Space-based Parameter Evolving with Lightweight Optimization for Graph Adaptation to Evolving Shifts

Adapting graph neural networks to evolving domain shifts presents a fundamental challenge: how to acquire new knowledge while preventing catastrophic forgetting. Existing continual learning methods often rely on memory replay or complex regularization schemes, incurring significant computational overhead. We propose STEM (State-based Parameter Evolving with Lightweight Optimization), a replay-free framework that transforms continual adaptation into controlled parameter space evolution via a controller-worker architecture. At its core is a Test-time Evolving State Space (TESS) controller with a selective gating mechanism that recursively updates its hidden state by integrating compact summaries of the current graph domain. Unlike traditional linear state space models, TESS enables nonlinear, input-dependent state transitions that capture temporal dynamics of domain evolution. A lightweight parameter generator decodes this evolving state into domain-specific adapter parameters injected into a frozen base GNN. We employ unsupervised Information Maximization and parameter space stability regularization that penalizes adapter changes across time steps, with theoretical guarantees of forgetting mitigation and stable convergent adaptation. Extensive experiments validate that our method achieves state-of-the-art performance while maintaining minimal computational overhead. The code is available at https://github.com/miaomiao1220/stem