Statistics: high dimensional geometry, approximate Bayesian inferences.
Machine learning: statistical learning theory, theory of deep learning, generative modeling.
Applied probability: spin glass theory, random matrix theory.
Preprints
The generalization error of random features regression: Precise asymptotics and double descent curve. [Pdf] [Slides] Song Mei and Andrea Montanari, 2019.
Linearized two-layers neural networks in high dimension. [Pdf] [Slides] Behrooz Ghorbani, Song Mei, Theodor Misiakiewicz, and Andrea Montanari, 2019.
TAP free energy, spin glasses, and variational inference. [Pdf] [Slides] Zhou Fan, Song Mei, and Andrea Montanari, 2018.
Journal Publications
The landscape of the spiked tensor model. [Pdf] Gerard Ben Arous, Song Mei, Andrea Montanari, and Mihai Nica.
Communications on Pure and Applied Mathematics (CPAM), 2019.
A mean field view of the landscape of two-layers neural network. [Pdf] [Slides] [Poster] Song Mei, Andrea Montanari, and Phan-Minh Nguyen.
Proceedings of the National Academy of Sciences (PNAS), 2018.
The landscape of empirical risk for non-convex losses. [Pdf] [Slides] Song Mei, Yu Bai, and Andrea Montanari.
Annals of Statistics, 2018.
Conference Publications
Limitations of lazy training of two-layers neural networks. [Pdf] Behrooz Ghorbani, Song Mei, Theodor Misiakiewicz, and Andrea Montanari, 2019.
NeurIPS, 2019. Spotlight presentation.
Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit.[Pdf] [Slides] Song Mei, Theodor Misiakiewicz, and Andrea Montanari.
Conference on Learning Theory (COLT), 2019.
Solving SDPs for synchronization and MaxCut problems via the Grothendieck inequality. [Pdf] [Slides] [Poster] Song Mei, Theodor Misiakiewicz, Andrea Montanari, and Roberto I. Oliveira.
Conference on Learning Theory (COLT), 2017.
Others
On a molecular based Q-tensor model for liquid crystals with density variations. [Pdf] Song Mei and Pingwen Zhang.
SIAM Multiscale Modeling and Simulation, 2015. Undergraduate Thesis.
Analysis of sequential quadratic programming through the lens of Riemannian optimization. [Pdf] Yu Bai and Song Mei, 2018.
A nice short notes on first order constrained optimization.