arXiv Machine Learning
Approximation Property of Dropout Neural Networks: Sobolev Rates and Confidence Bounds
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arXiv Machine Learning
Sep 18
Error bounds in Sobolev norms for approximations with norm constrained ReLU neural networks
arXiv:2609. 19937v1 Announce Type: cross Abstract: Recent studies have shown that smooth functions can be well approximated by ReLU neural networks with path norm constraint on the weights.
Hugging Face Trending Papers
Sep 17
Error bounds in Sobolev norms for approximations with norm constrained ReLU neural networks
Recent studies have shown that smooth functions can be well approximated by ReLU neural networks with path norm constraint on the weights. We extend these results from uniform approximation to approximation in Sobolev norm.
arXiv Machine Learning
2d ago
Optimal approximation of smooth functions by ReLU neural networks
arXiv:2610.22693v1 Announce Type: cross Abstract: We study uniform approximation of the H\"older ball $\mathcal H_1^s([0,1]^D)$ by fully connected ReLU networks. Except in the one-dimensional Lipschi...
arXiv Machine Learning
Sep 11
Near-optimal estimates for the $\ell^p$-Lipschitz constants of deep random ReLU neural networks
This paper investigates the ρ^p-Lipschitz constants of deep ReLU neural networks with random weights drawn from a He‑style initialization. For zero‑bias networks, it provides high‑probability upper and lower bounds that differ by at most a logarithmic factor in depth, and shows a sharp contrast between the regimes p∈[1,2) and p∈[2,∞], with the former behaving like the Euclidean norm of a Gaussian vector and the latter like its dual norm. The analysis is extended to networks with non‑zero biases from symmetric distributions, yielding bounds that differ by a logarithmic factor in width and a linear factor in depth.
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.
arXiv Machine Learning
Jun 16
Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy
arXiv:2606. 16975v1 Announce Type: cross Abstract: In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks.