LoCA: Location-Aware Cosine Adaptation for Parameter-Efficient Fine-Tuning

TL;DR

LoCA introduces a frequency-domain fine-tuning method using inverse DCT with selective learnable components, surpassing low-rank adaptation in expressivity and efficiency for large models.

Contribution

The paper presents a novel frequency-domain adaptation method, LoCA, with theoretical analysis and dynamic selection of frequency components for improved parameter efficiency.

Findings

LoCA outperforms low-rank methods in expressivity.

LoCA achieves comparable computational efficiency to low-rank approaches.

Experiments show LoCA enhances parameter efficiency across language and vision tasks.

Abstract

Low-rank adaptation (LoRA) has become a prevalent method for adapting pre-trained large language models to downstream tasks. However, the simple low-rank decomposition form may constrain the hypothesis space. To address this limitation, we introduce Location-aware Cosine Adaptation (LoCA), a novel frequency-domain parameter-efficient fine-tuning method based on inverse Discrete Cosine Transform (iDCT) with selective locations of learnable components. We begin with a comprehensive theoretical comparison between frequency-domain and low-rank decompositions for fine-tuning pre-trained large models. Our analysis reveals that frequency-domain decomposition with carefully selected frequency components can surpass the expressivity of traditional low-rank-based methods. Furthermore, we demonstrate that iDCT offers a more efficient implementation compared to inverse Discrete Fourier Transform (iDFT), allowing for better selection and tuning of frequency components while maintaining equivalent expressivity to the optimal iDFT-based adaptation. By employing finite-difference approximation to estimate gradients for discrete locations of learnable coefficients on the DCT spectrum, LoCA dynamically selects the most informative frequency components during training. Experiments on diverse language and vision fine-tuning tasks demonstrate that LoCA offers enhanced parameter efficiency while maintains computational feasibility comparable to low-rank-based methods.