3 citations · 13 across the 25 of their papers we have counts for
12 papers · 1 filter
Supporting Evidence for the Adaptive Feature Program across Diverse Models
Yicheng Li, Qian Lin
Theoretically exploring the advantages of neural networks might be one of the most challenging problems in the AI era. An adaptive feature program has recently been proposed to ana…
Alignment-Sensitive Minimax Rates for Spectral Algorithms with Learned Kernels
Dongming Huang, Zhifan Li, Yicheng Li +1
We study spectral algorithms in the setting where kernels are learned from data. We introduce the effective span dimension (ESD), an alignment-sensitive complexity measure that dep…
Neural Tangent Kernel of Neural Networks with Loss Informed by Differential Operators
Weiye Gan, Yicheng Li, Qian Lin +1
Spectral bias is a significant phenomenon in neural network training and can be explained by neural tangent kernel (NTK) theory. In this work, we develop the NTK theory for deep ne…
Diagonal Over-parameterization in Reproducing Kernel Hilbert Spaces as an Adaptive Feature Model: Generalization and Adaptivity
Yicheng Li, Qian Lin
This paper introduces a diagonal adaptive kernel model that dynamically learns kernel eigenvalues and output coefficients simultaneously during training. Unlike fixed-kernel method…
Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories
Yicheng Li, Haobo Zhang, Jianfa Lai +2
A primary advantage of neural networks lies in their feature learning characteristics, which is challenging to theoretically analyze due to the complexity of their training dynamic…
Improving Adaptivity via Over-Parameterization in Sequence Models
Yicheng Li, Qian Lin
It is well known that eigenfunctions of a kernel play a crucial role in kernel regression. Through several examples, we demonstrate that even with the same set of eigenfunctions, t…
The phase diagram of kernel interpolation in large dimensions
Haobo Zhang, Weihao Lu, Qian Lin
The generalization ability of kernel interpolation in large dimensions (i.e., for some ) might be one of the most interesting problems in the recent renaissance…
Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions
Haobo Zhang, Yicheng Li, Weihao Lu +1
Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the…
Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay
Yicheng Li, Weiye Gan, Zuoqiang Shi +1
The generalization error curve of certain kernel regression method aims at determining the exact order of generalization error with various source condition, noise level and choice…
On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay
Yicheng Li, Haobo Zhang, Qian Lin
The widely observed 'benign overfitting phenomenon' in the neural network literature raises the challenge to the 'bias-variance trade-off' doctrine in the statistical learning theo…
On the Optimality of Misspecified Kernel Ridge Regression
Haobo Zhang, Yicheng Li, Weihao Lu +1
In the misspecified kernel ridge regression problem, researchers usually assume the underground true function , a less-smooth interpolation space of…
Kernel interpolation generalizes poorly
Yicheng Li, Haobo Zhang, Qian Lin
One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help…