SSH: Sparse Spectrum Adaptation via Discrete Hartley Transformation

Low-rank adaptation (LoRA) has been demonstrated effective in reducing the trainable parameter number when fine-tuning a large foundation model (LLM). However, it still encounters computational and memory challenges when scaling to larger models or addressing more complex task adaptation.In this work, we introduce **Sparse Spectrum Adaptation via Discrete Hartley Transformation (SSH)**, a novel approach that significantly reduces the number of trainable parameters while enhancing model performance. It selects the most informative spectral components across all layers, under the guidance of the initial weights after a discrete Hartley transformation (DHT). The lightweight inverse DHT then projects the spectrum back into the spatial domain for updates.Extensive experiments across both single-modality tasks—such as language understanding and generation—and multi-modality tasks—such as video-text understanding—demonstrate that SSH outperforms existing parameter-efficient fine-tuning (PEFT) methods while achieving substantial reductions in computational cost and memory requirements. For instance, during instruction tuning on the LLaMA3.1 8B model, SSH achieves higher accuracy with only 0.048M trainable parameters compared to LoRA’s 33.5M, while reducing computational intensity up to 55% compared to FourierFT.