Zong Shang — CREST-ENSAE, Institut Polytechnique de Paris

Interests

• Feature Space Decomposition (FSD) for refined uniform-convergence analyses of non-asymptotic population excess risk in supervised learning.

• Benign overfitting and related phenomena in modern statistical learning theory.

• New mathematical developments inspired by statistical learning learning, especially in empirical process theory and the geometry of Banach spaces.

I am interested in the foundational questions that may shape the future of mathematical statistics.
If you have perspectives on where the field should go, I would be glad to exchange ideas.

Publications

• A geometrical viewpoint on the benign overfitting and self-induced regularization properties of the minimum \ell_2-norm interpolant estimator, Probability Theory and Related Fields, 2022, with G.Lecué.

• A Geometrical Analysis of kernel ridge regression  and its applications, Annals of Statistics, to appear, with G. Gavrilopoulos and G.Lecué, invited poster at NeurIPS 2025 upon recommendation by the Editors of the Annals of Statistics

All papers are listed in lexicographic order.

Preprints

• Upper bounds for the Lq empirical process via generic chaining, arXiv 2511.06338, submitted. Here is an introduction of this paper.

Working papers

• Feature Space Decomposition I: Benign overfitting property of the minimum norm interpolant estimator in regression and classification, with G.Lecué.

• Feature Space Decomposition II: Spectral Algorithm and generalized saturation effect, with G.Lecué and  Z. Li , Preprint available upon request. Here is an introduction to this work.

• Generalization Error of Mean Field Shallow Neural Networks, with G.Lecué, T. Suzuki and, T. Wakayama, Preprint available upon request. Here is an introduction to this work.

Long-term visiting

• Center for Statistical Science, Tsinghua University, China. Host by Qian Lin. Dec 2023 - Jan 2024. Outcome: Research paper.

• RIKEN-AIP, Japan. Host by Taiji Suzuki. Funded by RIKEN-AIP Overseas Student Collaboration Program. Aug 2025 - Oct 2025. Outcome: Research paper.

• Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland. Host by Radoslaw Adamczak. Funded by Erasmus+ PhD mobility grant. Oct 2025 - Dec 2025.

Talks

• Center for Statistical Science, Tsinghua University, China, 2023.

• RIKEN - AIP, Tokyo University, Japan, 2024.

• Seminar on Probability Theory and Mathematical Statistics, Department of Mathematics, Bielefeld University, Germany, 2024.

• Meeting in Mathematical Statistics, Rencontres de Statistique Mathématique, New challenges in high-dimensional statistics, CIRM, France, 2024.

• Seminar Series on the Mathematics of Data Science  - Department of Applied Mathematics, Twente, Netherlands, 2025.

• Seminar of Probability Group, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland, 2025.

• Meeting in Mathematical Statistics, Rencontres de Statistique Mathématique, Statistical thinking in the age of AI: decision-making and reliability, CIRM, France, 2025.

Teaching

• AI-CS1013 - M3 - Integrals & Differential Calculus - TD, Bachelor in Artificial Intelligence, Data and Management Sciences, 2025 Spring, CentraleSupélec, Paris Saclay.

Grants

• Visiting Grant, RIKEN-AIP Overseas Student Collaboration Program, 2025.

• Visiting Grant, Erasmus+ PhD mobility grant, 2025.

• PhD-track fellowship by Institut Polytechnique de Paris, 2021-2023.

• PhD early call fellowship by l'Ecole Doctorale de Mathématiques Hadamard (EDMH), 2023-2026.