Mixtures of Neural Operators Reduce Active Complexity in Operator Learning

The paper presents a novel approach using Mixtures of Neural Operators (MoNOs) to enhance operator learning efficiency by reducing active complexity compared to traditional single-neural-operator models. The main theorem demonstrates that MoNOs can achieve lower depth, width, and rank scaling for approximating scalar uniformly continuous nonlinear operators, with expert quantities bounded by $\mathcal{O}(\varepsilon^{-1})$ for Lipschitz targets. This work is significant for practitioners as it provides a framework for optimizing neural operator architectures, potentially leading to more efficient models that require fewer resources for complex function approximations.