Low-rank adaptation (LoRA) has been developed as an efficient approach for adapting large language models (LLMs) by fine-tuning two low-rank matrices, thereby reducing the number of trainable parameters. However, prior research indicates that many of the weights in these matrices are redundant, leading to inefficiencies in parameter utilization. To address this limitation, we introduce Dense Low-Rank Adaptation (DenseLoRA), a novel approach that enhances parameter efficiency while achieving superior performance compared to LoRA. DenseLoRA builds upon the concept of representation fine-tuning, incorporating a single Encoder-Decoder to refine and compress hidden representations across all adaptation layers before applying adaptation. Instead of relying on two redundant low-rank matrices as in LoRA, DenseLoRA adapts LLMs through a dense low-rank matrix, improving parameter utilization and adaptation efficiency. We evaluate DenseLoRA on various benchmarks, showing that it achieves 83.8% accuracy with only 0.01% of trainable parameters, compared to LoRA’s 80.8% accuracy with 0.70% of trainable parameters on LLaMA3-8B. Additionally, we conduct extensive experiments to systematically assess the impact of DenseLoRA’s components on overall model performance.

Large Language Models (LLMs) have shown that their reasoning ability could be enhanced through approaches like Chain-of-Thought (CoT) prompting. However, these methods use single prompts for different types of questions and do not design appropriate prompts for questions with different characteristics. In this paper, we aim to explore a methodology that generates differentially diverse reasoning paths for different types of questions. To achieve this, we propose a novel prompting strategy called Differential Diversity Prompting (DDPrompt). Firstly, we generate the optimal prompts collection based on question characteristics. Then, we use this optimal prompts collection to generate multiple answers for a question and choose the final answer by voting. We evaluated DDPrompt on twelve reasoning benchmarks and significant improvement in the performance of LLMs on complex reasoning tasks (e.g., GSM8K 75%->84%, Tracking Shuffled Objects (68.8%->83.9%))