1. kan.png
    KAN: Kolmogorov-arnold networks
    Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljačić, Thomas Y Hou, and Max Tegmark
    arXiv:2404.19756, 2024
  2. optpde.png
    OptPDE: Discovering Novel Integrable Systems via AI-Human Collaboration
    Subhash Kantamneni, Ziming Liu, and Max Tegmark
    arXiv:2405.04484, 2024
  3. sid.png
    Interpretable conservation laws as sparse invariants
    Ziming Liu, Patrick Obin Sturm, Saketh Bharadwaj, Sam J. Silva, and Max Tegmark
    Phys. Rev. E, 2024
  4. resource.png
    A Resource Model For Neural Scaling Law
    Jinyeop Song, Ziming Liu, Max Tegmark, and Jeff Gore
    arXiv:2402.05164, 2024
  5. geneft.png
    GenEFT: Understanding Statics and Dynamics of Model Generalization via Effective Theory
    David D Baek, Ziming Liu, and Max Tegmark
    arXiv:2402.05916, 2024
  6. factorization.png
    Do Diffusion Models Learn Semantically Meaningful and Efficient Representations?
    Qiyao Liang, Ziming Liu, and Ila Fiete
    arXiv:2402.03305, 2024


  1. bimt.png
    Seeing is believing: Brain-inspired modular training for mechanistic interpretability
    Ziming Liu, Eric Gan, and Max Tegmark
    Entropy, 2023
  2. grokking_compression.png
    Grokking as Simplification: A Nonlinear Complexity Perspective
    Ziming Liu, Ziqian Zhong, and Max Tegmark
    In UniReps: the First Workshop on Unifying Representations in Neural Models , 2023
  3. hypernetwork.png
    Generating interpretable networks using hypernetworks
    Isaac Liao, Ziming Liu, and Max Tegmark
    arXiv:2312.03051, 2023
  4. growbrain.png
    Growing Brains in Recurrent Neural Networks for Multiple Cognitive Tasks
    Ziming Liu, Mikail Khona, Ila Fiete, and Max Tegmark
    In NeurIPS 2023 Workshop on Symmetry and Geometry in Neural Representations , 2023
  5. lottery.png
    A Neural Scaling Law from Lottery Ticket Ensembling
    Ziming Liu, and Max Tegmark
    arXiv preprint arXiv:2310.02258, 2023
  6. naturereview.png
    Scientific discovery in the age of artificial intelligence
    Nature, 2023
  7. pizza.png
    The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks
    Ziqian Zhong, Ziming Liu, Max Tegmark, and Jacob Andreas
    In Thirty-seventh Conference on Neural Information Processing Systems , 2023
  8. restart.png
    Restart Sampling for Improving Generative Processes
    Yilun Xu, Mingyang Deng, Xiang Cheng, Yonglong Tian, Ziming Liu, and Tommi S. Jaakkola
    In Thirty-seventh Conference on Neural Information Processing Systems , 2023
  9. pfgmpp.png
    PFGM++: Unlocking the Potential of Physics-Inspired Generative Models
    Yilun Xu, Ziming Liu, Yonglong Tian, Shangyuan Tong, Max Tegmark, and Tommi Jaakkola
    In Proceedings of the 40th International Conference on Machine Learning , 2023
  10. genphys.png
    Genphys: From physical processes to generative models
    Ziming Liu, Di Luo, Yilun Xu, Tommi Jaakkola, and Max Tegmark
    arXiv:2304.02637, 2023
  11. omnigrok.png
    Omnigrok: Grokking Beyond Algorithmic Data
    Ziming Liu, Eric J Michaud, and Max Tegmark
    In The Eleventh International Conference on Learning Representations , 2023
  12. precision.png
    Precision machine learning
    Eric J Michaud, Ziming Liu, and Max Tegmark
    Entropy, 2023
  13. quanta.png
    The Quantization Model of Neural Scaling
    Eric J Michaud, Ziming Liu, Uzay Girit, and Max Tegmark
    In Thirty-seventh Conference on Neural Information Processing Systems , 2023


  1. pfgm.png
    Poisson Flow Generative Models
    Yilun Xu, Ziming Liu, Max Tegmark, and Tommi S. Jaakkola
    In Advances in Neural Information Processing Systems , 2022
  2. tug.png
    Towards Understanding Grokking: An Effective Theory of Representation Learning
    Ziming Liu, Ouail Kitouni, Niklas Nolte, Eric J Michaud, Max Tegmark, and Mike Williams
    In Advances in Neural Information Processing Systems , 2022
  3. poincare2.png
    Machine learning conservation laws from differential equations
    Ziming Liu, Varun Madhavan, and Max Tegmark
    Phys. Rev. E, 2022
  4. ekhmc.png
    Second order ensemble Langevin method for sampling and inverse problems
    Ziming Liu, Andrew M Stuart, and Yixuan Wang
    arXiv:2208.04506, 2022
  5. hiddensymmetry.png
    Machine Learning Hidden Symmetries
    Ziming Liu, and Max Tegmark
    Phys. Rev. Lett., 2022


  1. nnphd.png
    Machine-learning nonconservative dynamics for new-physics detection
    Ziming Liu, Bohan Wang, Qi Meng, Wei Chen, Max Tegmark, and Tie-Yan Liu
    Phys. Rev. E, 2021
  2. pal.png
    Physics-Augmented Learning: A New Paradigm Beyond Physics-Informed Learning
    Ziming Liu, Yuanqi Du, Yunyue Chen, and Max Tegmark
    In NeurIPS 2021 AI for Science Workshop , 2021
  3. schpca.png
    Schrödinger principal-component analysis: On the duality between principal-component analysis and the Schrödinger equation
    Ziming Liu, Sitian Qian, Yixuan Wang, Yuxuan Yan, and Tianyi Yang
    Phys. Rev. E, 2021
  4. nnhydro.png
    Applications of deep learning to relativistic hydrodynamics
    Hengfeng Huang, Bowen Xiao, Ziming Liu, Zeming Wu, Yadong Mu, and Huichao Song
    Phys. Rev. Res., 2021
  5. poincare.png
    Machine Learning Conservation Laws from Trajectories
    Ziming Liu, and Max Tegmark
    Phys. Rev. Lett., 2021


  1. pca_limitation.png
    Robustness of principal component analysis of harmonic flow in heavy ion collisions
    Ziming Liu, Arabinda Behera, Huichao Song, and Jiangyong Jia
    Phys. Rev. C, 2020


  1. qhmc.png
    Quantum-inspired hamiltonian monte carlo for bayesian sampling
    Ziming Liu, and Zheng Zhang
    arXiv:1912.01937, 2019
  2. pcaflow.png
    Principal component analysis of collective flow in relativistic heavy-ion collisions
    Ziming Liu, Wenbin Zhao, and Huichao Song
    The European Physical Journal C, 2019