[Paper] Harness In-Context Operator Learning with Chain of Operators

Source: arXiv - 2606.12318v1

Overview

Neural operators approximate mappings between function spaces, but often generalize poorly to other operators and usually require fine-tuning or retraining. In-Context Operator Networks (ICON) addresses this issue by prompting the model with numerical context so that the model learns specific operators from prompts and adapt to different operators without fine-tuning. However, ICON may still fail to generalize to out-of-distribution (OOD) operator tasks. Inpired by the success of harness engineering of Large Language models (LLMs), we introduce Chain of Operators (CHOP), a framework that harness a frozen ICON to OOD operator tasks without updating its parameters. Specifically, CHOP constructs a chain of operators consisting of explicit elementary transformations and the frozen ICON. Experiments on a scalar conservation law and a mean-field control problem show that CHOP reduces relative inference error over direct ICON evaluation, while each operator in the chain remains interpretable and in closed form. A chain constructed on one PDE family further generalizes to a different family, indicating shared mechanisms across harness systems.

Key Contributions

This paper presents research in the following areas:

• cs.LG
• cs.AI

Methodology

Please refer to the full paper for detailed methodology.

Practical Implications

This research contributes to the advancement of cs.LG.

Authors

• Minghui Yang
• Ling Guo
• Liu Yang

Paper Information

• arXiv ID: 2606.12318v1
• Categories: cs.LG, cs.AI
• Published: June 10, 2026
• PDF: Download PDF