Stability of Measure-to-Measure Transformers on Sub-Gaussian Data
Transformers have exhibited impressive empirical success across various domains, but their theoretical foundations remain less developed. This work constitutes a mathematical study of the measure-to-measure operators defined by transformers. We show that transformers map sub-Gaussian inputs to sub-Gaussian outputs; this ensures that taking arbitrary-length compositions of the softmax operator is well-defined. We then show that transformers are Hölder continuous with respect to the 1-Wasserstein distance on appropriate spaces of sub-Gaussian inputs. This allows us to establish estimates on the error propagation along a transformer between a sub-Gaussian input and its empirical approximatio...
| Authors | Frank Cole, Nicholas H. Nelsen, Takashi Furuya |
|---|---|
| Primary category | stat.ML |
| Published | 6 October 2026 |
| Last updated at source | 6 October 2026 |
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