6 citations · 6 across the 1 of their papers we have counts for
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Hessian Eigenspectra of More Realistic Nonlinear Models
Zhenyu Liao, Michael W. Mahoney
Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model…
Sparse Quantized Spectral Clustering
Zhenyu Liao, Romain Couillet, Michael W. Mahoney
Given a large data matrix, sparsifying, quantizing, and/or performing other entry-wise nonlinear operations can have numerous benefits, ranging from speeding up iterative algorithm…
Kernel regression in high dimensions: Refined analysis beyond double descent
Fanghui Liu, Zhenyu Liao, Johan A. K. Suykens
In this paper, we provide a precise characterization of generalization properties of high dimensional kernel ridge regression across the under- and over-parameterized regimes, depe…
Inner-product Kernels are Asymptotically Equivalent to Binary Discrete Kernels
Zhenyu Liao, Romain Couillet
This article investigates the eigenspectrum of the inner product-type kernel matrix under a bina…
High Dimensional Classification via Regularized and Unregularized Empirical Risk Minimization: Precise Error and Optimal Loss
Xiaoyi Mai, Zhenyu Liao
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regular…
The Dynamics of Learning: A Random Matrix Approach
Zhenyu Liao, Romain Couillet
Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why d…