@inproceedings{park-etal-2026-kernelquant,
title = "{K}ernel{Q}uant: Post-Training Quantization via Representation Kernel Preservation",
author = "Park, JuneYoung and
Kwon, Youngwook and
Kim, Seongwan and
Lee, Jaeho",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.856/",
pages = "19833--19850",
ISBN = "979-8-89176-459-0",
abstract = "Post-training quantization methods universally minimize element-wise reconstruction error, yet we show this is the wrong objective. A systematic correlation study on LLaMA models reveals that the \textit{representation kernel} (the matrix of pairwise cosine similarities among calibration inputs) is a substantially stronger proxy for downstream task performance than weight MSE or output MSE. Building on this finding, we propose KernelQuant, a training-free PTQ framework comprising: KPQ, which selects weight-quantization scales via kernel-MSE grid search followed by least-squares error compensation; model-level Hadamard rotation; and KPC, a kernel-preserving per-channel activation clipping scheme. KernelQuant introduces zero inference overhead beyond QuaRot and calibrates in minutes rather than hours. On LLaMA 3B{--}70B, KernelQuant achieves state-of-the-art W4A16 perplexity and competitive W4A4 results. On reasoning benchmarks (MMLU), where 4-bit quantization causes a ``reasoning cliff,'' KernelQuant retains the highest fraction of FP16 accuracy among all evaluated baselines, both rotation-based (QuaRot, SpinQuant, FlatQuant) and element-wise, reversing the perplexity-based ranking and supporting the view that reasoning depends on the geometric relations the kernel preserves."
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<abstract>Post-training quantization methods universally minimize element-wise reconstruction error, yet we show this is the wrong objective. A systematic correlation study on LLaMA models reveals that the representation kernel (the matrix of pairwise cosine similarities among calibration inputs) is a substantially stronger proxy for downstream task performance than weight MSE or output MSE. Building on this finding, we propose KernelQuant, a training-free PTQ framework comprising: KPQ, which selects weight-quantization scales via kernel-MSE grid search followed by least-squares error compensation; model-level Hadamard rotation; and KPC, a kernel-preserving per-channel activation clipping scheme. KernelQuant introduces zero inference overhead beyond QuaRot and calibrates in minutes rather than hours. On LLaMA 3B–70B, KernelQuant achieves state-of-the-art W4A16 perplexity and competitive W4A4 results. On reasoning benchmarks (MMLU), where 4-bit quantization causes a “reasoning cliff,” KernelQuant retains the highest fraction of FP16 accuracy among all evaluated baselines, both rotation-based (QuaRot, SpinQuant, FlatQuant) and element-wise, reversing the perplexity-based ranking and supporting the view that reasoning depends on the geometric relations the kernel preserves.</abstract>
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%0 Conference Proceedings
%T KernelQuant: Post-Training Quantization via Representation Kernel Preservation
%A Park, JuneYoung
%A Kwon, Youngwook
%A Kim, Seongwan
%A Lee, Jaeho
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F park-etal-2026-kernelquant
%X Post-training quantization methods universally minimize element-wise reconstruction error, yet we show this is the wrong objective. A systematic correlation study on LLaMA models reveals that the representation kernel (the matrix of pairwise cosine similarities among calibration inputs) is a substantially stronger proxy for downstream task performance than weight MSE or output MSE. Building on this finding, we propose KernelQuant, a training-free PTQ framework comprising: KPQ, which selects weight-quantization scales via kernel-MSE grid search followed by least-squares error compensation; model-level Hadamard rotation; and KPC, a kernel-preserving per-channel activation clipping scheme. KernelQuant introduces zero inference overhead beyond QuaRot and calibrates in minutes rather than hours. On LLaMA 3B–70B, KernelQuant achieves state-of-the-art W4A16 perplexity and competitive W4A4 results. On reasoning benchmarks (MMLU), where 4-bit quantization causes a “reasoning cliff,” KernelQuant retains the highest fraction of FP16 accuracy among all evaluated baselines, both rotation-based (QuaRot, SpinQuant, FlatQuant) and element-wise, reversing the perplexity-based ranking and supporting the view that reasoning depends on the geometric relations the kernel preserves.
%U https://aclanthology.org/2026.emnlp-main.856/
%P 19833-19850
Markdown (Informal)
[KernelQuant: Post-Training Quantization via Representation Kernel Preservation](https://aclanthology.org/2026.emnlp-main.856/) (Park et al., EMNLP 2026)
ACL