Decomposing weight matrices into quantization and low-rank components ( W≈ Q+LR) is a widely used technique for compressing large language models (LLMs). Existing joint optimization methods iteratively alternate between quantization and low-rank approximation. However, these methods tend to prioritize one component at the expense of the other, resulting in suboptimal decompositions that fail to leverage each component’s unique strengths. In this work, we introduce Outlier-Driven Low-Rank Initialization (ODLRI), which assigns low-rank components the specific role of capturing activation-sensitive weights. This structured decomposition mitigates outliers’ negative impact on quantization, enabling more effective balance between quantization and low-rank approximation. Experiments on Llama2 (7B, 13B, 70B), Llama3-8B, and Mistral-7B demonstrate that incorporating ODLRI into the joint optimization framework consistently reduces activation-aware error, minimizes quantization scale, and improves perplexity and zero-shot accuracy in low-bit settings.

Existing fairness benchmarks for large language models (LLMs) primarily focus on simple tasks, such as multiple-choice questions, overlooking biases that may arise in more complex scenarios like long-text generation. To address this gap, we introduce the Long Text Fairness Test (LTF-TEST), a framework that evaluates biases in LLMs through essay-style prompts. LTF-TEST covers 14 topics and 10 demographic axes, including gender and race, resulting in 11,948 samples. By assessing both model responses and the reasoning behind them, LTF-TEST uncovers subtle biases that are difficult to detect in simple responses. In our evaluation of five recent LLMs, including GPT-4o and LLaMA3, we identify two key patterns of bias. First, these models frequently favor certain demographic groups in their responses. Second, they show excessive sensitivity toward traditionally disadvantaged groups, often providing overly protective responses while neglecting others. To mitigate these biases, we propose REGARD-FT, a finetuning approach that pairs biased prompts with neutral responses. REGARD-FT reduces gender bias by 34.6% and improves performance by 1.4 percentage points on the BBQ benchmark, offering a promising approach to addressing biases in long-text generation tasks.