KVarN: Variance-Normalized KV-Cache Quantization Mitigates Error Accumulation in Reasoning Tasks

Abstract

Test-time scaling is a powerful approach to obtain better reasoning in large language models, but it becomes memory-bottlenecked during long-horizon decoding, as the KV-cache grows. KV-cache quantization can help improve this, but current methods are evaluated under prefill-like settings and errors behave differently under autoregressive decoding. We show that in the latter regime, quantization errors accumulate across timesteps, driven primarily by incorrect token scales. We introduce KVarN, a calibration-free KV-cache quantizer that applies a Hadamard rotation followed by a dual-scaling variance normalization across both axes of the K and V matrices. We find that this combination fixes outlying token-scale errors and substantially reduces error accumulation over existing baselines. KVarN establishes a new state-of-the-art for KV-cache quantization on generative benchmarks, including MATH500, AIME24 and HumanEval, at 2-bit precision. Code is supplied in the supplementary.

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Cite this work

@misc{kvarn,
  title = {KVarN: Variance-Normalized KV-Cache Quantization Mitigates Error Accumulation in Reasoning Tasks},
  author = {Lorenz Mueller and Philippe Bich and Chiara Boretti and Hyun Min Chang and Jiawei Zhuang and Lukas Cavigelli},
  year = {2026},
  note = {arXiv},
  url = {https://arxiv.org/abs/2606.03458}
}

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