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. We resolve this issue by introducing the Chinese Remainder Theorem as a constructive encoding mechanism. For Lipschitz continuous functions on $[0,1]^D$, we construct a width-$\max\{D,4\}$, depth-$5$ network with explicit parameter-error trade-offs. For Hölder-smooth functions in $C^{r,γ}_A\left([0,1]^D\right)$, our fixed network of width $\ma...
| Authors | Feng-Lei Fan, Ze-Yu Li, Chen-Yu Wang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 7 July 2026 |
| Last updated at source | 7 July 2026 |
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