When Is Rank-1 Enough? Geometry-Guided Initialization for Parameter-Efficient Fine-Tuning
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914300480716800 |
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| author | Zhao, Haoran Han, Soyeon Caren Hovy, Eduard |
| author_facet | Zhao, Haoran Han, Soyeon Caren Hovy, Eduard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01522 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | When Is Rank-1 Enough? Geometry-Guided Initialization for Parameter-Efficient Fine-Tuning Zhao, Haoran Han, Soyeon Caren Hovy, Eduard Machine Learning Computer Vision and Pattern Recognition 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. |
| title | When Is Rank-1 Enough? Geometry-Guided Initialization for Parameter-Efficient Fine-Tuning |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2602.01522 |