Graduate Education: PhD (UC Berkeley), MA (UC Berkeley), MS (MIT)

Academic Employment: Associate Professor of Economics (with tenure), UCSD, since July 2025; Assistant Professor of Economics, UCSD, 2019-2025; Assistant Professor of Statistics and Computer Science, Purdue University, West Lafayette, 2018-2019

Active Interests: LLM Post Training Theory, Scattered Data Approximation Theory, Reinforcement Learning, Invariance Learning, Economic AI Agents, Financial Markets

Past Research Areas: Mathematical Foundations of Machine Learning, Nonasymptotic Statistics, High-Dimensional Estimation and Inference, Semiparametric and Nonparametric Methods, Algorithmic Economics 

Curriculum Vitae 

To prospective PhD students: I do not operate a traditional, hierarchical lab. Instead, I view research as a direct partnership. When I work with a student, we act as true coauthors—co-developing an idea we are both genuinely excited about and tackling the execution side-by-side. If you are looking for a hands-on, highly collaborative environment where we build the project together from the ground up, our working styles will align well. 

Below, ** indicates papers that were either single authored or co-authored with a (former or current) student.

New Papers

1. Complementing reinforcement learning with SFT through logit averaging in the post training of LLMs** by Xingwei Gan, Ying Zhu (alphabetical ordering)

(We are currently exploring industry collaborations to test and scale the following findings to larger foundation models.)

• KL-Free & Critic-Free Architecture: Replaces explicit KL regularization and critic architectures by mixing trainable logits with frozen SFT reference logits during post-training.

• Compute Overhead Reduction: Eliminates the computational overhead of computing gradients for the explicit KL penalty term, maintaining memory footprints comparable to GRPO.

• Empirical Validation: Logit-averaging post training consistently outperforms canonical KL-regularized GRPO across reasoning benchmarks. On the Qwen2.5-Instruct 1.5B, 3B and 7B models, we achieve a 7% – 15% gain on MATH, 2% – 5% gain on cn_k12 and MMLU.

• Complementary Skill Composition: Couples a trainable reasoning policy with a frozen SFT anchor directly in the logit space, retaining SFT formatting rigor while allowing the trainable policy to reason more freely.

• Pathway to 1x Inference Deployment: The mixed policy acts as a high-capacity teacher to distill capabilities back into a single student network. This restores standard single-model inference latency and memory efficiency.

2. Approximating invariant functions with the sorting trick is theoretically justified** by Wee Chaimanowong, Ying Zhu (alphabetical ordering), R&R at SIAM Journal on Mathematics of Data Science (SIMODS)

• The Gap in AI Practice: In modern AI, models often need to process unordered data—such as 3D point clouds in autonomous driving (e.g., PointNet), molecular structures in Graph Neural Networks, or set-based Transformers. To handle this, developers widely use a practical "sorting trick" (a form of canonicalization) because it is computationally much faster and more efficient than calculating all possible data arrangements (group averaging). 

• The Mathematical Skepticism: Despite its widespread practical use, the mathematical foundation of this sorting trick has been heavily doubted because it breaks traditional rules; sorting data makes the underlying mathematical functions "rough" or jumpy (non-differentiable and discontinuous). 

• The Certification: This paper explores the approximation theory behind this practice and provides the formal mathematical certification that justifies using the sorting trick in machine learning and AI models.

• Error Reduction: This paper proves that sorting reorganizes the data points efficiently, which fundamentally reduces the model's overall approximation error by a significant factor. 

Publications and Accepted Papers

• Permutation Invariant Functions: Statistical Testing, Density Estimation and Metric Entropy** by Wee Chaimanowong, Ying Zhu (alphabetical ordering) - AISTATS 2025

• On the limitations of data-based price discrimination** by Haitian Xie, Ying Zhu, Denis Shishkin (Xie and Zhu share the first authorship and are listed alphabetically). 

  • Theoretical Economics, 2025

  • An extended abstract in ACM Economics and Computation 2024 (full paper peer refereed)

• Phase transitions in nonparametric regressions** by Ying Zhu - Accepted at Journal of Econometrics, 2023

• Omitted Variable Bias of Lasso-Based Inference Methods: A Finite Sample Analysis by Kaspar Wuthrich, Ying Zhu (alphabetical ordering) - The Review of Economics and Statistics, 2023

• Inference in Approximately Sparse Correlated Random Effects Probit Models with Panel Data by Jeffrey Wooldridge, Ying Zhu (alphabetical ordering) - The Journal of Business & Economic Statistics, 2020 

• High Dimensional Inference in Partially Linear Models by Ying Zhu, Zhuqing Yu, Guang Cheng,  AISTATS 2019

• Sparse Linear Models and l1-Regularized 2SLS with High-Dimensional Endogenous Regressors and Instruments** {Additional materials from 2013} by Ying Zhu - The Journal of Econometrics, 2018

• Nonasymptotic Analysis of Semiparametric Regression Models with High-Dimensional Parametric Coefficients** by Ying Zhu - The Annals of Statistics, 2017

• Nonparametric Density Estimation Based on Truncated Mean** by Ying Zhu - Statistics and Probability Letters, 2013 

Unpublished Manuscripts

• Classes of ODE Solutions: Smoothness, Covering Numbers, Implications for Noisy Function Fitting, and a "Loss of Smoothness" Phenomenon** by Ying Zhu, Mozhgan Mirzaei  

• Statistical Inference and Feasibility Determination: A Nonasymptotic Approach** by Ying Zhu