多任务算子学习可实现近似最优性能，共享表示不增加总体成本。
Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning
- 基于MNO架构，构建共享表示的多任务算子学习框架。
- 理论证明逼近与泛化误差均达到近似最优，与单任务同阶。
- 适合研究多任务深度算子网络、高维函数映射的学者参考。
我们研究在共享多任务设置下学习算子族的逼近与统计复杂性，聚焦于多重神经算子（MNO）架构。对于广泛的Lipschitz多重算子映射类，我们推导出逼近和统计泛化误差的近似最优上界。从下界角度，揭示了参数复杂性的诅咒，并证明了相应的极小极大率。结果表明，任务间的共享表示不会增加整体代价：多任务算子学习遵循与单任务学习相同的标度律。此外，我们将MNO与基于拼接任务输入的DeepONet多任务扩展进行比较，从最坏情况逼近复杂性视角看，两者具有基本相同的渐近率。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。