Factual knowledge stored in Large Language Models (LLMs) inevitably becomes outdated or erroneous over time, making it critical to update these models without incurring the high cost of retraining. Existing sequential knowledge editing methods predominantly rely on strict orthogonal projection to preserve previously edited knowledge. However, this excessive constraint limits gradient expressiveness, resulting in a significant degradation of model generalization and overall performance as the number of edits increases. To address this challenge, we propose Dual-Importance Projection Editing (DipEdit). This method leverages Singular Value Decomposition (SVD) to identify critical gradient subspaces and introduces a dual mechanism comprising “accumulated importance” and “projection importance.” Unlike traditional approaches that enforce strict orthogonality, DipEdit dynamically scales gradient components parallel to key subspaces based on their projection importance rather than discarding them directly. This approach enhances the model’s adaptability to new knowledge while maximally preserving historical knowledge. Extensive experiments conducted on five mainstream LLMs using the ZsRE and Counterfact datasets demonstrate that DipEdit effectively handles thousands of sequential edits. The proposed method achieves an average comprehensive performance improvement of 10.36% and effectively maintains the model’s general capabilities on downstream tasks. Code is available at: https://github.com/czhhhla/DipEdit.

Low-bit quantization is crucial for deploying Large Language Models (LLMs) on resource-constrained hardware. However, existing Post-Training Quantization (PTQ) methods adopt a monolithic view of outliers, overlooking their global spatial patterns within LLM architectures and weights that are quantization-sensitive but not numerically large. To overcome these challenges, we introduce MOAQ, a novel finetuning-free weight-only PTQ framework based on a new perspective for outlier analysis. MOAQ holistically addresses the outlier problem by three core components: (1) Spatial Calibration (SC) uses a clustering-optimized Hadamard matrix to reorganize disordered outliers into both discrete and clustered patterns. (2) Local Awareness and Suppression (LAS) adopts a dual strategy guided by our outlier metric. It assigns higher bit-widths to clustered outliers via Clustered Outlier Bit Search (COBS), enabling flexible fractional-bit quantization, while further refining quantization parameters for local discrete outliers through Local Outlierness-Aware Calibration (LOAC). (3) Global Feedback and Denoising (GFD) introduces a dynamic correction mechanism informed by our outlier metric to mitigate the progressive cross-layer enrichment of outliers. Extensive experiments show that MOAQ achieves state-of-the-art performance, outperforming both finetuning-free and many finetuning-based methods with substantially lower computational cost.