Distributionally robust approximation property of neural networks
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Abstract (arXiv)
The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby extending classical universal approximation theorems even beyond the traditional Lp-setting. The covered classes of neural networks include widely used architectures like feedforward neural networks with non-polynomial activation functions, deep narrow networks with ReLU activation functions and functional input neural networks.
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4 of 19 references.
References · 4
- 2016Understanding Deep Neural Networks with Rectified Linear Unitscited by 253
- 2023Global universal approximation of functional input maps on weighted spacescited by 19
- 2023Wasserstein distributional robustness of neural networkscited by 15
- 2024Universal approximation results for neural networks with non-polynomial activation function over non-compact domainscited by 7
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