Post-Training Quantization (PTQ) is critical for the efficient deployment of Large Language Models (LLMs). While 4-bit quantization is widely regarded as an optimal trade-off, reducing the precision to 2-bit usually triggers a catastrophic “performance cliff.” It remains unclear whether the underlying mechanisms differ fundamentally. Consequently, we conduct a systematic mechanistic analysis, revealing two qualitatively distinct failure modes: Signal Degradation, where the computational patterns remain intact but information precision is impaired by cumulative error; and Computation Collapse, where key components fail to function, preventing correct information processing and destroying the signal in the early layers. Guided by this diagnosis, we conduct mechanism-aware interventions, demonstrating that targeted, training-free repair can mitigate Signal Degradation, but remains ineffective for Computation Collapse. Our findings provide a systematic diagnostic framework for PTQ failures and suggest that addressing Computation Collapse requires structural reconstruction rather than mere compensation.

Post-Training Quantization (PTQ) is a critical strategy for efficient large language models (LLMs) deployment. However, existing scaling laws primarily focus on general performance, overlooking crucial fine-grained factors and how quantization differentially impacts diverse knowledge capabilities. To address this, we establish Task-Stratified Knowledge Scaling Laws. By stratifying capabilities into memorization, application, and reasoning, we develop a framework that unifies model size, bit-width, and fine-grained factors: group size and calibration set size. Validated on 293 diverse PTQ configurations, our framework demonstrates strong fit and cross-architecture consistency. It reveals distinct sensitivities across knowledge capabilities: reasoning is precision-critical, application is scale-responsive, and memorization is calibration-sensitive. We highlight that in low-bit scenarios, optimizing these fine-grained factors is essential for preventing performance collapse. These findings provide an empirically-backed foundation for designing knowledge-aware quantization strategies.

Large language models (LLMs) reach state-of-the-art performance across many NLP tasks, but their large parameter counts introduce heavy computational and memory overhead, which complicates deployment in resource-constrained settings. Pruning is a standard compression strategy that induces sparsity to lower these costs. However, most pruning methods for LLMs depend on calibration data and expensive weight updates, which limits practical scalability. To address these limitations, we introduce Haar Wavelet Subband Pruning (), a post-training framework that requires no calibration data and no weight updates. applies a two-dimensional Haar wavelet transform to each weight matrix and decomposes it into four frequency subbands. It then assigns a uniform sparsity ratio to all subbands so that both low- and high-frequency components are retained in a balanced manner. Our theoretical analysis shows that the subband design of provides a deterministic per-subband retention guarantee, which helps mitigate the potential bias of global magnitude pruning toward dominant frequency components. Experiments on the LLaMA, OPT and Qwen model families show that achieves competitive accuracy relative to strong pruning baselines while substantially reducing pruning time. Compared with magnitude pruning, which serves as a simple calibration-free baseline, generally achieves better downstream performance across a wide range of sparsity levels and model scales.