GLT-PEFT: Gated Lie-Tucker Parameter-Efficient Fine-Tuning for Alzheimer's Disease Diagnosis with Hippocampal Segmentation Pretraining

Adapting large pretrained vision models to medical image classification is often limited by memory, computation, and task-specific specializations. Parameter-efficient fine-tuning (PEFT) methods like LoRA reduce this cost by learning low-rank updates, but operating directly in feature space can struggle to capture the localized, multi-scale features common in medical imaging. We propose WaRA, a wavelet-structured adaptation module that performs low-rank adaptation in a wavelet domain. WaRA reshapes patch tokens into a spatial grid, applies a fixed discrete wavelet transform, updates subband coefficients using a shared low-rank adapter, and reconstructs the additive update through an inverse wavelet transform. This design provides a compact trainable interface while biasing the update toward both coarse structure and fine detail. For extremely low-resource settings, we introduce Tiny-WaRA, which further reduces trainable parameters by learning only a small set of coefficients in a fixed basis derived from the pretrained weights through a truncated SVD. Experiments on medical image classification across four modalities and datasets demonstrate that WaRA consistently improves performance over strong PEFT baselines, while retaining a favorable efficiency profile. Our code is publicly available at https://github.com/moeinheidari7829/WaRA.

Low-rank adaptation (LoRA) has become the dominant paradigm for parameter-efficient fine-tuning (PEFT) of large language models (LLMs). However, its bilinear structure introduces a critical limitation: the mapping from trainable parameters to weight updates is not distance-preserving, distorting the optimization landscape. Methods that project a low-dimensional vector into LoRA's parameter space, such as Uni-LoRA, improve parameter efficiency, but the subsequent bilinear LoRA map breaks end-to-end isometry, leaving the core distance-preservation problem unresolved. We propose GPart (Global Partition fine-tuning), a highly parameter-efficient fine-tuning method which removes the low-rank bottleneck entirely. Our method uses a single isometric partition matrix to map a $d$-dimensional trainable vector directly into the full weight space of the model. The result is an extremely minimal fine-tuning pipeline: one random projection, end-to-end isometric, with a single clean hyperparameter ($d$) and storage cost of $d+1$ values (the trainable vector plus a random seed). GPart builds on the theoretical premise that effective fine-tuning can emerge from random low-dimensional subspaces of the full weight space, without imposing low-rank matrix structure. We empirically demonstrate the superior or comparable performance of GPart to existing PEFT methods on natural language understanding, computer vision tasks, and mathematical reasoning. Overall, GPart achieves state-of-the-art efficiency and performance by removing structural constraints, offering a straightforward and elegant path to PEFT.

Parameter-efficient fine-tuning (PEFT) has emerged as an critical technique for adapting large-scale foundation models across natural language processing and computer vision. While existing methods such as low-rank adaptations achieve parameter efficiency via low-rank weight updates, they are limited in their ability to preserve the geometric structure of pretrained representations. We introduce Low-rank Compositional Orthogonal fine-tuning (LoCO), a novel PEFT method that constructs orthogonal transformations through low-rank skew-symmetric matrices and compositional rotation chains. We propose an approximation scheme that enables fully parallel computation of compositional rotations, making the approach practical for high-dimensional feature spaces. Our method maintains low computational complexity while maintaining orthogonality with controlled approximation error. We validate LoCO across diverse domains, including diffusion transformer fine-tuning, vision transformer adaptation, and language model adaptation. Our method demonstrates superior or competitive performance compared to both existing orthogonal and non-orthogonal methods.