Mamba-CL: Optimizing Selective State Space Model in Null Space for Continual Learning

Abstract: Continual Learning (CL) aims to equip AI models with the ability to learn a sequence of tasks over time, without forgetting previously learned knowledge. Recently, State Space Models (SSMs), particularly the Mamba model, have achieved notable success in computer vision. Building on the strengths of SSMs, this study explores leveraging the Mamba model for CL. Therefore, we introduce Mamba-CL, a framework that continuously fine-tunes the core SSMs of the large-scale Mamba foundation model by updating parameters orthogonal to the feature subspace of previous tasks. This approach theoretically guarantees the consistency objective aiming to preserves consistent output for each SSM module across both previous and current tasks, so as to overcome catastrophic forgetting issue. Specifically, we achieve this goal by deducing the overall consistency constraints on four key time-invariant parameters in the Mamba model, streamlining its recurrent state-space structure and non-linear discretization process in SSM. In practice, we apply the null-space projection to efficiently implement the orthogonality within Mamba model. Extensive experiments on four class-incremental benchmarks demonstrate the effectiveness of Mamba-CL for anti-forgetting, achieving superior performances to state-of-the-art methods. Code is available in the supplementary materials.