CGaLore: Curvature-Guided GaLore for Memory-Efficient Continual Adaptation of ASR Foundation Models

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Automatic speech recognition models suffer from catastrophic forgetting when adapted to new domains, accents, or downstream tasks. This problem becomes increasingly important with the growing use of speech foundation models, where adaptation should be both memory-efficient and safe, preserving the broad capabilities learned during pretraining. Gradient Low-Rank Projection (GaLore) has recently been proposed as a memory-efficient fine-tuning method that keeps model parameters full-rank while reducing the optimizer memory through low-rank gradient projection. However, GaLore does not account for catastrophic forgetting. We propose Curvature-Guided GaLore (CGaLore), which incorporates old-task curvature information when selecting the low-rank projection bases. Specifically, CGaLore filters current-task gradients using Kronecker-factored approximate curvature from previous tasks before computing the gradient subspace. Our experiments show that CGaLore enables effective adaptation while alleviating forgetting, outperforming state-of-the-art continual learning baselines. Extensive ablation studies confirm the practical applicability of CGaLore.