Publications

Conferences:

1. Y. Du, Z. Ling, R. C. Qiu, Z. Liao, “High-dimensional Learning Dynamics of Deep Neural Nets in the Neural Tangent Regime”, High-dimensional Learning Dynamics Workshop, The Fortieth International Conference on Machine Learning (ICML'2023), 2023.

2. Z. Ling, Z. Liao, R. C. Qiu, “On the Equivalence Between Implicit and Explicit Neural Networks: A High-dimensional Viewpoint”, High-dimensional Learning Dynamics Workshop, The Fortieth International Conference on Machine Learning (ICML'2023), 2023.

3. L. Gu, Y. Du, Y. Zhang, D. Xie, S. Pu, R. C. Qiu, Z. Liao, ““Lossless” Compression of Deep Neural Networks: A High-dimensional Neural Tangent Kernel Approach”, The 36th Conference on Neural Information Processing Systems (NeurIPS'2022), 2022.

4. H. Tiomoko, Z. Liao, R. Couillet, “Random matrices in service of ML footprint: ternary random features with no performance loss”, The Tenth International Conference on Learning Representations (ICLR'2022), 2022. preprint

5. Z. Liao, M. W. Mahoney, “Hessian Eigenspectra of More Realistic Nonlinear Models” (oral), The 35th Conference on Neural Information Processing Systems (NeurIPS'2021), 2021. preprint

6. M. Dereziński, Z. Liao, E. Dobriban, M. W. Mahoney, “Sparse sketches with small inversion bias”, The 34th Annual Conference on Learning Theory (COLT'2021), 2021. preprint

7. F. Liu, Z.Liao, J. A.K. Suykens, “Kernel regression in high dimension: Refined analysis beyond double descent”, The 24th International Conference on Artificial Intelligence and Statistics (AISTATS'2021), 2021. preprint

8. Z.Liao, R. Couillet, M. W. Mahoney, “Sparse Quantized Spectral Clustering” (spotlight), The Ninth International Conference on Learning Representations (ICLR'2021), 2021. poster, slides, and preprint

9. Z.Liao, R. Couillet, M. W. Mahoney, “A Random Matrix Analysis of Random Fourier Features: Beyond the Gaussian Kernel, A Precise Phase Transition, and the Corresponding Double Descent”, The 34th Conference on Neural Information Processing Systems (NeurIPS'2020), Vancouver, Canada, 2020. poster and preprint

10. M. Dereziński, F. Liang, Z. Liao, M. W. Mahoney, “Precise expressions for random projections: Low-rank approximation and randomized Newton”, The 34th Conference on Neural Information Processing Systems (NeurIPS'2020), Vancouver, Canada, 2020. preprint

11. Z.Liao, R. Couillet, “On Inner-product Kernels of High Dimensional Data”, IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP'2019), Guadeloupe, French West Indies, 2019. preprint

12. X. Mai, Z. Liao, R. Couillet, “A Large Scale Analysis of Logistic Regression: Asymptotic Performance and New Insights”, 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'2019), Brighton, UK, 2019. poster and preprint

13. R. Couillet, Z. Liao, X. Mai, “Classification Asymptotics in the Random Matrix Regime”, The 26th European Signal Processing Conference (EUSIPCO'2018), Rome, Italy, 2018. preprint

14. Z. Liao, R. Couillet, “On the Spectrum of Random Features Maps of High Dimensional Data”, Proceedings of the 35th International Conference on Machine Learning (ICML'2018), Stockholm, Sweden, 2018. (long talk) slides and preprint

15. Z. Liao, R. Couillet, “The Dynamics of Learning: A Random Matrix Approach”, Proceedings of the 35th International Conference on Machine Learning (ICML'2018), Stockholm, Sweden, 2018. (long talk) slides and preprint

16. Z. Liao, R. Couillet, “Random Matrices Meet Machine Learning: A Large Dimensional Analysis of LS-SVM”, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'2017), New Orleans, USA, 2017. slides and preprint

Journals:

1. J. Wang, S. Zhang, J. Cai, Z. Liao, C. Arenz, R. Betzholz, “Robustness of random-control quantum-state tomography”, Physical Review A 108 (2 Aug. 2023), 022408. preprint

2. Y. Chitour, Z. Liao, R. Couillet, “A geometric approach of gradient descent algorithms in linear neural networks”, Mathematical Control and Related Fields, 13(3) (2023), 918–945. preprint

3. Z.Liao, R. Couillet, M. W. Mahoney, “A random matrix analysis of random Fourier features: beyond the Gaussian kernel, a precise phase transition, and the corresponding double descent”, Journal of Statistical Mechanics: Theory and Experiment 2021(12) (Dec. 2021), 124006. preprint

4. Z. Liao, R. Couillet, “A Large Dimensional Analysis of Least Squares Support Vector Machines”, IEEE Transactions on Signal Processing 67 (4) (Feb. 2019), 1065-1074. (University of Paris-Saclay ED STIC Ph.D. Paper Award) preprint and supplementary material

5. C. Louart, Z. Liao, R. Couillet, “A Random Matrix Approach to Neural Networks”, The Annals of Applied Probability 28 (2) (Apr. 2018), 1190-1248. preprint

Preprints:

• W. Yang, Z. Wang, Z. Ling, H. Tiomoko Ali, R. C. Qiu, Z. Liao “Asymptotic Consistency of ESPRIT DoA Estimation with Large Arrays”, 2023.

• Z. Liao, Y. Xia, C. Niu, Y. Xiao, “Analysis and Approximate Inference of Large and Dense Random Kronecker Graphs”, 2023.

• Y. Song, K. Wan, Z. Liao, G. Caire, “An Achievable and Analytic Solution to Information Bottleneck for Gaussian Mixtures”, 2023.

• Z. Feng, Y. Wang, J. Li, F. Yang, J. Lou, T. Mi, R. C. Qiu, Z. Liao, “Robust and Communication-Efficient Federated Domain Adaptation via Random Features”, 2023.

• Z. Liao, R. Couillet, “Inner-product Kernels are Asymptotically Equivalent to Binary Discrete Kernels”, 2019.

• X. Mai, Z. Liao, “High Dimensional Classification via Regularized and Unregularized Empirical Risk Minimization: Precise Error and Optimal Loss”, 2019.

Ph.D. thesis:

Z. Liao, “A random matrix framework for large dimensional machine learning and neural networks”, CentraleSupélec, University Paris-Saclay, September 2019. [slides]