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

2026-05-21 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

The study investigates the approximation and statistical complexity of learning operator collections within a shared multi-task setting, focusing on the Multiple Neural Operators (MNO) architecture. For broad classes of Lipschitz multiple operator maps, the research derives near-optimal upper bounds for approximation and statistical generalization. Concurrently, it establishes a curse of parametric complexity and proves corresponding minimax rates. These findings demonstrate that shared representations across tasks do not increase the overall cost, implying multi-task operator learning follows the same scaling laws as single operator learning. The MNO architecture is also compared with a multi-task extension of DeepONet, showing both achieve essentially the same asymptotic rates from a worst-case approximation-complexity perspective.

Key takeaway

For AI Scientists and Machine Learning Engineers developing multi-task operator learning systems, this research indicates that architectures like Multiple Neural Operators (MNO) can achieve near-optimal performance without incurring additional complexity costs compared to single-task models. You should consider implementing shared representation approaches to maintain efficiency and scalability in your multi-operator learning applications, as they follow the same favorable scaling laws. This suggests a viable path for consolidating models across related tasks.

Key insights

Shared representations in multi-task operator learning achieve near-optimal rates without increasing overall cost.

Principles

• Multi-task operator learning scales like single operator learning.
• Shared representations across tasks do not increase overall cost.
• MNO and multi-task DeepONet exhibit similar asymptotic approximation rates.

Topics

• Neural Operators
• Multi-Task Learning
• Approximation Theory
• Statistical Complexity
• DeepONet
• Operator Learning

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.