Measure Neural Mappings
We introduce and define measure neural mappings (MNMs), which combine measure-dependent neural transport with ensemble consistency for learning operators on probability measures. Ensemble consistency requires outputs from growing ensembles sampled from an input law to converge to the specified population output in probability. We establish quantitative continuum limits for attention on noncompact laws under strong sub-Gaussian and tail-integrability assumptions. These laws accommodate unbounded state spaces in scientific machine learning, including Bayesian inference and uncertainty quantification. For fixed self-attention transformers, the expected output Wasserstein error is bounded by ...
| Authors | Ricardo Baptista, Edoardo Calvello, Bohan Chen et al. |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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