Large Language Models (LLMs) have demonstrated exceptional proficiency in language-related tasks. However, their deployment presents significant challenges due to their substantial memory and storage requirements. To address this challenge, weight-only quantization has emerged as a promising solution. Previous research has indicated that fine-tuning through up and down rounding can enhance performance. In this study, we introduce SignRound, a method that utilizes signed gradient descent (SignSGD) to optimize rounding values and weight clipping within just 200 steps, combining the strengths of both Quantization-Aware Training (QAT) and Post-Training Quantization (PTQ). SignRound achieves outstanding results compared to recent methods across 2 to 4 bits, while maintaining low tuning costs and without introducing any additional inference overhead. For instance, SignRound led to absolute average accuracy improvements ranging from 6.91\% to 33.22\% at 2 bits. Furthermore, it demonstrates robust generalization to various recent models and achieves near-lossless quantization in most scenarios at 4 bits. The source code is publicly available at \url{https://github.com/intel/auto-round}.
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