Continual learning (CL) learns from a non-stationary data stream without storing or re-training on all seen samples. Meta-continual learning (MCL) casts CL as sequence prediction and meta-learns the continual learner itself as a sequence model, with Transformers as natural choices. However, despite decent performance, a Transformer learner relies on a linearly growing key-value cache to store all past representations, conflicting with CL's objective of not storing all seen samples. Sequence models with a constant-size state, e.g., linear-attention models and state-space models (SSMs), match CL's requirement by definition; however, with past samples compressed and mixed in the bounded state, such learners are harder to meta-learn, and earlier kernel-based ones performed poorly on MCL. We thus aim to obtain effective continual learners with constant-size states and make them work for MCL. By formulating the selective SSM for MCL, we propose MambaCL, with Mamba as the main model in practice. We meta-train the learner with a proposed selectivity regularization, which supervises the implicit associations within the compressed state and applies across constant-state models. Furthermore, we conduct a systematic empirical study of how Mamba and other constant-state models behave across various MCL scenarios, covering effectiveness, generalization, and model designs. The results highlight promising performance and strong generalization, demonstrating the potential of constant-state learners for efficient continual learning and adaptation.

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