Learning Theory of Transformers: Local-to-Global Approximation via Softmax Partition of Unity
This paper investigates the learning theory of Transformer networks for regression tasks on the compact Euclidean domain $[0,1]^d$ and $d$-dimensional compact Riemannian manifolds. We propose a novel constructive approximation framework for Transformers that builds local approximations of the target function and aggregates them into a global approximation via softmax partition of unity. This approach leverages the attention mechanism to achieve spatial localization through affine transformations of the input. The softmax activation plays a crucial role in aggregating local approximations to a global output. From an approximation perspective, we prove that a dense Transformer equipped with...
| Authors | Zhongjie Shi, Wenjing Liao |
|---|---|
| Primary category | stat.ML |
| Published | 9 May 2026 |
| Last updated at source | 9 May 2026 |
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