Arbitrary-Accuracy Neural Approximation with Optimal Neuron Count and Near-Optimal Bit Complexity
We study the minimum number of hidden neurons required for arbitrary-accuracy approximation of multivariate Hölder-continuous functions on $[0,1]^d$ and the associated encoding complexity. For $d\geq 2$, we construct a fixed, explicitly defined activation function for which a closed-form network with two hidden layers of widths $d$ and $1$ achieves arbitrary accuracy in the uniform norm. We prove that $d+1$ is the exact minimum total number of hidden neurons among standard feedforward networks with locally integrable activations and affine outputs. We further give a simpler construction using a single elementary activation that combines the floor and exponential functions. This constructi...
| Authors | Zilan Cheng, Li-Lian Wang, Zhongjian Wang |
|---|---|
| Primary category | cs.LG |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.