Approximation Error Upper and Lower Bounds for Hölder Class with Transformers
We explore the expressive power of Transformers by establishing precise approximation error upper and lower bounds for Hölder class. Specifically, a new approximation upper bound is derived for the standard Transformer architecture equipped with Softmax operators, ReLU activation functions, and residual connections. We prove that a Transformer network composed of at most $\mathcal{O}(\varepsilon^{-{d_{0}}/α})$ blocks can approximate any bounded Hölder function with $d_{0}$-dimensional input and smoothness $α\in(0,1]$ under any accuracy $\varepsilon>0$. In the case of approximation lower bounds, leveraging the VC-dimension upper bound, we are the first to rigorously prove that Transformers...
| Authors | Xin He, Yuling Jiao, Xiliang Lu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 22 June 2026 |
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