning Representations, 2018.
[30] M. N. Müller, R. Staab, M. Fischer, and M. Vechev. Effective certification of monotone deep equilibrium models. arXiv preprint arXiv:2110.08260, 2021.
[31] C. Pabbaraju, E. Winston, and J. Z. Kolter. Estimating Lipschitz constants of monotone deep equilibrium models. In International Conference on Learning Representations, 2020.
[32] P. Pauli, A. Koch, J. Berberich, P. Kohler, and F. Allgower. Training robust neural networks using Lipschitz bounds. IEEE Control Systems Letters, 6:121-126, 2021.
[33] A. Pokle, Z. Geng, and J. Z. Kolter. Deep equilibrium approaches to diffusion models. Advances in Neural Information Processing Systems, 35:37975-37990, 2022.
[34] B. Prach and C. H. Lampert. Almost-orthogonal layers for efficient general-purpose Lipschitz networks. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022, Proceedings, Part XXI, pages 350–365. Springer, 2022.
[35] M. Revay, R. Wang, and I. R. Manchester. Lipschitz bounded equilibrium networks. arXiv preprint arXiv:2010.01732, 2020.
[36] H. Salman, J. Li, I. Razenshteyn, P. Zhang, H. Zhang, S. Bubeck, and G. Yang. Provably robust deep learning via adversarially trained smoothed classifiers. In Advances in Neural Information Processing Systems, 2019.
[37] S. Singla and S. Feizi. Skew orthogonal convolutions. In International Conference on Machine Learning, pages 9756-9766. PMLR, 2021.
[38] S. Singla and S. Feizi. Improved techniques for deterministic 12 robustness. In Advances in Neural Information Processing Systems, 2022.
[39] I. Sutskever, J. Martens, G. Dahl, and G. Hinton. On the importance of initialization and momentum in deep learning. In International conference on machine learning, pages 1139-1147. PMLR, 2013.
[40] C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus. Intriguing properties of neural networks. In International Conference on Learning Representations, 2014.
[41] A. Trockman et al. Orthogonalizing convolutional layers with the Cayley transform. In International Conference on Learning Representations, 2021.