Post-training quantization (PTQ) is a widely adopted technique for compressing large language models (LLMs) without retraining. Existing second-order PTQ methods, including GPTQ, construct quantization objectives exclusively from input activation statistics, effectively assuming that all output channels contribute equally to the layer-wise reconstruction objective. We propose KronQ, a PTQ framework that challenges this assumption by introducing the gradient covariance into the quantization pipeline. Under the Kronecker-factored Hessian approximation, the quantization loss depends jointly on both the activation and gradient covariances, and KronQ exploits this at two complementary levels. (1) KronQ introduces bidirectional incoherence processing, extending the existing input-side random rotation to the output dimension using the gradient covariance, reducing weight magnitude variance across both input and output dimensions. (2) KronQ derives a new sensitivity metric for inter-layer mixed-precision allocation, driven by the gradient and activation Hessian traces. Notably, in the case of 2-bit weight-only quantization on LLaMA-3-70B, while GPTQ and GPTAQ diverge or produce degenerate quantizations (>2000 perplexity on WikiText-2), KronQ achieves 7.93 perplexity.
Post-training quantization (PTQ) is essential for deploying large language models (LLMs) under strict resource constraints. State-of-the-art PTQ methods quantize each layer with a single closed-form second-order solver: to remain analytically tractable, they heavily approximate the global loss (dropping cross-channel coupling, pooling output rows into groups), and they then freeze the resulting Hessian across the entire layer, with no way to refresh it as the loss landscape shifts column by column--a phenomenon we call information misalignment. We propose REAL-Q (Real-time E2E-loss Aligned LLM Quantization), a novel PTQ paradigm that breaks this compromise: instead of diluting the objective for the sake of analytic tractability, REAL-Q targets an end-to-end-aligned surrogate of the global loss and refines it via fine-grained, dynamic Block-wise Gradient Descent applied after every column block (128 columns). By coupling this fine-grained correction with a sliding window mechanism for smooth cross-layer transitions, REAL-Q effectively mitigates error propagation across the network. On LLaMA-3.1 (8B and 70B) and Qwen3 (0.6B-32B) at W4A16, REAL-Q reduces end-to-end KL divergence by up to ~49% relative to state-of-the-art globally-guided methods.
Post-training quantization (PTQ) has become an important technique for reducing the inference cost of Large Language Models (LLMs). While recent mixed-precision methods improve ultra-low bit quantization by preserving critical subspaces in high precision, they typically construct these subspaces relying solely on activation statistics. This ignores the fundamental nature of linear operations, where the output perturbation is jointly driven by both activation and weight quantization noise. In this paper, we propose CoQuant, a joint weight-activation subspace projection method. By theoretically modeling the expected output error, CoQuant formulates a closed-form weighted PCA solution that balances activation and weight covariances to select the optimal high-precision subspace. Extensive experiments on Llama-3.2 and Qwen2.5 models show that CoQuant consistently outperforms strong PTQ baselines in both WikiText perplexity and zero-shot common-sense reasoning accuracy. These results demonstrate that joint weight-activation subspace modeling provides a principled and effective direction for low-bit LLM quantization. The source code is available at https://github.com/Zachary5895/CoQuant.
Quantization is an effective strategy to reduce the storage and computation footprint of large language models (LLMs). Post-training quantization (PTQ) is a leading approach for compressing LLMs. Popular weight quantization procedures, including GPTQ and RTN, suffer in model utility, especially at aggressive quantization levels (sub-4-bit). We propose ADMM-Q, a novel weight quantization algorithm that considers the layer-wise quantization problem. Our algorithm is based on a combinatorial variant of the Alternating Direction Method of Multipliers (ADMM). Our operator-splitting procedure updates weights continuously to minimize the layer-wise reconstruction error, while gradually enforcing the quantization constraints with convergence guarantees. We propose additional algorithmic enhancements (e.g., penalty scheduling, preconditioning, and a local search post-processing step) to make ADMM-Q efficient at LLM scale. ADMM-Q is modular and can be used as a drop-in replacement for any weight quantizer within existing quantization pipelines: ADMM-Q is fully composable with existing techniques including range clipping, learned or random rotations, and activation scaling. Using ADMM-Q in place of GPTQ on Qwen3-8B, we decrease WikiText-2 perplexity in: (i) the W3A16 weight-only setting (12.85 → 10.06); (ii) the W4A8 SmoothQuant procedure (9.29 → 8.68); and (iii) the W2A4KV4 SpinQuant procedure (66.11 → 19.42).