Title: Fourier Minds, Forget Less: Discrete Fourier Transform for Fast and Robust Continual Learning in LLMs
Primary area: transfer learning, meta learning, and lifelong learning
Keywords: Fourier Transform, Continual Learning

Abstract: Continual learning (CL) for large language models (LLMs) is challenged by both catastrophic forgetting and efficiency constraints when facing long sequential tasks. While low-rank adaptation in LoRA-based approaches reduces per-task trainable parameters, the cumulative parameter budget grows with stream length and can be substantial. This limits their applicability in lifelong learning scenarios, especially under strict resource constraints. In this work, we explore the potential of the parameter-efficient Sparse Fourier Transform (SFT) in the context of continual learning. Our preliminary experiments reveal that directly applying SFT in CL settings leads to temporal instability and forgetting.  Motivated by this finding, we propose Discrete Fourier Continual Learning (DF-CL), which leverages a spectral decomposition strategy to disentangle shared and task-specific knowledge components, facilitating more stable continual learning. By leveraging the orthogonality properties inherent to the SFT bases, DF-CL ensures that task-specific knowledge is encoded within its own dedicated parameter space, minimizing interference between tasks. Furthermore, we introduce a max-magnitude task-weight merging strategy, which enables efficient knowledge consolidation and transfer across sequential tasks. Extensive experiments on both T5-Large and LLaMA2-7B demonstrate the scalability, efficiency, and effectiveness of DF-CL.