Fairness in machine learning has attracted increasing attention in recent years.

Studying the sensitivity of weight perturbation in neural networks and its impacts on model performance, including generalization and robustness, is an active research topic due to its implications on a wide range of machine learning tasks such as model compression, generalization gap assessment, and adversarial attacks. In this paper, we provide the first integral study and analysis for feed-forward neural networks in terms of the robustness in pairwise class margin and its generalization behavior under weight perturbation.

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.

Our findings reveal that the dynamics of standard SAM effectively reduce to applying SAM solely in the last layer in wide neural networks, even with optimal hyperparameters.