FlexLoRA: Entropy-Guided Flexible Low-Rank Adaptation

Large pre-trained models achieve remarkable success across diverse domains, yet fully fine-tuning incurs prohibitive computational and memory costs. Parameter-efficient fine-tuning (PEFT) has thus become a mainstream paradigm. Among them, Low-Rank Adaptation (LoRA) introduces trainable low-rank matrices and shows strong performance, nevertheless, its fixed-rank design limits flexibility. Dynamic rank allocation methods mitigate this issue by pruning redundant directions; however, they often rely on heuristic, element-level metrics that globally sort rank directions without matrix-wise distinction, and they lack mechanisms to expand capacity in layers requiring additional adaptation. To overcome these limitations, we propose FlexLoRA, an entropy-guided flexible low-rank adaptation framework that (i) evaluates matrix importance via spectral energy entropy, (ii) supports rank pruning and expansion under a global budget, and (iii) employs zero-impact initialization for newly added singular directions to ensure stability. By addressing granularity, flexibility, and stability limitations, FlexLoRA provides a more principled solution for PEFT. Extensive experiments show that FlexLoRA consistently outperforms state-of-the-art baselines across benchmarks. Codes are available at https://github.com/Chongjie-Si/Subspace-Tuning.

Weight Spectra Induced Efficient Model Adaptation

Large-scale foundation models have demonstrated remarkable versatility across a wide range of downstream tasks. However, fully fine-tuning these models incurs prohibitive computational costs, motivating the development of Parameter-Efficient Fine-Tuning (PEFT) methods such as LoRA, which introduces low-rank updates to pre-trained weights. Despite their empirical success, the underlying mechanisms by which PEFT modifies model parameters remain underexplored. In this work, we present a systematic investigation into the structural changes of weight matrices during fully fine-tuning. Through singular value decomposition (SVD), we reveal that fine-tuning predominantly amplifies the top singular values while leaving the remainder largely intact, suggesting that task-specific knowledge is injected into a low-dimensional subspace. Furthermore, we find that the dominant singular vectors are reoriented in task-specific directions, whereas the non-dominant subspace remains stable. Building on these insights, we propose a novel method that leverages learnable rescaling of top singular directions, enabling precise modulation of the most influential components without disrupting the global structure. Our approach achieves consistent improvements over strong baselines across multiple tasks, highlighting the efficacy of structurally informed fine-tuning.