Large Language Models (LLMs) suffer severe performance degradation when facing extremely low-bit (sub 2-bit) quantization. Several existing sub 2-bit post-training quantization (PTQ) methods utilize a mix-precision scheme by leveraging an unstructured fine-grained mask to explicitly distinguish salient weights, while which introduces an extra 1-bit or more per weight. To explore the real limit of PTQ, we propose an extremely low-bit PTQ method called PTQ1.61, which enables weight quantization to 1.61-bit for the first time. Specifically, we first introduce a one-dimensional structured mask with negligibly additional 0.0002-bit per weight based on input activations from the perspective of reducing the upper bound of quantization error to allocate corresponding salient weight channels to 4-bit. For non-salient channels binarization, an efficient block-wise scaling factors optimization framework is then presented to take implicit row-wise correlations and angular biases into account. Different from prior works that concentrate on adjusting quantization methodologies, we further propose a novel paradigm called quantization preprocessing, where we argue that transforming the weight distribution of the pretrained model before quantization can alleviate the difficulty in per-channel extremely low-bit PTQ. Extensive experiments indicate our PTQ1.61 achieves state-of-the-art performance in extremely low-bit quantization. Codes are available at https://github.com/zjq0455/PTQ1.61.

Post-training quantization (PTQ) for large language models (LLMs) significantly accelerates model inference and relieves memory constraints, without incurring model training. A “smoothing paradigm” is commonly used in LLM quantization, which transfers the quantization difficulty of activation to weight quantization using mathematically equivalent transformations. However, existing methods face two issues: 1) Most smoothing parameters are hand-crafted defined which leads to suboptimal results; 2) There are significant performance degradations when tested on unseen datasets. To address these challenges, this paper introduces a robust learnable smooth-based PTQ framework, called LRQuant. Firstly, we consider a learnable paradigm to find optimal smoothing parameters which are initialized by logarithmic activation equivalent. In addition, we empirically found that only relying on MSE loss could hardly lead to optimal quantization results, and we then propose a novel loss function based on the negative logarithm of cosine similarity (NLC loss) between outputs of full-precision and quantized block. At last, we pioneeringly introduce Test-time adaptation (TTA) into LLM quantization, which allows for rapid model adaptation during testing to improve generalization performance. More surprisingly, we find that by using our TTA method, we can achieve better results on test sets than directly using test sets for calibration in some cases while avoiding catastrophic forgetting. Codes are available at https://github.com/zjq0455/RLQ.