SECURA: Sigmoid-Enhanced CUR Decomposition with Uninterrupted Retention and Low-Rank Adaptation in Large Language Models

With the rapid development of large language models (LLMs), fully fine-tuning (FT) these models has become increasingly impractical due to the high computational demands. Additionally, FT can lead to catastrophic forgetting. As an alternative, Low-Rank Adaptation (LoRA) has been proposed, which fine-tunes only a small subset of parameters, achieving similar performance to FT while significantly reducing resource requirements. However, since LoRA inherits FT's design, the issue of catastrophic forgetting remains. To address these challenges, we propose SECURA: Sigmoid-Enhanced CUR Decomposition LoRA, a novel parameter-efficient fine-tuning (PEFT) variant that mitigates catastrophic forgetting while improving fine-tuning performance. Our method introduces a new normalization technique, SigNorm, to enhance parameter retention and overall performance. SECURA has been evaluated on a variety of tasks, including mathematical problem-solving (GSM8K), challenging question-answering (CNNDM), translation (NewsDE), and complex multiple-choice reasoning (LogiQA). Experimental results show that SECURA achieves an average fine-tuning improvement of 3.59% across four multiple-choice question (MCQ) tasks and a 2.51% improvement across five question-answering (QA) tasks on models such as Gemma2 2b, Qwen2 1.5b, Qwen 2 7b, Llama3 8b, and Llama3.1 8b, compared to DoRA. Moreover, SECURA demonstrates superior knowledge retention capabilities, maintaining more than 70% accuracy on basic LLM knowledge across 16 continual learning tests, outperforming Experience Replay (ER), Sequential Learning (SEQ), EWC, I-LoRA, and CUR-LoRA.