This work systematically study weight-only post-training quantization across bit-widths, quantization methods, model scales and downstream tasks and establishes that quantization degradation is governed by how errors are introduced at the source and how they accumulate across the network.
Abstract
Post-training quantization reduces the deployment cost of large language models, yet how severely a quantized model degrades is not determined by bit-width alone. We systematically study weight-only post-training quantization across bit-widths, quantization methods, model scales and downstream tasks on multiple model families. We observe that such degradation varies substantially across these factors: 4-bit quantization usually preserves performance, 2-bit often causes broad degradation, and at 3-bit, degradation becomes apparent but varies markedly with task type, quantization method and model scale. To explain this variability, we use the signal-to-noise ratio (SNR) to measure how strongly quantization perturbs full-precision representations. We trace degradation back to two linked processes: how quantization errors arise within individual modules, and how they accumulate across layers. First, a source SNR decomposition shows that newly introduced errors depend on three factors: the magnitude of the weight error, the strength of the task-specific signal, and how strongly the quantization error aligns with task-specific activations. Different factors affect these components in distinct ways. Second, a cross-layer propagation analysis shows that these errors can be attenuated, preserved, or amplified as they pass across layers, and that larger models benefit from weaker error amplification. Together, these results establish that quantization degradation is governed by how errors are introduced at the source and how they accumulate across the network.
RDQ (Residual Distribution Quantization), a PTQ framework whose central contribution is Cascaded Error Compensation, a sequential calibration procedure that captures the actual drifted activations each layer receives and fits per-channel AWQ-style scales against those drifted inputs, with scales folded into preceding RMSNorm weights for exact mathematical equivalence at zero inference overhead.
ACBQ is presented, a simple yet effective framework that simultaneously addresses weight–activation joint quantization and extreme low-bit weight quantization and an adaptive cross-block quantization strategy that explicitly accounts for cross-layer dependencies by encouraging consistency across blocks.
Hailing Wang, Jianglin Lu, Yitian Zhang et al.· Annual Meeting of the Associ...· 0 citations
Layer-wise post-training quantization of large language models minimizes each layer's reconstruction error in isolation, allowing quantization errors to accumulate across depth and causing severe degradation in extreme low-bit regimes. We formulate quantization as a joint optimization over the discrete codes and scales of all layers, driven by two mechanisms: (i) cross-layer error compensation, which maintains the network-level accumulated error through the recursion e_{l+1} = A_l e_l + q_l, with a propagation operator A_l derived from the layer's input differential and a local quantization residual q_l evaluated at teacher features; and (ii) finite-sample feature-statistics matching, which aligns means, projected covariances, and centered empirical kernels between the full-precision and quantized networks under relative normalization. We prove that instantiating the propagation operator as a finite difference of the quantized network makes the recursion exact for arbitrary nonlinear layers, enabling an efficient forward-difference implementation. Binary weights are optimized via a mirror-descent parameterization u = tanh(beta*z) with annealed inverse temperature and group-wise log-scales. On Qwen2.5-1.5B with 1.125-bit group-binary weights, error compensation alone reaches a perplexity ratio of 9.56 +/- 0.15 over the FP16 teacher, outperforming logit distillation (14.09 +/- 0.53; 32 percent relative, more than 8 sigma over 3 seeds) and layer-local reconstruction by two orders of magnitude. The same objective transfers unchanged to 4-bit quantization (1.060 vs. 1.088 for layer-local). Out-of-domain evaluations (C4, CNN/DailyMail) show the advantage of error compensation grows off-domain, while statistics matching keeps feature-statistics discrepancy low off-domain (0.42-0.88 vs. 1.41-2.99 without it), revealing a complementary division of labor between the two mechanisms.
Mixed-precision quantization improves the accuracy of post-training quantization by allocating higher bitwidths to sensitive layers, but existing methods solve the allocation for a single fixed memory budget. In practice the budget varies across deployments and is unknown at calibration time. Adaptive quantization addresses this with one offline calibration that serves any budget, yet current methods score layer sensitivity in a manner that does not consider its dependency on quantization levels of other layers. We show that a layer's sensitivity depends strongly on the bitwidths of its upstream layers and that this dependence shifts the resulting preferred bit allocation. We propose MixQuant, a technique-agnostic adaptive framework that wraps any base quantizer. MixQuant marginalizes each layer's distortion over random quantized upstream configurations to obtain budget-agnostic scores, calibrates the quantizer's parameters on plans the allocator itself produces, and penalizes allocations that leave layers at the lowest bitwidths. A single greedy pass then serves any budget at deployment. Across Llama-3.2-3B, Llama-2-7B, and Mistral-7B under AWQ and GPTQ, MixQuant outperforms adaptive and mixed-precision baselines in every setting, improving average accuracy by up to 8 points and reducing perplexity from 12.43 to 10.70 at the tightest budget, while matching an ILP solver at negligible deployment cost.
Ashitabh Misra, Madhav Agrawal, Arham Jain et al.· 0 citations
Quantization of Large Language Models (LLMs) is often hindered by the sensitivity of the self-attention mechanism to discretization errors. We identify the softmax operator as a bottleneck for quantization stability due to its sensitivity to outliers and state-dependent Jacobian. We theoretically establish that suppressing the norm of this Jacobian helps in bounding quantization-induced performance degradation. Based on this, we propose Jacobian-Guided Noise Injection, a training strategy that injects zero-mean Gaussian noise into pre-attention logits, with variance derived directly from the Jacobian Frobenius norm. Unlike prior approaches that rely on heuristic or penalise jacobian directly, our method provides a way to identify the optimal noise variance based on the local attention sensitivity. We evaluate the method on SOTA LLM architectures, where it demonstrates improved robustness over popular PTQ methods. Empirical analysis reveals that the proposed method gives up to +37% relative gains on Top-1 accuracy on ImageNet-1K for SigLIP and improves relative perplexity by upto 40% on WikiText for language models in low bit quantisation settings, proving the efficacy of the approach.
D. Pandey, Arnav Chavan, Nahush Lele et al.· 0 citations
As large language models (LLMs) grow, their compute and memory demands become pro-hibitive for on-device deployment. Quantization is a crucial technique to shrink model footprint and accelerate inference, but aggressively low-bit weight-activation quantization schemes often sacrifice accuracy. Quantization Aware Training (QAT) is a commonly used paradigm to minimize quantization noise, but is extremely expensive to train and often un-scalable to large models. We introduce PE-QAT, a parameter-efficient framework targeting per-channel 4-bit weight-activation quantization of LLMs, which aims to preserve model accuracy while significantly reducing resource requirements. The proposed method freezes the base model and trains lightweight LoRA adapters by fake quantizing the merged-weight model, enabling PE-QAT to scale efficiently unlike full QAT. We apply fake quantization with Straight-Through Estimators (STE) to the merged weights, allowing the adapters to explicitly compensate for quantization noise during training. One of the biggest challenges with quantizing activations alongside weights is addressing outliers that are orders of magnitude larger than other activations, which in-flate quantization scales and suppress lower-magnitude values. To mitigate the impact of severe activation outliers, PE-QAT jointly learns per-channel smoothing factors and symmetric activation clipping thresholds. PE-QAT retains accuracy within 0.11 percentage points of the full-precision baseline on Llama-2-7B zero-shot tasks while training only 1.26% of total parameters.
Shresth Mishra· Annual Meeting of the Associ...· 0 citations