arXiv Machine Learning By Shijun Zhang, Zuowei Shen, Yuesheng Xu

Layer-wise Geometric Approximation Rates for Deep Networks

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arXiv:2604. 20219v2 Announce Type: replace Abstract: Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers largely unclear.

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arXiv Machine Learning
Jul 14

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width

arXiv:2607. 10589v1 Announce Type: cross Abstract: In contrast to most studies on neural network approximation theory that characterize results through a single parameter, such as the total number of network parameters, \cite{shen2020deep} pioneered the characterization of approximation rates as a joint function of the width parameter $N$ and the depth parameter $L$, thereby granting greater architectural flexibility.

By Yanming Lai, Defeng Sun, Yang Wang
arXiv Machine Learning
Jun 2

Multigrade Neural Network Approximation

arXiv:2601. 16884v3 Announce Type: replace Abstract: We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks.

By Shijun Zhang, Zuowei Shen, Yuesheng Xu
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On Explicit Super-Expressive Approximation for Neural Networks

In this work, we investigate the fixed-architecture neural network approximation with explicit parameter bounds and elementary activations. While prior work demonstrated super-expressive approximation using fixed-size networks, they lack quantitative and non-asymptotic characterizations of parameter magnitude with respect to the approximation error.