Organizations: School of Computer and Communication Sciences, EPFL, Switzerland · 2Huawei, Switzerland · 3Swiss Data Science Center, ETHZ & EPFL, Switzerland
Abstract
Low-bit quantization has been widely adopted to accelerate the inference of large language models (LLMs) by significantly reducing computational cost and memory usage. However, activation outliers pose a major challenge to effective quantization, often leading to notable performance degradation. In this paper, we introduce OffQ, a method designed to mitigate activation outliers in low-bit quantization through a novel offsetting mechanism. Specifically, OffQ first identifies a low-dimensional outlier subspace in the activations using a proposed top-1 PCA, and then concentrates high-magnitude activations into 1 channel via rotation. OffQ then absorbs this concentrated outlier channel by converting its magnitude into a shared offset, thereby reducing the standard deviation of the activations. This offsetting strategy enables effective W4A4KV4 quantization of LLMs using deployment-friendly uniform-grid and uniform-precision quantization. Extensive experiments across diverse LLM architectures and benchmarks demonstrate that OffQ outperforms state-of-the-art baselines, consistently improving model accuracy while preserving low-bit efficiency.
Large Language Models (LLMs) have demonstrated remarkable capabilities. However, their massive parameter scale leads to significant resource consumption and latency during inference. Post-training weight-only quantization offers a promising solution by reducing model size and accelerating token generation through alleviating the memory-bound issue. Nevertheless, the presence of inherent systematic outliers in weights continues to be a major obstacle. While existing methods, such as scaling and rotation, attempt to address this issue, the performance remains unsatisfactory. In this paper, we propose Outlier Self-Absorption Quantization (OSAQ), which performs additive weight suppression guided by the second-order low-rank property for low-bit weight-only quantization of LLMs. Specifically, we observe that the Hessian exhibits low-rank consistency across different inputs, with certain directions consistently showing vanishing curvature. Leveraging this property, we identify a stable null space of the Hessian and then construct an additive weight transformation by linearly combining the vectors within this null space, thereby suppressing weight outliers without affecting the task loss. This additive transformation can be absorbed into the weights offline, requiring no inter-layer transformations and introducing no inference overhead. Moreover, the construction is efficiently achieved by a closed-form solution, without resource-intensive training or iterative procedures. Extensive experiments demonstrate that OSAQ effectively suppresses outliers and enhances low-bit quantization performance. For instance, in 2-bit quantization, OSAQ, when integrated with GPTQ, achieves over 40% lower perplexity compared to vanilla GPTQ.
Low-bit activation quantization remains a major bottleneck in efficient large language model (LLM) deployment. The difficulty is not only that activations contain outliers, but that their distributions are often poorly matched to a low-bit uniform quantizer. Existing post-training quantization (PTQ) methods suppress peaks, balance channels, or minimize reconstruction error, yet they rarely specify what activation distribution is actually easy to discretize. As a result, activations may appear numerically smoother while still incurring large quantization error because the quantization range remains wide or most values collapse into a few levels near the mean. We recast activation transformation as quantizer-facing distribution design and analyze quantization error from an information-theoretic perspective. Our analysis shows that quantization-friendly activations should jointly have a smaller numerical range and sufficient dispersion within that range. Guided by this analysis, we propose InfoQuant, a train-free method that employs Peak Suppression Orthogonal Transformation (PSOT) to shape activations into more quantization-friendly distributions. We further introduce adaptive outlier-token selection to improve the robustness of PSOT during optimization. Across multiple LLM families, InfoQuant consistently outperforms prior PTQ and end-to-end training baselines. Under W4A4KV4, it preserves 97% of floating-point accuracy on average and reduces the LLaMA-2 13B performance gap by 42% over the previous state of the art. Code is available at https://github.com/LLIKKE/InfoQuant
Post-training quantization has emerged as a widely adopted technique for compressing and accelerating the inference of Large Language Models (LLMs). The primary challenges in LLMs quantization stem from activation outliers, which significantly degrade model performance especially at lower bit precision. While recent approaches attempt to mitigate outliers through linear transformations across feature dimensions, our analysis reveals that the transformed weights and activations still exhibit persistent outlier patterns with concentrated magnitude distributions. In this paper, we first model the mathematical relationship between quantization error and outliers, and then introduce a new metric Flatness to quantify the distribution of outliers. Based on this, we derive the theoretical optimal solution with respect to Flatness. Building on these insights, we propose Bidirectional Diagonal Quantization (BDQ), a novel post-training quantization framework that effectively disperses outlier patterns through optimized matrix transformations. BDQ strategically distributes outlier magnitudes across matrix dimensions via learned diagonal operations. Extensive experiments demonstrate that BDQ establishes a new quantization benchmark. It achieves less than 1% accuracy drop in W4A4 quantization on the LLaMA-3-8B model. In the more challenging W2A4KV16 experiment, compared to state-of-the-art approaches, BDQ reduces the performance gap by 39.1% on the DeepSeek-R1-Distill-LLaMA-70B model.