Large Language Models (LLMs) showcase remarkable performance and robust deductive capabilities, yet their expansive size complicates deployment and raises environmental concerns due to substantial resource consumption. The recent development of a quantization technique known as Learnable Singular-value Increment (LSI) has addressed some of these quantization challenges. Leveraging insights from LSI and our extensive research, we have developed innovative methods that enhance the performance of quantized LLMs, particularly in low-bit settings. Our methods consistently deliver state-of-the-art results across various quantization scenarios and offer deep theoretical insights into the quantization process, elucidating the potential of quantized models for widespread application.