Determine whether transformer structure improves high-dimensional sample-complexity rates

Determine whether the parametric complexity of mean-field transformers can be leveraged to improve the high-dimensional sample-complexity rates established for sub-Gaussian data, and determine whether faster rates arise for probability measures with low-dimensional structure.

Background

The paper’s sample-complexity estimates for mean-field transformer operators exhibit a dimension-dependent rate, reflecting the usual curse of dimensionality in nonparametric Wasserstein estimation. The authors explicitly leave unresolved whether the parametric structure of transformers can yield improved rates, as well as whether distributions possessing low-dimensional structure admit faster convergence.

References

First, our sample complexity results suffer from a curse of dimensionality which is intrinsic to high-dimensional nonparametric statistical problems; it is unclear whether the parametric complexity of transformers can be leveraged to improve these rates, or whether faster rates occur for probability measures with low-dimensional structure.

— Stability of Measure-to-Measure Transformers on Sub-Gaussian Data  (2610.07717 - Cole et al., 6 Oct 2026) in Section 4, Conclusion