When Is Rank-1 Enough? Geometry-Guided Initialization for Parameter-Efficient Fine-Tuning

Haoran Zhao, Caren Han, Eduard Hovy
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:161458-161475, 2026.

Abstract

Parameter-efficient fine-tuning (PEFT) is a standard way to adapt multimodal large language models, yet extremely low-rank settings—especially rank-1 LoRA—are often unstable. We show that this instability is not solely due to limited capacity: in the rank-1 regime, optimization is highly sensitive to the update direction. Concretely, pretrained vision and text features form mismatched anisotropic regions, yielding a dominant "gap" direction that acts like a translation component and disproportionately steers early gradients under rank-1 constraints. Analyzing pretrained representations, we identify a modality-gap axis that dominates early gradient flow, while a random rank-1 initialization is unlikely to align with it, leading to weak gradients and training collapse. We propose Gap-Init, a geometry-aware initialization that aligns the rank-1 LoRA direction with an estimated modality-gap vector from a small calibration set, while keeping the initial LoRA update zero. Across multiple vision-language tasks and backbones, Gap-Init consistently stabilizes rank-1 training and can match or outperform strong rank-8 baselines. Our results suggest that at the extreme low-rank limit, initial alignment can matter as much as rank itself.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-zhao26o, title = {When Is Rank-1 Enough? {G}eometry-Guided Initialization for Parameter-Efficient Fine-Tuning}, author = {Zhao, Haoran and Han, Caren and Hovy, Eduard}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {161458--161475}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/zhao26o/zhao26o.pdf}, url = {https://proceedings.mlr.press/v306/zhao26o.html}, abstract = {Parameter-efficient fine-tuning (PEFT) is a standard way to adapt multimodal large language models, yet extremely low-rank settings—especially rank-1 LoRA—are often unstable. We show that this instability is not solely due to limited capacity: in the rank-1 regime, optimization is highly sensitive to the update direction. Concretely, pretrained vision and text features form mismatched anisotropic regions, yielding a dominant "gap" direction that acts like a translation component and disproportionately steers early gradients under rank-1 constraints. Analyzing pretrained representations, we identify a modality-gap axis that dominates early gradient flow, while a random rank-1 initialization is unlikely to align with it, leading to weak gradients and training collapse. We propose Gap-Init, a geometry-aware initialization that aligns the rank-1 LoRA direction with an estimated modality-gap vector from a small calibration set, while keeping the initial LoRA update zero. Across multiple vision-language tasks and backbones, Gap-Init consistently stabilizes rank-1 training and can match or outperform strong rank-8 baselines. Our results suggest that at the extreme low-rank limit, initial alignment can matter as much as rank itself.} }
Endnote
%0 Conference Paper %T When Is Rank-1 Enough? Geometry-Guided Initialization for Parameter-Efficient Fine-Tuning %A Haoran Zhao %A Caren Han %A Eduard Hovy %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-zhao26o %I PMLR %P 161458--161475 %U https://proceedings.mlr.press/v306/zhao26o.html %V 306 %X Parameter-efficient fine-tuning (PEFT) is a standard way to adapt multimodal large language models, yet extremely low-rank settings—especially rank-1 LoRA—are often unstable. We show that this instability is not solely due to limited capacity: in the rank-1 regime, optimization is highly sensitive to the update direction. Concretely, pretrained vision and text features form mismatched anisotropic regions, yielding a dominant "gap" direction that acts like a translation component and disproportionately steers early gradients under rank-1 constraints. Analyzing pretrained representations, we identify a modality-gap axis that dominates early gradient flow, while a random rank-1 initialization is unlikely to align with it, leading to weak gradients and training collapse. We propose Gap-Init, a geometry-aware initialization that aligns the rank-1 LoRA direction with an estimated modality-gap vector from a small calibration set, while keeping the initial LoRA update zero. Across multiple vision-language tasks and backbones, Gap-Init consistently stabilizes rank-1 training and can match or outperform strong rank-8 baselines. Our results suggest that at the extreme low-rank limit, initial alignment can matter as much as rank itself.
APA
Zhao, H., Han, C. & Hovy, E.. (2026). When Is Rank-1 Enough? Geometry-Guided Initialization for Parameter-Efficient Fine-Tuning. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:161458-161475 Available from https://proceedings.mlr.press/v306/zhao26o.html.

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