SORSA: Singular Values and Orthonormal Regularized Singular Vectors Adaptation of Large Language Models
<|reference_start|>SORSA: Singular Values and Orthonormal Regularized Singular Vectors Adaptation of Large Language Models: The rapid advancement in large language models (LLMs) comes with a significant increase in their parameter size, presenting challenges for adaptation and fine-tuning. Parameter-efficient fine-tuning (PEFT) methods are widely used to adapt LLMs for downstream tasks efficiently. In this paper, we propose Singular Values and Orthonormal Regularized Singular Vectors Adaptation, or SORSA, a novel PEFT method. We introduce a method to analyze the variation of the parameters by performing singular value decomposition (SVD) and discuss and analyze SORSA's superiority in minimizing the alteration in the SVD aspect. Each SORSA adapter consists of two main parts: trainable principal singular weights $W_p = U_p \text{diag}(S_p) V^\top_p$, and frozen residual weights $W_r = U_r \text{diag}(S_r) V^\top_r$. These parts are initialized by performing SVD on pre-trained weights. Moreover, we implement and analyze an orthonormal regularizer, which we prove could decrease the condition number of $W_p$ and allows the optimization to be more efficient. SORSA adapters could be merged during inference, thus eliminating any inference latency. After all, SORSA shows a faster convergence than PiSSA and LoRA in our experiments. On the GSM-8K benchmark, Llama 2 7B adapted using SORSA achieved 56.03% accuracy, surpassing LoRA (42.30%), Full FT (49.05%), and PiSSA (53.07%). On the MATH benchmark, SORSA achieved 10.36% accuracy, outperforming LoRA (5.50%), Full FT (7.22%), and PiSSA (7.44%). We conclude that SORSA offers a new perspective on parameter-efficient fine-tuning, demonstrating remarkable performance. The code is available at https://github.com/Gunale0926/SORSA.<|reference_end|>
@article{cao2024sorsa:,
    title={SORSA: Singular Values and Orthonormal Regularized Singular Vectors
  Adaptation of Large Language Models},
    author={Yang Cao},
    journal={arXiv preprint arXiv:2409.00055},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.00055},
    primaryClass={cs.LG cs.CL}
}