Liam Madden
Postdoctoral Fellow
I am an applied mathematician working in probability theory, linear algebra, and real analysis with applications to machine learning, quantum computing, and optimization. My work can be categorized into five main projects: time-varying optimization, quantum circuit compilation, stochastic optimization, memory capacity, and next-token prediction capacity. I received my BS from California Polytechnic State University in 2017 with a double major in Mechanical Engineering and Mathematics. I received my MS from the Department of Applied Mathematics at the University of Colorado Boulder in 2020 and my PhD in 2022, advised by Emiliano Dall’Anese and Stephen Becker. I held a Data Science Institute Postdoctoral Fellowship at the University of British Columbia from 2022-2024, supervised by Christos Thrampoulidis and Mark Schmidt. In my free time, I enjoy walking in the woods, composing poems, and dancing with friends.
selected publications
- Bounds For the Tracking Error of First-Order Online Optimization MethodsJournal of Optimization Theory and Applications, 2021
- Best Approximate Quantum Compiling ProblemsACM Transactions on Quantum Computing, 2022
- Memory capacity of two layer neural networks with smooth activationsSIAM Journal on Mathematics of Data Science, 2024
- High-probability Convergence Bounds for Non-convex Stochastic Gradient Descent with Sub-Weibull noiseJournal of Machine Learning Research, 2024
- Upper and lower memory capacity bounds of transformers for next-token predictionarXiv preprint arXiv:2405.13718, 2024