Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning
Abstract
We study the approximation and statistical complexity of learning collections of operators in a shared multi-task setting, with a focus on the Multiple Neural Operators (MNO) architecture. For broad classes of Lipschitz multiple operator maps, we derive near-optimal upper bounds for approximation and statistical generalization. On the lower-bound side, we establish a curse of parametric complexity and prove corresponding minimax rates. Together, these results show that shared representations across tasks do not increase the overall cost: multi-task operator learning follows the same scaling laws as single operator learning. We also compare MNO with a multi-task extension of DeepONet based on concatenated task inputs and show that, from a worst-case approximation-complexity perspective, both architectures satisfy essentially the same asymptotic rates.
Cite
@article{arxiv.2605.22724,
title = {Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning},
author = {Adrien Weihs and Hayden Schaeffer},
journal= {arXiv preprint arXiv:2605.22724},
year = {2026}
}