Generalization Bounds and Statistical Guarantees for Multi-Task and Multiple Operator Learning with MNO Networks
Multiple operator learning concerns learning operator families $\{G[α]:U\to V\}_{α\in W}$ indexed by an operator descriptor $α$. Training data are collected hierarchically by sampling operator instances $α$, then input functions $u$ per instance, and finally evaluation points $x$ per input, yielding noisy observations of $G[α][u](x)$. While recent work has developed expressive multi-task and multiple operator learning architectures and approximation-theoretic scaling laws, quantitative statistical generalization guarantees remain limited. We provide a covering-number-based generalization analysis for separable models, focusing on the Multiple Neural Operator (MNO) architecture: we first d...
| Authors | Adrien Weihs, Hayden Schaeffer |
|---|---|
| Primary category | cs.LG |
| Published | 2 April 2026 |
| Last updated at source | 2 April 2026 |
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