Out-of-distribution detection in continual learning (OOD-CL) is highly challenging, as it requires (i) learning a sequence of tasks without catastrophic forgetting, and (ii) identifying unknown samples (OOD) without access to known (in-distribution (ID)) data from past tasks, where standard confidence-based OOD scores tend to degrade. Existing methods largely rely on a rehearsal buffer of past data or assume closed-world settings, limiting their scalability and reliability in real-world scenarios. In this paper, we propose a novel OOD detection framework for rehearsal-free continual learning, inspired by Kolmogorov-Arnold Networks (KAN), which mitigate catastrophic forgetting via their inherent local neuroplasticity. To better leverage KAN in OOD-CL, we introduce a task-adaptive classifier architecture, TA-KAN, which mitigates recency bias and enhances ID--OOD separability through task-specific control of activation locality. Furthermore, we propose a geometry-guided OOD score that complements TA-KAN classifier confidence without relying on past ID data. Our method significantly improves OOD detection while maintaining strong ID classification performance, achieving state-of-the-art results in OOD-CL.

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