Portrait of Liu Ziyin

Liu Ziyin

Email: liu.ziyin.p (at) gmail.com / ziyinl (at) mit.edu
Office: Room 26-209, MIT

I am a researcher at MIT and NTT Research. My research lies at the mysterious-and-fantastic union and intersection of mathematics, physics, neuroscience and artificial intelligence. At MIT, I work with Prof. Isaac Chuang. I also collaborate with Prof. Tomaso Poggio in the BCS department. My research focus is on the theoretical foundation of deep learning. Prior to coming to MIT, I received my PhD in physics at the University of Tokyo under the supervision of Prof. Masahito Ueda. I received a Bachelor's degree in physics and mathematics at Carnegie Mellon University. I also serve as an Area Chair for NeurIPS and ICLR. Personally, I am interested in art, literature, and philosophy. I also play Go. If you have questions or want to collaborate, or just want to say hi, feel free to send an email.

About my name: My first name is Ziyin and last name is Liu, though on publications I stick to the the eastern convention of [last name] [first name]. So please feel free to call me Ziyin or Dr. Liu, but when adding my name to publications write "Liu Ziyin."

Talks I gave recently:
Universal Phenomena, Irreversibility, and Thermodynamics in Deep Representation Learning
How does physics help understand deep learning?

Doctor thesis: Symmetry breaking in deep learning (深層学習に於ける対称性の破れ, 2023).
Master thesis: Mean-field learning dynamics of deep neural networks (2020).

Research Interest

I am particularly interested identifying scientific principles of artificial intelligence (what is a principle?), and I think tools and intuitions from other fields of sciences an be of great help. Broadly speaking, I work to advance the following fields

For my selected works, see below, and for my full list of publication and preprints, see publications.

NTT interns I work(ed) with

Tutorial / Notes

Proof of a perfect platonic representation hypothesis (2025)

Selected Work

(* denotes equal contribution or corresponding author)

  1. A universal compression theory: Lottery ticket hypothesis and superpolynomial scaling laws [arXiv]
    Hong-Yi Wang, Di Luo, Tomaso Poggio, Isaac L. Chuang, Liu Ziyin*
    ICLR 2026
  2. Topological Invariance and Breakdown in Learning [arXiv]
    Yongyi Yang, Tomaso Poggio, Isaac Chuang, Liu Ziyin*
    3. Topological invariance demo 1
    Topological invariance demo 2
    Topological invariance demo 3
  3. Neural Thermodynamics I: Entropic Forces in Deep and Universal Representation Learning [arXiv]
    Liu Ziyin*, Yizhou Xu*, Isaac Chuang
    NeurIPS 2025
  4. Heterosynaptic Circuits Are Universal Gradient Machines [arXiv]
    Liu Ziyin, Isaac Chuang, Tomaso Poggio
    Preprint 2025
  5. Parameter Symmetry Potentially Unifies Deep Learning Theory [arXiv]
    Liu Ziyin, Yizhou Xu, Tomaso Poggio, Isaac Chuang
    Preprint 2025
  6. Formation of Representations in Neural Networks [paper]
    Liu Ziyin, Isaac Chuang, Tomer Galanti, Tomaso Poggio
    ICLR 2025 (spotlight: 5% of all submissions)
  7. Parameter Symmetry and Noise Equilibrium of Stochastic Gradient Descent [arXiv]
    Liu Ziyin, Mingze Wang, Hongchao Li, Lei Wu
    NeurIPS 2024
  8. Symmetry Induces Structure and Constraint of Learning [arXiv]
    Liu Ziyin
    ICML 2024
  9. Sparsity by Redundancy: Solving L1 with SGD [arXiv]
    Liu Ziyin*, Zihao Wang*
    ICML 2023
  10. SGD Can Converge to Local Maxima [arXiv]
    Liu Ziyin, Botao Li, James B. Simon, Masahito Ueda
    ICLR 2022 (spotlight: 5% of all submissions)
  11. Neural Networks Fail to Learn Periodic Functions and How to Fix It [arXiv]
    Liu Ziyin, Tilman Hartwig, Masahito Ueda
    NeurIPS 2020

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