[1] Sungjin Ahn, Anoop Korattikara, and Max Welling. Bayesian posterior sampling via stochastic gradient fisher scoring. In ICML, pages 1591-1598. PMLR, 2012.
[2] Zeyuan Allen-Zhu, Yuzhhi Li, and Yingyu Liang. Learning and generalization in overparameterized neural networks, going beyond two layers. In Advances in Neural Information Processing Systems, volume 32, 2019.
[3] Zeyuan Allen-Zhu, Yuanzhi Li, and Zhao Song. A convergence theory for deep learning via overparameterization. In ICML, pages 242-252. PMLR, 2019.
[4] Sanjeev Arora, Rong Ge, Behnam Neyshabur, and Yi Zhang. Stronger generalization bounds for deep nets via a compression approach. In ICML, pages 254-263. PMLR, 2018.
[5] Sanjeev Arora, Simon Du, Wei Hu, Zhiyuan Li, and Ruosong Wang. Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks. In ICML, pages 322-332. PMLR, 2019.
[6] Haim Avron and Sivan Toledo. Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix. Journal of the ACM (JACM), 58(2):1-34, 2011.
[7] Peter Bartlett, Dylan J Foster, and Matus Telgarsky. Spectrally-normalized margin bounds for neural networks. arXiv preprint arXiv:1706.08498, 2017.
[8] Jeremy Bernstein and Yisong Yue. Computing the information content of trained neural networks. arXiv preprint arXiv:2103.01045, 2021.
[9] Charles Blundell, Julien Cornebise, Koray Kavukcuoglu, and Daan Wierstra. Weight uncertainty in neural network. In ICML, pages 1613-1622. PMLR, 2015.
[10] Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. In Advances in Neural Information Processing Systems, volume 33, pages 1877–1901, 2020.
[11] Yuan Cao and Quanquan Gu. Generalization bounds of stochastic gradient descent for wide and deep neural networks. Advances in Neural Information Processing Systems, 32:10836-10846, 2019.
[12] Yuan Cao and Quanquan Gu. Generalization error bounds of gradient descent for learning overparameterized deep relu networks. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 3349-3356, 2020.
[13] O Catoni. Pac-bayesian supervised classification: The thermodynamics of statistical learning. institute of mathematical statistics lecture notes—monograph series 56. IMS, Beachwood, OH. MR2483528, 5544465, 2007.
[14] Tianqi Chen, Emily Fox, and Carlos Guestrin. Stochastic gradient hamiltonian monte carlo. In ICML, pages 1683-1691. PMLR, 2014.
[15] Eugenio Clerico, George Deligiannidis, and Arnaud Doucet. Conditional gaussian pac-bayes. arXiv preprint arXiv:2110.11886, 2021.
[16] Arnak S Dalalyan. Theoretical guarantees for approximate sampling from smooth and log-concave densities. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79(3):651-676, 2017.
[17] Monroe D Donsker and SR Srinivasa Varadhan. Asymptotic evaluation of certain markov process expectations for large time—iii. Communications on pure and applied Mathematics, 29(4):389–461, 1976.
[18] Simon Du, Jason Lee, Haochuan Li, Liwei Wang, and Xiyu Zhai. Gradient descent finds global minima of deep neural networks. In ICML, pages 1675-1685. PMLR, 2019.
[19] David Duvenaud, Dougal Maclaurin, and Ryan Adams. Early stopping as nonparametric variational inference. In Artificial Intelligence and Statistics, pages 1070-1077. PMLR, 2016.
[20] Ethan Dyer and Guy Gur-Ari. Asymptotics of wide networks from feynman diagrams. In International Conference on Learning Representations, 2020.