Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning

• URL: http://arxiv.org/abs/2605.22724v1
• Date: Thu, 21 May 2026 16:57:33 GMT
• Title: Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning
• Abstract summary: We study the approximation and statistical complexity of learning collections of operators in a shared multi-task setting.<n>For broad classes of Lipschitz multiple operator maps, we derive near-optimal upper bounds for approximation and statistical generalization.<n>On the lower-bound side, we establish a curse of parametric complexity and prove corresponding minimax rates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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