Liam Madden

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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

  1. Best Approximate Quantum Compiling Problems
    Liam Madden, and Andrea Simonetto
    ACM Transactions on Quantum Computing, 2022
  2. Memory capacity of two layer neural networks with smooth activations
    Liam Madden, and Christos Thrampoulidis
    SIAM Journal on Mathematics of Data Science, 2024
  3. High-probability Convergence Bounds for Non-convex Stochastic Gradient Descent with Sub-Weibull noise
    Liam Madden, Emiliano Dall’Anese, and Stephen Becker
    Journal of Machine Learning Research, 2024
  4. Next-token Prediction Capacity: General Upper Bounds and a Lower Bound for Transformers
    Liam Madden, Curtis Fox, and Christos Thrampoulidis
    IEEE Transactions on Information Theory, 2025