Xinyu (Rain) Wei 魏昕雨

I am a quantitative analyst at Capula Investment Management. I received my B.S. in Computer Science from Columbia University in 2024, summa cum laude. At Columbia, I was fortunate to be advised by John Wright, Kaizheng Wang, and Garud Iyengar.

I study how learning systems use structure in data to make better decisions. My research spans learning on low-dimensional manifolds, adaptive statistical estimation, and decision-focused optimization. I am also interested in how intelligent systems can represent individual expertise, update with new evidence, and reason under uncertainty.

I grew up in Hebei, China, moved to Sydney at 15, and later moved to New York for college and work. I am currently living and working in London. Outside work and research, I am a professional Latin dancer.

Xinyu Rain Wei in Columbia graduation attire

Research

TpopT: Efficient Trainable Template Optimization on Low-Dimensional Manifolds

J. Yan, S. Wang, X. R. Wei, J. Wang, Z. Márka, S. Márka, and J. Wright

TpopT replaces exhaustive template-bank search with trainable optimization on a low-dimensional signal manifold. I led the core theoretical analysis, establishing curvature-dependent convergence guarantees for Riemannian gradient descent under Gaussian noise and estimation bounds governed primarily by intrinsic dimension. The analysis characterizes its computational advantage over matched filtering.

Slab Certificate: Learning Noisy Manifold-Structured Data

T. Wang, X. R. Wei, and J. Wright

This project investigates neural-network learning from noisy observations near a low-dimensional manifold in the neural tangent kernel regime. The analysis seeks a small-norm certificate whose image under the kernel operator approximates the initial fitting error. I contributed proofs involving kernel concentration, local manifold geometry, and smooth-function approximation to this framework for studying training dynamics.

Adaptive Statistical Estimation and Multi-Task Learning

Research with Kaizheng Wang

I studied Gaussian multi-task estimation to characterize when pooling related tasks improves on separate estimation, deriving the bias–variance tradeoff and the role of task heterogeneity. In related work, I derived K-fold cross-validation estimators for regularized Gaussian mean estimation and evaluated their risk against maximum-likelihood, Bayesian, and oracle benchmarks using analytical calculations and Monte Carlo experiments.

End-to-End Variational Inference for Robust Portfolio Construction

X. R. Wei, G. Costa, and G. N. Iyengar

This work integrates a variational inference neural network with a Monte Carlo-based portfolio-optimization layer, training the predictive distribution using both statistical and downstream task losses. I derived gradient expressions using KKT-based implicit differentiation and contributed to the PyTorch implementation and synthetic-data experiments evaluating decision quality.

Patent

Professional experience

Capula Investment Management

I design LLM-based systems that translate investment hypotheses into executable research workflows, alongside statistical models and constrained optimization methods for systematic strategies and portfolio allocation. My work also spans derivatives pricing and computational infrastructure for research and risk analysis.

Education

Columbia University

Summa cum laude · GPA: 4.092

Bonomi Research Scholar (2023); Electrical Engineering Summer Research Grant (2023); Columbia Math Undergraduate Summer Research Fellowship (2022); Mathematical Modeling Research Grant (2021). Honor societies: Tau Beta Pi and Upsilon Pi Epsilon.

Courses taken

Meriden School

ATAR: 99.95 —  highest rank in Australia. HSC All-Round Achiever and Distinguished Achiever; High Distinction in the Australian Physics and Chemistry Olympiads (2018).

Teaching

Columbia University

Led office hours and assessed coursework for:

  • Machine Learning — COMS 4771
  • Computer Science Theory — COMS 3261
  • Discrete Mathematics — COMS 3203

Beyond research

Entrepreneurship

Axon

An AI venture focused on systems that learn from individual expertise and represent expert judgment. Co-founder and CTO.

Elite Youth Education

An international education company providing tutoring and academic support through a team of more than 70 tutors and staff. Founder and CEO.

Professional ballroom dance

International Latin Dance

I have trained professionally in International Latin dance since the age of four. I compete internationally and teach private and group lessons.

International and national competition results include a semifinal at The Open Worlds Latin Solo (2026), 3rd place in The Open Worlds Latin A (2025), and finalist titles at the United States Dance Championship, King’s Ball, and Emerald Ball. 

Competition awards · Dance photo library