USC's Donghyun Lee team has published KronQ — a post-training quantization (PTQ) framework based on Kronecker-factored Hessian, directly hitting the 2-bit quantization dead end of the GPTQ family of methods. The paper has been accepted to COLM 2026, and the code and models are open-sourced under Apache 2.0. Second-order methods like GPTQ and GPTAQ both use the input activation's Hessian H_X as the quantization target, which is equivalent to assuming all output channels are equally important. KronQ's key rewrite: under the K-FAC approximation, decompose the target into H ≈ H_X ⊗ H_G, pulling the output-side curvature H_G back into the optimization objective — letting quantization truly distinguish the output channels that matter most to the final loss. Two new ideas in method: BiIP (Bidirectional Incoherence Processing) does an incoherence rotation plus rescale on both input and output sides, simultaneously suppressing weight variance; mixed-precision allocation between layers uses tr(H_G)·tr(H_X) as the sub-layer sensitivity indicator, dynamically slicing the bit budget to critical sub-layers, so a low-bit budget no longer means even allocation. The numbers are most convincing: on 2-bit weight quantization of LLaMA-3-70B, GPTQ and GPTAQ degrade directly to a WikiText-2 perplexity of >2000 (essentially unusable), while KronQ hits 7.93 — a difference of three orders of magnitude at the same level. On LLaMA-2-7B, W4/W2 PPL is 5.56/8.23 (fp16 baseline 5.47), almost no point loss, and W4 quantization is even more stable than the original bf16. On the deployment side, KronQ takes the packaged int4/int2 + fused dequant+BiIP CUDA matvec path; on A100, single-token decode is 6.30 ms (W2/W4 same speed), even faster than fp16's 11.6 ms — the traditional notion that "quantization equals slowing down" is completely flipped. For on-device LLM deployment and long-context inference, 2-bit has moved from a lab toy to a deployable tier, and Hugging Face has already released Llama-2/3 full-series W2/W3/W4 quantized models.