Large Language Models (LLMs) have demonstrated exceptional proficiency in language-related tasks, but their deployment poses significant challenges due to substantial memory and storage requirements. Weight-only quantization has emerged as a promising solution to address these challenges. Previous research suggests 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. SignRound integrates the advantages of Quantization-Aware Training (QAT) and Post-Training Quantization (PTQ), achieving exceptional results across 2 to 4 bits while maintaining low tuning costs and avoiding additional inference overhead. For example, SignRound achieves absolute average accuracy improvements ranging from 6.91\% to 33.22\% at 2 bits. It also demonstrates robust generalization to 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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