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

arXiv: https://arxiv.org/abs/2606.03458 · HTML: https://mlsanity.com/paper/2606.03458/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Efficient LLM inference and serving / [KV cache quantization](https://mlsanity.com/inference/kv-cache-quantization/)

## Builds on (most cited first, 6 of 6)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [Kitty: Accurate and Efficient 2-bit KV Cache Quantization with Dynamic Channel-wise Precision Boost](https://mlsanity.com/paper/2511.18643/) (2025)
- [Advancing Intelligent Sequence Modeling: Evolution, Trade-offs, and Applications of State-Space Architectures from S4 to Mamba](https://mlsanity.com/paper/2503.18970/) (2025)
- [SINQ: Sinkhorn-Normalized Quantization for Calibration-Free Low-Precision LLM Weights](https://mlsanity.com/paper/2509.22944/) (2025)

## Built on by (most cited first, 6 of 6)

- [WitCert: Sound Runtime Risk Observability and Gating for KV-Cache Quantization](https://mlsanity.com/paper/2607.28699/) (2026)
- [Regularize or Localize: When Training-Time KV-Cache Geometry Pays Under Quantization](https://mlsanity.com/paper/2607.17019/) (2026)
- [Faithfulness Is Not Free: Auditing Offline KV-Cache Quantization in Retrieval-Augmented Generation](https://mlsanity.com/paper/2608.30996/) (2026)
- [Quality Recovery for Quantized KV Caches via Low-Rank Attention Adaptation](https://mlsanity.com/paper/2609.04263/) (2026)
- [Low-Bit Recurrent States in Hybrid Language Models](https://mlsanity.com/paper/2609.30950/) (2026)
- [Spend Bytes on Breadth: Precision-Count Trade-offs for Decode-Time KV Compression in Long Chain-of-Thought Reasoning](https://mlsanity.com/paper/2610.05685/) (2026)

## Abstract (arXiv)

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-theart for KV-cache quantization on generative benchmarks, including MATH500, AIME24 and HumanEval, at 2-bit precision. A vLLM implementation of the KVarN method is available at https://github.com/huawei-csl/KVarN