Approximation Error and Complexity Bounds for ReLU Networks on Low-Regular Function Spaces
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Abstract (arXiv)
In this work, we consider the approximation of a large class of bounded functions, with minimal regularity assumptions, by ReLU neural networks. We show that the approximation error can be bounded from above by a quantity proportional to the uniform norm of the target function and inversely proportional to the product of network width and depth. We inherit this approximation error bound from Fourier features residual networks, a type of neural network that uses complex exponential activation functions. Our proof is constructive and proceeds by conducting a careful complexity analysis associated with the approximation of a Fourier features residual network by a ReLU network.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 10 of its 24 references that are in the map. First posted on arXiv 10 May 2024.
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References · 10
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