Derives explicit approximation and generalization rates for multi-input neural operators in Sobolev spaces that quantify each input's contribution to the error.
Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning
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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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cs.LG 1years
2026 1verdicts
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Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces
Derives explicit approximation and generalization rates for multi-input neural operators in Sobolev spaces that quantify each input's contribution to the error.