Extend cross-attention sample-complexity bounds to unbounded supports

Extend the sample-complexity bounds for mean-field cross-attention operators to the case in which both input probability measures have unbounded support.

Background

The paper derives sample-complexity estimates for mean-field cross-attention operators of the form (μ,η)↦Γ(μ,⋅)#η(\mu,\eta)\mapsto\Gamma(\mu,\cdot)_{\#}\eta. The stated results cover settings in which the first input measure is compactly supported and the second is sub-Gaussian, or in which both measures are compactly supported. The unbounded-support case for both inputs is not treated, leaving open the extension of these rates beyond the compact-support assumption.

References

We leave extending the cross-attention sample complexity bounds in the case where both $\mu$ and $\gamma$ have unbounded support to future work.

— Stability of Measure-to-Measure Transformers on Sub-Gaussian Data  (2610.07717 - Cole et al., 6 Oct 2026) in Section 3.4, subsection “Transformers With Mean-Field Cross-Attention”