publications

2026

1. Preprint

   Rates of Estimation for Semi-supervised Learning with Latent Space Models*

   Guy Bresler, Alina Harbuzova, and Leqi Zhou

   2026

   In submission; manuscript available upon request.
2. arXiv

   Least-Squares Multi-Step Koopman Operator Learning for Model Predictive Control

   Liang Wu, Wallace Gian Yion Tan, Leqi Zhou, Richard D. Braatz, and Jan Drgona

   2026

   Abs arXiv

   MPC is widely used in real-time applications, but practical implementations are typically restricted to convex QP formulations to ensure fast and certified execution. Koopman-based MPC enables QP-based control of nonlinear systems by lifting the dynamics to a higher-dimensional linear representation. However, existing approaches rely on single-step EDMD. Consequently, prediction errors may accumulate over long horizons when the EDMD operator is applied recursively. Moreover, the multi-step prediction loss is nonconvex with respect to the single-step EDMD operator, making long-horizon model identification particularly challenging. This paper proposes a multi-step EDMD framework that directly learns the condensed multi-step state-control mapping required for Koopman-MPC, thereby bypassing explicit identification of the lifted system matrices and subsequent model condensation. The resulting identification problem admits a convex least-squares formulation. We further show that the problem decomposes across prediction horizons and state coordinates, enabling parallel computation and row-wise -regularization for automatic dictionary pruning. A non-asymptotic finite-sample analysis demonstrates that, unlike one-step EDMD, the proposed method avoids error compounding and yields error bounds that depend only on the target multi-step mapping. Numerical examples validate improved long-horizon prediction accuracy and closed-loop performance.

2025

1. arXiv

   Shotgun Assembly of Random Regular Graphs*

   Brice Huang, Elchanan Mossel, Nike Sun, Claire Zhang, and Leqi Zhou

   2025

   Abs arXiv

   Mossel and Ross (2019) introduce the shotgun assembly problem for random graphs: what radius $R$ ensures that the random graph $G$ can be uniquely recovered from its list of rooted $R$-neighborhoods, with high probability? Here we consider this question for random regular graphs of fixed degree $d\ge3$. A result of Bollobás (1982) implies efficient recovery at $R = (1 + \epsilon) \tfrac12 \log_{d-1}n$ with high probability — moreover, this recovery algorithm uses only a summary of the distances in each neighborhood. We show that using the full neighborhood structure gives a sharper bound \(R = \frac{\log n + \log\log n}{2\log(d-1)} + O(1),\) which we prove is tight up to the $O(1)$ term. One consequence of our proof is that if $G,H$ are independent graphs where $G$ follows the random regular law, then with high probability the graphs are non-isomorphic; furthermore, this can be efficiently certified by testing the $R$-neighborhood list of $H$ against the $R$-neighborhood of a single adversarially chosen vertex of $G$.