# FAN-LoRA: A Fourier-Adaptive Nonlinear Low-Rank Adaptor for Medical Foundation Model Domain Adaptation

arXiv: https://arxiv.org/abs/2608.26531 · HTML: https://mlsanity.com/paper/2608.26531/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 36 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Builds on (most cited first, 22 of 22)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [AdaptFormer: Adapting Vision Transformers for Scalable Visual Recognition](https://mlsanity.com/paper/2205.13535/) (2022)
- [FDA: Fourier Domain Adaptation for Semantic Segmentation](https://mlsanity.com/paper/2004.05498/) (2020)
- [Medical SAM Adapter: Adapting Segment Anything Model for Medical Image Segmentation](https://mlsanity.com/paper/2304.12620/) (2023)
- [CHAOS Challenge -- Combined (CT-MR) Healthy Abdominal Organ Segmentation](https://mlsanity.com/paper/2001.06535/) (2020)
- [Segment Anything Model for Medical Image Analysis: an Experimental Study](https://mlsanity.com/paper/2304.10517/) (2023)
- [FedDG: Federated Domain Generalization on Medical Image Segmentation via Episodic Learning in Continuous Frequency Space](https://mlsanity.com/paper/2103.06030/) (2021)
- [Customized Segment Anything Model for Medical Image Segmentation](https://mlsanity.com/paper/2304.13785/) (2023)
- [Scaling Down to Scale Up: A Guide to Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.15647/) (2023)
- [Medical Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2009.13120/) (2020)
- [Segment Anything Is Not Always Perfect: An Investigation of SAM on Different Real-world Applications](https://mlsanity.com/paper/2304.05750/) (2023)
- [Evaluation of Algorithms for Multi-Modality Whole Heart Segmentation: An Open-Access Grand Challenge](https://mlsanity.com/paper/1902.07880/) (2019)
- [Parameter-Efficient Fine-Tuning with Discrete Fourier Transform](https://mlsanity.com/paper/2405.03003/) (2024)
- [Segment Anything Model for Medical Images?](https://mlsanity.com/paper/2304.14660/) (2023)
- [AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mapping](https://mlsanity.com/paper/2505.18738/) (2025)
- [Towards Foundation Models and Few-Shot Parameter-Efficient Fine-Tuning for Volumetric Organ Segmentation](https://mlsanity.com/paper/2303.17051/) (2023)
- [Recent Advances in Medical Imaging Segmentation: A Survey](https://mlsanity.com/paper/2505.09274/) (2025)
- [Rapid Switching and Multi-Adapter Fusion via Sparse High Rank Adapters](https://mlsanity.com/paper/2407.16712/) (2024)
- [Adaptation of Foundation Models for Medical Image Analysis: Strategies, Challenges, and Future Directions](https://mlsanity.com/paper/2511.01284/) (2025)
- [Adaptive Frequency Domain Alignment Network for Medical image segmentation](https://mlsanity.com/paper/2512.16393/) (2025)

## Abstract (arXiv)

The advent of vision foundation models, notably the Segment Anything Model (SAM), has catalyzed significant advancements in natural image segmentation. However, their direct transfer to medical imaging remains severely bottlenecked by profound domain gaps, such as cross-modality and cross-center shifts. Existing Parameter-Efficient Fine-Tuning (PEFT) methods facilitate the adaptation of SAM to medical domains; nevertheless, they frequently suffer from performance degradation under severe distribution shifts. This vulnerability primarily stems from the implicit entanglement of heterogeneous frequency components within a shared low-rank subspace, which directly exacerbates sub-optimal structural alignment and localized boundary blurring. To overcome this representational bottleneck, we propose the Fourier-Adaptive Nonlinear Low-Rank Adaptor (FAN-LoRA), a novel frequency-decoupled fine-tuning architecture. FAN-LoRA explicitly separates the optimization space by employing a B-spline-driven low-pass branch for global structural alignment, synergistically coupled with a discrete Fourier high-pass branch for local textural compensation. Extensive experiments across three challenging cross-modality and cross-center benchmarks demonstrate that FAN-LoRA consistently outperforms state-of-the-art PEFT baselines. Compared to the strongest competitors, our method achieves consistent improvements in average Dice scores and notable reductions in boundary errors, while maintaining a compact module size without compromising computational efficiency.