# HeadQ: Model-Visible Distortion and Score-Space Correction for KV-Cache Quantization

arXiv: https://arxiv.org/abs/2605.03562 · HTML: https://mlsanity.com/paper/2605.03562/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in KV cache quantization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 20 of its 24 references that are in the map.
- First posted on arXiv 5 May 2026.

## Placed in

- Efficient LLM inference and serving / [KV cache quantization](https://mlsanity.com/inference/kv-cache-quantization/)

## Builds on (most cited first, 20 of 20)

- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache](https://mlsanity.com/paper/2402.02750/) (2024)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [RotateKV: Accurate and Robust 2-Bit KV Cache Quantization for LLMs via Outlier-Aware Adaptive Rotations](https://mlsanity.com/paper/2501.16383/) (2025)
- [KVTuner: Sensitivity-Aware Layer-Wise Mixed-Precision KV Cache Quantization for Efficient and Nearly Lossless LLM Inference](https://mlsanity.com/paper/2502.04420/) (2025)
- [TriAttention: Efficient Long Reasoning with Trigonometric KV Compression](https://mlsanity.com/paper/2604.04921/) (2026)
- [AsymKV: Enabling 1-Bit Quantization of KV Cache with Layer-Wise Asymmetric Quantization Configurations](https://mlsanity.com/paper/2410.13212/) (2024)
- [Quantize What Counts: More for Keys, Less for Values](https://mlsanity.com/paper/2502.15075/) (2025)
- [LOOKAT: Lookup-Optimized Key-Attention for Memory-Efficient Transformers](https://mlsanity.com/paper/2601.10155/) (2026)
- [Exact Attention Sensitivity and the Geometry of Transformer Stability](https://mlsanity.com/paper/2602.18849/) (2026)
- [PolyKV: A Shared Asymmetrically-Compressed KV Cache Pool for Multi-Agent LLM Inference](https://mlsanity.com/paper/2604.24971/) (2026)
- [AXELRAM: Quantize Once, Never Dequantize](https://mlsanity.com/paper/2604.02638/) (2026)

## Abstract (arXiv)

KV-cache quantizers usually optimize storage-space reconstruction, even though attention reads keys through logits and values through attention-weighted readout. We argue that persistent cache error should be measured in model-visible coordinates. For keys, the visible object is score error modulo constant shifts; this yields HeadQ, a key-side method that stores a low-rank residual side code in a calibration-learned query basis and applies it as an additive logit correction. For values, fixed-attention readout gives an A2-weighted token-distortion surrogate. Across six models, Fisher/score-space error predicts attention KL far better than raw key MSE; same-budget counterexamples, null-space interventions, query-PCA controls, and wrong-sign HeadQ falsify storage-MSE alternatives. Matched Pythia checkpoints localize the main anomaly to a small-model low-entropy route-flip boundary. In K-only WikiText-103 decode experiments with dense values, HeadQ removes roughly 84--94% of the excess perplexity on the strongest 2-bit rows; in an auxiliary full-KV 2-bit composition, HeadQ plus an A2 value policy improves all six models.