# IsoQuant: Hardware-Aligned SO(4) Isoclinic Rotations for LLM KV Cache Compression

arXiv: https://arxiv.org/abs/2603.28430 · HTML: https://mlsanity.com/paper/2603.28430/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in KV cache quantization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 5 of its 15 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Placed in

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

## Builds on (most cited first, 5 of 5)

- [KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache](https://mlsanity.com/paper/2402.02750/) (2024)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [QJL: 1-Bit Quantized JL Transform for KV Cache Quantization with Zero Overhead](https://mlsanity.com/paper/2406.03482/) (2024)
- [RiemannFormer: A Framework for Attention in Curved Spaces](https://mlsanity.com/paper/2506.07405/) (2025)

## Built on by (most cited first, 2 of 2)

- [OScaR: The Occam's Razor for Extreme KV Cache Quantization in LLMs and Beyond](https://mlsanity.com/paper/2605.19660/) (2026)
- [Hurwitz Quaternion Multiplicative Quantization for KV Cache Compression](https://mlsanity.com/paper/2605.27646/) (2026)

## Abstract (arXiv)

Orthogonal feature decorrelation is effective for low-bit online vector quantization, but dense random orthogonal transforms incur prohibitive O(d2) storage and compute. RotorQuant reduces this cost with blockwise 3D Clifford rotors, yet the resulting 3D partition is poorly aligned with modern hardware and offers limited local mixing. We propose IsoQuant, a blockwise rotation framework based on quaternion algebra and the isoclinic decomposition of SO(4). It represents each 4D block as a quaternion and applies a closed-form transform T(v)=qL v overlineqR. This yields two main variants: IsoQuant-Full, which realizes the full SO(4) rotation, and IsoQuant-Fast, which keeps only one isoclinic factor for lower cost; the framework also admits a lightweight 2D special case. At d=128, IsoQuant-Full reduces forward rotation cost from about 2,408 FMAs in RotorQuant to 1,024, while IsoQuant-Fast further reduces it to 512. Across 18 fused CUDA settings with d ∈ 128,256,512, bit widths 2,3,4, and FP16/FP32 execution, IsoQuant achieves mean kernel-level speedups of about 4.5×--4.7× over RotorQuant while maintaining comparable reconstruction MSE, with peak speedups above 6×. Current validation is limited to the stage-1 quantize--dequantize path on synthetic normalized vectors; end-to-end KV-cache evaluation remains future work.