PrunedLoRA: Robust Gradient-Based structured pruning for Low-rank Adaptation in Fine-tuning

Low-rank adaptation (LoRA) has become a widely used paradigm for parameter-efficient fine-tuning of large language models, yet its representational capacity often lags behind full fine-tuning. Within the context of LoRA, a key open question is how to obtain expressive low-rank adapters from over-parameterized spaces. We propose \textit{PrunedLoRA}, a new framework that leverages structured pruning to obtain highly representative low-rank adapters from an over-parameterized initialization. Unlike prior approaches that impose a fixed low-rank budget, PrunedLoRA dynamically prunes less important components during fine-tuning and prevents their reactivation, enabling flexible and adaptive rank allocation. For structured pruning, by minimizing the pruning error for overall loss, we provide fine-grained pruning and recovery updates in a gradient-based pruning strategy with grounded interpretation. We provide the first theoretical analysis of the robustness of structured pruning and provably show that under the impact of weight perturbation, gradient-based pruning is more robust than activation-based pruning with respect to overall loss. Empirically, PrunedLoRA consistently outperforms LoRA and its variants across supervised fine-tuning tasks in mathematical reasoning, code generation, and natural language understanding, and it also demonstrates advantages over existing structured pruning methods across diverse sparsity levels.