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

arXiv: https://arxiv.org/abs/2602.01522 · HTML: https://mlsanity.com/paper/2602.01522/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompt learning and adaptation of CLIP, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 11 of its 15 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Prompt learning and adaptation of CLIP](https://mlsanity.com/mllm/prompt-learning-and-adaptation-of-clip/)

## Builds on (most cited first, 11 of 11)

- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [VL-Adapter: Parameter-Efficient Transfer Learning for Vision-and-Language Tasks](https://mlsanity.com/paper/2112.06825/) (2021)
- [All-but-the-Top: Simple and Effective Postprocessing for Word Representations](https://mlsanity.com/paper/1702.01417/) (2017)

## Abstract (arXiv)

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.