I am a PhD student in the Department of Mathematics at UC San Diego (since 2023), working with Prof. Alex Cloninger, Prof. Rahul Parhi, and Prof. Yu-Xiang Wang on deep learning research. Before turning to deep learning, I worked in algebraic topology and algebraic geometry. I received both my B.S. and M.S. degrees in Mathematics from Southern University of Science and Technology, where I was advised by Prof. Yifei Zhu.

My research studies how gradient-based training writes information into neural networks. A central theme in my recent work is that gradient descent naturally induces certain forms of internal representation, and these forms determine whether a network learns reusable structure or memorizes individual samples. Through the lens of dynamical stability, I identified neural shattering: a memorizing representation that emerges during training, where networks fit data through highly sample-specific features. I then studied how data geometry and architecture can suppress or amplify this behavior.

I am currently extending this viewpoint to modern deep learning systems, including sparse architecture design for vision models and memorization in multimodal generation.

Papers

Does Sparse Connectivity Improve Generalization? Convolutional Networks Below the Edge of Stability
Tongtong Liang, Esha Singh, Rahul Parhi, Alexander Cloninger, Yu-Xiang Wang
Preprint · arXiv

IsoCompute Playbook: Optimally Scaling Sampling Compute for LLM RL
Zhoujun Cheng, Yutao Xie, Yuxiao Qu, Amrith Setlur, Shibo Hao, Varad Pimpalkhute, Tongtong Liang, Feng Yao, Zhengzhong Liu, Eric Xing, Virginia Smith, Ruslan Salakhutdinov, Zhiting Hu, Taylor Killian, Aviral Kumar
ICML 2026 · arXiv · blog

Generalization Below the Edge of Stability: The Role of Data Geometry
Tongtong Liang, Alexander Cloninger, Rahul Parhi, Yu-Xiang Wang
ICLR 2026 · arXiv

Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon
Tongtong Liang, Dan Qiao, Yu-Xiang Wang, Rahul Parhi
NeurIPS 2025 Spotlight · arXiv