Jacobian-guided Noise Injection for Quantization Robustness in Large Language Models

Quantization-aware training (QAT) is widely deployed but typically relies on the Straight-Through Estimator (STE), which passes gradients through non-differentiable quantizers by fiat. This often makes training brittle near bin boundaries and weakly aligned with the actual behavior of the low-precision model. We introduce JacQuant, a QAT framework that learns a lightweight surrogate of the model's local sensitivity to parameter changes and uses it to stabilize and accelerate training within standard variance-reduced optimizers. The surrogate is inexpensive (diagonal or block-diagonal), data-driven, and compatible with common weight and activation quantizers. On code-preserving training phases, we prove convergence for non-convex objectives and obtain linear rates under a PL condition, and we relate the learned sensitivity to end-to-end output fidelity via a simple calibration argument. Across LLM benchmarks at $\leq 2$ bits, JacQuant consistently reaches higher accuracy than STE-based QAT, and the runtime analyses on various models show that the added cost remains negligible under practical group sizes. The method is drop-in and requires no changes to the forward quantizers; our empirical claims are scoped to ultra-low-bit LLM QAT.

Large Language Models (LLMs) are widely used across many domains, but their scale makes deployment challenging. Post-Training Quantization (PTQ) reduces memory footprint without retraining by leveraging a small calibration set. Recent Hessian-based PTQ methods compensate quantization error via cross-channel dependencies, but such approaches degrade at low bit-widths due to noisy curvature estimates from limited calibration data. We propose DASH-Q, a robust PTQ framework using diagonal Hessian approximation and iterative weighted least squares. By discarding noise-prone dependencies, DASH-Q filters sampling noise while prioritizing the preservation of salient feature power. We outperform other PTQ baselines in ultra low-bit regime, improving zero-shot accuracy by 7.01% on average and up to 14.01% over the strongest baselines across five baseline LLM models, while showing robust and stable performance with very small calibration data.

Post-Training Quantization (PTQ) enables efficient deployment of Large Language Models (LLMs), yet activation outliers remain a key challenge for low-bit quantization. Existing global transformation methods overlook heterogeneous channel sensitivity to quantization noise, leading to suboptimal accuracy-efficiency trade-offs. To address this, we propose Locally Isolated Rotation Quantization (LIRQuant), a sensitivity-aware framework that selectively applies transformations. LIRQuant identifies sensitive channels using a noise-weighted sensitivity metric, applying expressive learnable rotations only to these channels and lightweight fixed rotations to the remaining ones. This decoupled design reduces optimization complexity without sacrificing outlier smoothing capability. Extensive experiments across the LLaMA-2/3, Mistral, Qwen3, and Mixtral families demonstrate that LIRQuant achieves state-of-the-art accuracy under the challenging W4A4KV4 setting. Meanwhile, LIRQuant calibrates LLaMA-3-8B in only 25 minutes with 20.3 GB peak GPU memory, achieving the fastest calibration and the lowest memory footprint among recent learnable-rotation methods, and its fused inference kernels deliver up to $2.3\times$ prefill speedup and $3.5\times$ memory saving over FP16.