Tong Ding

PhD candidate in the department of mathematics, Purdue University
Advisor: Jianlin Xia

Contact

Office: MATH 707
ding158@purdue.edu

Research Interests

Numerical Linear Algebra Randomized Algorithms Machine Learning Scientific Computing
Date Updates
Job seeking I am actively seeking postdoc positions.
Oct 2025 Attended the SIAM Central States Section Annual Meeting.
Dec 2025 Will attend the CBMS Workshop at the University of Houston.
Feb 2026 Will attend the ICERM Workshop on Randomized Numerical Linear Algebra (RNLA).

Research

My research bridges NLA and ML by (i) exploiting matrix structure arising in NN training and (ii) developing RNLA methods for data compression. The goal is to design fast, stable optimizers and accelerate training from an NLA perspective.

CV (PDF)

Publications

  1. Matrix analysis for shallow ReLU neural network least-squares approximations
    Zhiqiang Cai, Tong Ding, Min Liu, and Jianlin Xia
    Status: In preparation for submission
  2. A Structure-Guided Gauss-Newton Method for Shallow ReLU Neural Network
    Zhiqiang Cai, Tong Ding, Min Liu, Xinyu Liu, and Jianlin Xia
    Status: Submitted
    arXiv

Working Papers

  1. Fast direct solver in shallow ReLU neural network
    Tong Ding, Jianlin Xia
    Status: In progress

Presentations

Talks

Lightning talk
Why Neural Network Optimization Matrices Are Ill-Conditioned and Why That’s Okay
Workshop on Network Algorithms, Analysis, and Learning for Science, Berkeley, CA
2025/11
Minisymposium talk
Matrix Analysis and Fast Solvers in Neural Networks
SIAM Central States Section Annual Meeting, Fayetteville, AR
2025/10
Session talk
Matrix Analysis for Shallow ReLU Neural Network Least-Squares Approximations
22nd Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO
2025
Minisymposium talk
A Structure-Guided Gauss-Newton Method for Shallow ReLU Neural Networks
International Conference on Preconditioning, Atlanta, GA
2024

Posters

CBMS Conference on Research at the Interface of Applied Mathematics and Machine Learning, Houston, TX
2025/12
NSF Computational Mathematics PI Meeting, Salt Lake City, UT
2025
NSF Computational Mathematics PI Meeting, Seattle, WA
2024
Purdue Undergraduate Research Exhibition, West Lafayette, IN
2019

Professional Activities

President, SIAM Student Chapter, Purdue University
2024–present
  • Organized annual student conferences (2024, 2025 and 2026)
  • Co-ran CCAM seminar series
  • Community building and professional development
SIAM Purdue Website →

Teaching

I am passionate about teaching mathematics and helping students develop deep understanding. My teaching philosophy centers on three core principles: building internal understanding of the subject rather than rote memorization, using an enthusiastic voice to engage and inspire students, and encouraging interaction with abstract concepts through both mental reasoning and hands-on coding.

Teaching Experience

MA 303: Differential Equations and Partial Differential Equations for Engineering and the Sciences
Role: Guest Lecturer | Spring 2025
Department of Mathematics, Purdue University
Delivered lectures for undergraduate students, prepared course materials, and facilitated class discussions on differential equations topics.
MA 16600: Calculus II
Role: Teaching Assistant | Spring 2020
Department of Mathematics, Purdue University
Led recitation sessions and held office hours to support students in mastering calculus concepts.
Graduate Grading
Role: Graduate Grader
Department of Mathematics, Purdue University
Graded coursework for MA 52700 (Advanced Mathematics for Engineers), MA 35100 (Linear Algebra), and MA 45000 (Abstract Algebra).

Current Involvement

Fall 2025: Actively answering student questions on Piazza, providing timely support and clarification on course concepts.

Personal

Activities

Indoor rock climbing
Climbing
Forever V2.
Snowboarding at ski resort
Snowboarding
Started it for the first time while attending the Copper Mountain conference. I was in the mountains, so why not?