Norm-Bounded Low-Rank Adaptation (2501.19050v3)

Abstract: In this work, we propose norm-bounded low-rank adaptation (NB-LoRA) for parameter-efficient fine tuning. NB-LoRA is a novel parameterization of low-rank weight adaptations that admits explicit bounds on each singular value of the adaptation matrix, which can thereby satisfy any prescribed unitarily invariant norm bound, including the Schatten norms (e.g., nuclear, Frobenius, spectral norm). The proposed parameterization is unconstrained, smooth, and complete, i.e. it covers all matrices satisfying the prescribed rank and singular-value bounds. Comparative experiments on LLMs show that NB-LoRA achieves superior adaptation performance and faster training over a range of models, tasks and ranks. Vision fine-tuning experiments show that NB-LoRA can achieve strong adaptation performance while avoiding model catastrophic forgetting, and compared to existing approaches it is substantially more robust to a hyper-parameters such as including adaptation rank, learning rate and number of training epochs.