Align, Then Correct: Training-Free Two-Stage Low-Rank Compensation for Extremely Quantized Large Language Models

Abstract:Low-rank quantization error compensation (LQEC) recovers the accuracy lost under aggressive weight quantization by attaching a closed-form rank-$r$ adapter beside each frozen quantized weight, without any training. We show that existing compensators are limited by two shared simplifications. They calibrate symmetrically, evaluating the full-precision and compensated weights on the same activation, which yields a compensation target that is inherently high-rank -- so a fixed rank budget captures only a small fraction of it. And they minimize only the second-order term of the loss, although the compensated model is not stationary: a first-order descent direction larger than the applied compensation itself remains in every layer, and no reconstruction objective can absorb it. We propose a two-stage closed-form framework that removes both simplifications. Stage 1 aligns each layer's output with the full-precision model under a Fisher-weighted asymmetric objective, concentrating the rank budget on a rank-compressible target. Stage 2 re-measures statistics on the compensated model and applies a rank-constrained natural-gradient step that absorbs the remaining first-order signal. Every adapter is the result of a single truncated SVD; backward passes serve only to collect statistics. At 2 bits under QuIP#, our method reduces WikiText-2 perplexity from 12.43 to 10.26 on Qwen3-8B and from 21.11 to 13.22 on Qwen3-4B. On the held-out C4 corpus, it recovers 51% and 84% of the gap to FP16, versus 31% and 63% for the strongest baseline, with consistent gains in the seven-task zero-shot average, at higher bit-widths, and under a distinct quantizer.

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2610.08164 [cs.LG]

(or arXiv:2610.08164v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.08164 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.