DWTSG: Parameter-Efficient Fine-Tuning of Large Pre-trained Models via Discrete Wavelet Transform and Subband Guidance

Fully fine-tuning large pre-trained models for each downstream task is impractical due to prohibitive memory, computation, and storage costs. Although parameter-efficient finetuning (PEFT) methods address this issue, leading methods like LoRA still exhibit linear scaling of trainable parameters with hidden size. Recent studies have explored PEFT in the frequency domain to reduce computational costs by employing fast Fourier transform and discrete cosine transform with sparse frequency selection. These methods rely on global frequency representations that lack spatial locality and disperse energy across the domain. As a result, sparse coefficient selection struggles to preserve fine-grained structural information and often introduces artifacts such as ringing near boundaries. To address these limitations, we propose DWTSG, a novel PEFT framework based on discrete wavelet transform (DWT) and subband guidance. DWTSG decomposes pre-trained weights into four wavelet subbands that jointly encode global context and local details. It finetunes only the most informative coefficients in each subband through an energy-based selection strategy that prioritizes coefficients based on their individual importance and interactions. Finally, inverse DWT reconstructs the updated weights, enabling efficient and precise adaptation. Extensive experiments on natural language understanding, commonsense reasoning, and image classification demonstrate that DWTSG outperforms existing PEFT methods, achieving superior performance and higher parameter efficiency.