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However, directly updating their limited parameter space causes catastrophic forgetting. While memory-based methods naturally address this by decoupling knowledge retention from parameters, existing approaches designed for large language models (LLMs) rely on abundant storage and strong in-context reasoning that SLMs lack. To address these challenges, we propose MIITA, a Memory-Induced Inference-Time Adaptation framework for supervised CL under constrained storage. MIITA stores supervised experiences as compact correction-direction prototypes with semantic anchors, and retrieves them at inference time using semantic and uncertainty-based cues. 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