# Research

What is it that drives some people to do mathematics in the pursuit of knowledge so abstract it can be communicated to but a small group of people? The only answer I can give employs two words: mathematics is beautiful, and it is true.

— James Simons, Renaissance Technologies

My current research interests are (1) exchangeable structures, Bayesian nonparametric statistics, and machine learning (2) Coulomb gases and related dependent point processes (3) heavy-tailed random matrices. Below is a list of all of my research papers sorted by topic. They are not necessarily in chronological order.

## Bayesian Statistics and Neural Networks

• “Over-parameterised Shallow Neural Networks with Asymmetrical Node Scaling: Global Convergence Guarantees and Feature Learning”
Submitted (arXiv:2302.01002)
with François Caron, Fadhel Ayed, Hoil lee, Juho Lee, and Hongseok Yang.
• “Deep neural networks with dependent weights: Gaussian Process mixture limit, heavy tails, sparsity and compressibility”
Submitted (arXiv:2205.08187)
with Hoil lee, Fadhel Ayed, Juho Lee, Hongseok Yang, and François Caron.
• $\alpha$-Stable convergence of heavy-tailed infinitely-wide neural networks”
Advances in Applied Probability (to appear, issue 55.4, December 2023) (arXiv:2106.11064)
with Hoil Lee, Jiho Lee, and Hongseok Yang.
• “A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs”
Annales Henri Lebesgue (2021) 4:325-368
with Jiho Lee, Sam Staton, and Hongseok Yang.
Honorable mention poster, 12th International Conference on Bayesian Nonparametrics.