Adaptive Recurrent Message Passing for Test Time Computing on Graphs

2026-06-21

AI Summary

This work addresses the limited adaptability of existing pre-trained graph models, whose fixed architectures hinder effective performance across diverse downstream tasks during inference. To overcome this, the authors propose AdaR—an adaptive recursive graph neural network that dynamically adjusts its message-passing process at test time without updating model parameters. Theoretical analysis establishes, for the first time, that step-size dependency is both necessary and sufficient for the adaptive convergence of recursive processes. Guided by this insight, AdaR integrates normalized step-size embeddings with a representation–target relational modeling mechanism, further enhanced by gradient-guided supervision to promote convergence. Extensive experiments demonstrate that AdaR significantly outperforms strong baselines in both inductive and transductive settings, confirming its superior test-time adaptability and generalization capability.

Abstract

Pre-trained foundation models have demonstrated remarkable success in many domains, enabling a unified backbone to generalize across diverse downstream tasks. However, extending this paradigm to graph learning remains challenging due to the intrinsic mismatch between graph data and fixed architectural designs. In this work, we show that this limitation can be overcome via recurrent graph models. To achieve this, we conduct a systematic theoretical analysis, rigorously deriving step dependence as a necessary and sufficient condition for an adaptively convergent recurrent process. Building on this foundation, we propose AdaR, an Adaptive Recurrent graph model, empowering flexible test-time computing on various downstream tasks without changing model parameters. To enable adaptive inference, AdaR explicitly encodes normalized step information and representation-target relations into the recurrent updates. To ensure convergence of the recurrent process, AdaR employs gradient-based supervision signals that guide representation updates throughout the recurrence. Empirical results demonstrate that AdaR consistently outperforms strong baselines in both inductive and transductive settings.

Problem

• graph learning
• foundation models
• test time computing
• architectural mismatch
• recurrent models

Innovation

• Adaptive Recurrent Graph Model
• Test-Time Computing
• Step Dependence
• Convergent Message Passing
• Gradient-Based Supervision