This work proposes 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, which provides a way to identify the optimal noise variance based on the local attention sensitivity.
Abstract
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.
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.
Chenxi Zhou, Pengfei Cao, Jin Ye et al.· 0 citations
Deployment of Large Language Models (LLMs) on memory-constrained edge devices relies heavily on aggressive post-training quantization. However, evaluating these models is largely based on zero-shot task accuracy, which depends solely on argmax predictions and is insensitive to changes in the underlying predictive distribution. Consequently, accuracy can exhibit unstable, non-monotonic behavior under progressive quantization, masking substantial fidelity loss relative to the BFloat16 (BF16) uncompressed base model and providing misleading deployment signals. We introduce a distribution-sensitive evaluation framework quantifying information loss in quantized LLMs as the divergence between full-vocabulary predictive distributions at the token decision boundary. We compute statistical distances, including Jensen-Shannon Divergence and Total Variation Distance, between outputs of full-precision and quantized models, enabling a fine-grained analysis of distributional shift. Using this framework, we quantify probability mass displacement and distributional drift relative to the BF16 reference, capturing predictive distribution changes not reflected in top-1 accuracy. We conduct a 120-run experimental matrix across five foundation architectures and four reasoning benchmarks under progressive quantization regimes, from uncompressed BF16 to Q2_K, providing a systematic fidelity analysis. Our results show divergence metrics generally increase under stronger quantization, complementing task accuracy with a fidelity signal. Across tested llama-cpp schemes, mixed-precision Q4_K generally yields lower divergence than uniform Q4_0 at similar memory footprints. These findings motivate distribution-aware evaluation as a practical diagnostic complement to task accuracy; they do not directly establish correctness, calibration, safety, or user-perceived quality.
Shahzeb Qamar, L. Sparrenberg, Christian Bauckhage et al.· 0 citations
C-PTQ is proposed, a unified channel-wise PTQ method that harmonizes task-specific loss perturbation and quantization error and achieves state-of-the-art performance without auxiliary modules like LoRA, thereby maintaining high efficiency.
Jiameng Li, Han Zhou, M. Blaschko· arXiv.org· 0 citations
Post-training quantization compresses large language models (LLMs) by storing their weights at reduced precision, and each quantized weight introduces an error into the hidden states. Naively, these errors should accumulate with depth and corrupt next-token prediction; randomly initialized models accumulate these discrepancies rapidly, whereas quantized pretrained models accumulate much less hidden-state error and largely maintain downstream task performance, even though they were never trained with quantization noise. This raises the question we address: why does post-training quantization work? Comparing full-precision and quantized forward passes, we identify two mechanisms that characterize pretrained quantization robustness. First, the error a layer newly introduces tends to oppose the error it inherits from the layer's input. The two cancel partially such that the discrepancy between full-precision and quantized passes grows slowly. This counteracting residual interaction develops during pretraining. Our quantitative analysis identifies it as a major factor slowing hidden-error growth. Second, LM-head geometry preferentially preserves the scores and probabilities of high-ranked tokens, which typically represent the model's most confident predictions. Together, these mechanisms explain why quantization error that passes through numerous layers can still produce only small output changes, and we verify the findings across models and quantization settings.
Yu-Xiang Chen, Michael Beyer, Jun Zhu et al.· 0 citations
This work proposes a low-precision training framework based on 2D block FP4 quantization, which enforces transposition-invariant scaling and preserves consistency between forward and backward computations, and combines this with truncation-free scaling and stochastic rounding to control quantization error and maintain unbiased gradients.
Mehdi Rahimifar, Amin Darabi, Mehran Taghian Jazi et al.· arXiv.org· 2 citations
Noise injection is a well-known technique in stochastic optimization. We report its surprising effectiveness with an interleaved (on-off-on-off...) rather than the usual monotonic decay schedule. We present a theoretical analysis of noise injection, which confirms that corruption by impulse noise approximates a Jacobian regularization, whereas Gaussian noise acts as a curvature penalty. This regularization behavior has been invoked to explain why noise injection increases model robustness. But the interleaved nature of our proposed schedule produces superior results even for the optimization objective: mixing phases of noisy data permits the optimizer to escape local minima and increase exploration without the risk of catastrophically forgetting the important features from the clean data. To stabilize this training scheme against the rapid changes of the loss when switching between clean and noisy data, we introduce a gradient-norm stabilization technique that scales noisy updates based on clean gradient magnitudes. We compare this method with other common augmentation methods and find substantial improvements in corruption tolerance and robustness to real-world distribution shifts on CIFAR-100-C, ImageNet-C, and ImageNet-R for ResNet and ViT architectures, with the best results being achieved by stacking our method on top of other augmentations. Through saliency and attention maps we show that the effect of interleaved noise injection stems from penalizing the failure modes encouraged by the inductive bias of the models: impulse noise works against the locality bias of convolutional (ResNet) architectures, and Gaussian noise reduces the tendency of attention-based models to pick up large-scale spurious features. Interleaved noise injection is therefore an effective tool to improve the test performance on clean, noisy, and out-of-distribution data at essentially zero computational cost.
M. Wiemann, Peter Melchior, A. Saydjari· arXiv.org· 0 citations
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