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Autori principali: Zhang, Shao-Qun, Chen, Zong-Yi, Tian, Yong-Ming, Lu, Xun
Natura: Preprint
Pubblicazione: 2024
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Accesso online:https://arxiv.org/abs/2403.17467
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author Zhang, Shao-Qun
Chen, Zong-Yi
Tian, Yong-Ming
Lu, Xun
author_facet Zhang, Shao-Qun
Chen, Zong-Yi
Tian, Yong-Ming
Lu, Xun
contents Past decades have witnessed a great interest in the distinction and connection between neural network learning and kernel learning. Recent advancements have made theoretical progress in connecting infinite-wide neural networks and Gaussian processes. Two predominant approaches have emerged: the Neural Network Gaussian Process (NNGP) and the Neural Tangent Kernel (NTK). The former, rooted in Bayesian inference, represents a zero-order kernel, while the latter, grounded in the tangent space of gradient descents, is a first-order kernel. In this paper, we present the Unified Neural Kernel (UNK), which {is induced by the inner product of produced variables and characterizes the learning dynamics of neural networks with gradient descents and parameter initialization.} The proposed UNK kernel maintains the limiting properties of both NNGP and NTK, exhibiting behaviors akin to NTK with a finite learning step and converging to NNGP as the learning step approaches infinity. Besides, we also theoretically characterize the uniform tightness and learning convergence of the UNK kernel, providing comprehensive insights into this unified kernel. Experimental results underscore the effectiveness of our proposed method.
format Preprint
id arxiv_https___arxiv_org_abs_2403_17467
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Unified Kernel for Neural Network Learning
Zhang, Shao-Qun
Chen, Zong-Yi
Tian, Yong-Ming
Lu, Xun
Machine Learning
Artificial Intelligence
Past decades have witnessed a great interest in the distinction and connection between neural network learning and kernel learning. Recent advancements have made theoretical progress in connecting infinite-wide neural networks and Gaussian processes. Two predominant approaches have emerged: the Neural Network Gaussian Process (NNGP) and the Neural Tangent Kernel (NTK). The former, rooted in Bayesian inference, represents a zero-order kernel, while the latter, grounded in the tangent space of gradient descents, is a first-order kernel. In this paper, we present the Unified Neural Kernel (UNK), which {is induced by the inner product of produced variables and characterizes the learning dynamics of neural networks with gradient descents and parameter initialization.} The proposed UNK kernel maintains the limiting properties of both NNGP and NTK, exhibiting behaviors akin to NTK with a finite learning step and converging to NNGP as the learning step approaches infinity. Besides, we also theoretically characterize the uniform tightness and learning convergence of the UNK kernel, providing comprehensive insights into this unified kernel. Experimental results underscore the effectiveness of our proposed method.
title A Unified Kernel for Neural Network Learning
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2403.17467