Large Language Models (LLMs) possess astonishing capabilities but their size presents significant computational challenges. Quantization, a technique for compressing these models by reducing the precision of their numerical representations, offers a solution but often leads to performance degradation. Researchers have traditionally focused on minimizing quantization errors directly, either by compensating with other weights or by shifting quantization difficulty to other parts of the model. This new research introduces a novel approach called Learnable Singular value Increment (LSI), which ingeniously leverages these errors for model optimization. Inspired by image compression and efficient training methods, LSI strategically introduces small disturbances in the original weight distribution. This hierarchical restructuring groups weights to conform better to the quantized state, using the errors constructively. The approach incorporates existing smoothing and clipping techniques to fine-tune the process, effectively reducing outliers and optimizing quantization scales. Remarkably, the method is data-free in the post-training quantization context, meaning it doesn't require retraining on large datasets—a huge advantage in terms of time and resources. LSI achieves state-of-the-art performance across diverse quantization settings, from weight-only to weight-activation and even ultra-low bit scenarios. Crucially, LSI even enables efficient fine-tuning of quantized models, opening doors to specialized applications without compromising the overall capabilities of the model. While challenges like overfitting and training instability remain, this research marks a significant step toward more efficient and accessible large language models.