TR2025-130

LoDA: Low-Dimensional Adaptation of Large Language Models


    •  Liu, J., Koike-Akino, T., Wang, P., Brand, M., Parsons, K., Wang, Y., "LoDA: Low-Dimensional Adaptation of Large Language Models" in Springer Book, September 2025.
      BibTeX TR2025-130 PDF
      • @incollection{Liu2025sep,
      • author = {Liu, Jing and Koike-Akino, Toshiaki and Wang, Pu and Brand, Matthew and Parsons, Kieran and Wang, Ye},
      • title = {{LoDA: Low-Dimensional Adaptation of Large Language Models}},
      • booktitle = {Springer Book},
      • year = 2025,
      • month = sep,
      • url = {https://www.merl.com/publications/TR2025-130}
      • }
  • MERL Contacts:
  • Research Areas:

    Artificial Intelligence, Machine Learning

Abstract:

Parameter-Efficient Fine-Tuning (PEFT) has recently garnered significant attention, due to the enormous size of Large Language Models (LLMs). Among various PEFT methods, Low-Rank Adaptation (LoRA) demonstrates comparable performance to full fine-tuning, despite having significantly fewer trainable parameters. In this work, we first generalize LoRA from a low-rank linear adaptation/mapping to low-dimensional, non-linear adaptation/mapping, which we have named Low- Dimensional Adaptation (LoDA). We also propose LoDA+, which further improves the expressiveness of the non-linear adaptation, while still using nearly the same number of tunable parameters as LoRA. Both LoDA and LoDA+ include LoRA as a special case. To improve computational efficiency at inference, we further propose R-LoDA(+) and S-LoDA(+), by replacing the pre-trained weight matrix with its low-rank or sparse approximation, which is frozen during fine-tuning. Empirical evaluations on Natural Language Generation tasks demonstrate that variants of LoDA outperform LoRA and other baselines.