Riemannian Preconditioned LoRA for Fine-Tuning Foundation Models

Fangzhao Zhang, Mert Pilanci
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:59641-59669, 2024.

Abstract

Low-Rank Adaptation (LoRA) emerges as a popular parameter-efficient fine-tuning (PEFT) method, which proposes to freeze pretrained model weights and update an additive low-rank trainable matrix. In this work, we study the enhancement of LoRA training by introducing an $r\times r$ preconditioner in each gradient step where $r$ is the LoRA rank. We theoretically verify that the proposed preconditioner stabilizes feature learning with LoRA under infinite-width NN setting. Empirically, the implementation of this new preconditioner requires a small change to existing optimizer code and creates virtually minuscule storage and runtime overhead. Our experimental results with both large language models and text-to-image diffusion models show that with this new preconditioner, the convergence and reliability of SGD and AdamW can be significantly enhanced. Moreover, the training process becomes much more robust to hyperparameter choices such as learning rate. The new preconditioner can be derived from a novel Riemannian metric in low-rank matrix field.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-zhang24ax, title = {{R}iemannian Preconditioned {L}o{RA} for Fine-Tuning Foundation Models}, author = {Zhang, Fangzhao and Pilanci, Mert}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {59641--59669}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/zhang24ax/zhang24ax.pdf}, url = {https://proceedings.mlr.press/v235/zhang24ax.html}, abstract = {Low-Rank Adaptation (LoRA) emerges as a popular parameter-efficient fine-tuning (PEFT) method, which proposes to freeze pretrained model weights and update an additive low-rank trainable matrix. In this work, we study the enhancement of LoRA training by introducing an $r\times r$ preconditioner in each gradient step where $r$ is the LoRA rank. We theoretically verify that the proposed preconditioner stabilizes feature learning with LoRA under infinite-width NN setting. Empirically, the implementation of this new preconditioner requires a small change to existing optimizer code and creates virtually minuscule storage and runtime overhead. Our experimental results with both large language models and text-to-image diffusion models show that with this new preconditioner, the convergence and reliability of SGD and AdamW can be significantly enhanced. Moreover, the training process becomes much more robust to hyperparameter choices such as learning rate. The new preconditioner can be derived from a novel Riemannian metric in low-rank matrix field.} }
Endnote
%0 Conference Paper %T Riemannian Preconditioned LoRA for Fine-Tuning Foundation Models %A Fangzhao Zhang %A Mert Pilanci %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-zhang24ax %I PMLR %P 59641--59669 %U https://proceedings.mlr.press/v235/zhang24ax.html %V 235 %X Low-Rank Adaptation (LoRA) emerges as a popular parameter-efficient fine-tuning (PEFT) method, which proposes to freeze pretrained model weights and update an additive low-rank trainable matrix. In this work, we study the enhancement of LoRA training by introducing an $r\times r$ preconditioner in each gradient step where $r$ is the LoRA rank. We theoretically verify that the proposed preconditioner stabilizes feature learning with LoRA under infinite-width NN setting. Empirically, the implementation of this new preconditioner requires a small change to existing optimizer code and creates virtually minuscule storage and runtime overhead. Our experimental results with both large language models and text-to-image diffusion models show that with this new preconditioner, the convergence and reliability of SGD and AdamW can be significantly enhanced. Moreover, the training process becomes much more robust to hyperparameter choices such as learning rate. The new preconditioner can be derived from a novel Riemannian metric in low-rank matrix field.
APA
Zhang, F. & Pilanci, M.. (2024). Riemannian Preconditioned LoRA for Fine-Tuning Foundation Models. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:59641-59669 Available from https://proceedings.mlr.press/v235/zhang24ax.html.

Related Material