Deploying and fine-tuning Large Language Models (LLMs) on resource-constrained edge devices requires navigating a strict trade-off between memory footprint and task performance. Existing quantization-aware fine-tuning methods typically decouple weight precision and adapter capacity, overlooking that a layer’s ability to adapt is constrained by the information preserved in its frozen weights. Layers that are highly sensitive to quantization—whether due to representational specialization or accumulated error propagation—can become bottlenecks that adapter rank alone cannot recover. To address this issue, we introduce QR-Adaptor, a unified framework that jointly optimizes per-layer quantization bit-width and LoRA rank. We formulate resource allocation as a multi-objective discrete search guided by empirical layer-wise sensitivity, and implement it with a three-stage pipeline comprising KL-based sensitivity profiling, evolutionary exploration, and Bayesian refinement. Extensive experiments across LLaMA and Qwen models, including modern instruction tuning on OpenOrca and comparisons with strong PEFT baselines such as QDoRA, show that QR-Adaptor establishes a strong Pareto frontier: under a strict 4-bit memory budget, it matches or approaches 16-bit baselines while using substantially less memory.

Instruction tuning has achieved unprecedented success in NLP, turning large language models into versatile chatbots. However, the increasing variety and volume of instruction datasets demand significant computational resources. To address this, it is essential to extract a small and highly informative subset (i.e., Coreset) that achieves comparable performance to the full dataset. Achieving this goal poses non-trivial challenges: 1) data selection requires accurate data representations that reflect the training samples’ quality, 2) considering the diverse nature of instruction datasets, and 3) ensuring the efficiency of the coreset selection algorithm for large models. To address these challenges, we propose Task-Agnostic Gradient Clustered COreset Selection (TAGCOS). Specifically, we leverage sample gradients as the data representations, perform clustering to group similar data, and apply an efficient greedy algorithm for coreset selection. Experimental results show that our algorithm, selecting only 5% of the data, surpasses other unsupervised methods and achieves performance close to that of the full dataset.

Recent Large-Language Models (LLMs) pruning methods typically operate at the post-training phase without the expensive weight finetuning, however, their pruning criteria often rely on **heuristically hand-crafted metrics**, potentially leading to suboptimal performance. We instead propose a novel **optimization-based structural pruning** that learns the pruning masks in a probabilistic space directly by optimizing the loss of the pruned model. To preserve the efficiency, our method **eliminates the back-propagation** through the LLM *per se* during the optimization, requiring only **the forward pass of the LLM**. We achieve this by learning an underlying Bernoulli distribution to sample binary pruning masks, where we decouple the Bernoulli parameters from the LLM loss, thus facilitating an efficient optimization via *policy gradient estimator* without back-propagation. As a result, our method is able to 1) *support global and heterogeneous pruning* (*i.e.*, our method automatically determines different redundancy for different layers), and 2) *optionally initialize with a metric-based method* (for our Bernoulli distributions). Extensive experiments conducted on LLaMA, LLaMA-2, LLaMA-3, Vicuna, and Mistral models using the C4 and WikiText2 datasets demonstrate the promising performance of our method in efficiency and effectiveness.