# WUSH: Near-Optimal Adaptive Transforms for LLM Quantization

arXiv: https://arxiv.org/abs/2512.00956 · HTML: https://mlsanity.com/paper/2512.00956/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 30 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [FlatQuant: Flatness Matters for LLM Quantization](https://mlsanity.com/paper/2410.09426/) (2024)
- [QTIP: Quantization with Trellises and Incoherence Processing](https://mlsanity.com/paper/2406.11235/) (2024)
- [Do Large Language Model Benchmarks Test Reliability?](https://mlsanity.com/paper/2502.03461/) (2025)
- [Differentiable Model Compression via Pseudo Quantization Noise](https://mlsanity.com/paper/2104.09987/) (2021)
- [QUIK: Towards End-to-End 4-Bit Inference on Generative Large Language Models](https://mlsanity.com/paper/2310.09259/) (2023)
- ["Give Me BF16 or Give Me Death"? Accuracy-Performance Trade-Offs in LLM Quantization](https://mlsanity.com/paper/2411.02355/) (2024)
- [Bridging the Gap Between Promise and Performance for Microscaling FP4 Quantization](https://mlsanity.com/paper/2509.23202/) (2025)
- [The Geometry of LLM Quantization: GPTQ as Babai's Nearest Plane Algorithm](https://mlsanity.com/paper/2507.18553/) (2025)
- [Block Rotation is All You Need for MXFP4 Quantization](https://mlsanity.com/paper/2511.04214/) (2025)

## Built on by (most cited first, 15 of 15)

- [High-Rate Quantized Matrix Multiplication I](https://mlsanity.com/paper/2601.17187/) (2026)
- [Dissecting Quantization Error: A Concentration-Alignment Perspective](https://mlsanity.com/paper/2603.04359/) (2026)
- [HARP: Hadamard-Preconditioned Adaptive Rotation Processor for Extreme LLM Quantization](https://mlsanity.com/paper/2605.29843/) (2026)
- [Adaptive Block-Scaled Data Types](https://mlsanity.com/paper/2603.28765/) (2026)
- [Price of metric universality in vector quantization is at most 0.11 bit](https://mlsanity.com/paper/2602.05790/) (2026)
- [A Nuclear-Norm Lower Bound for Dithered Scalar Quantization of Matrix Products](https://mlsanity.com/paper/2609.05641/) (2026)
- [When Local Variance Optimality Is Not Enough: RoPE-Aligned Q/K Rotations for Dynamic 4-Bit Quantisation](https://mlsanity.com/paper/2608.13365/) (2026)
- [KBBQ: A Predictive Noise Law and the Limits of Spectrum Flattening in FP4 Quantization](https://mlsanity.com/paper/2609.08135/) (2026)
- [Product-Aware Deterministic Rounding for Quantized Matrix Multiplication](https://mlsanity.com/paper/2609.31641/) (2026)
- [QuantForge: Discovering Residual Decompositions for MXFP4 Post-Training Quantization](https://mlsanity.com/paper/2609.34680/) (2026)
- [WUSH-KV: KV Cache Quantization with Data-Adaptive Transforms](https://mlsanity.com/paper/2609.38121/) (2026)
- [The Devil Is in the Reconstruction Loss Scale: Rethinking Optimization in LLM Quantization](https://mlsanity.com/paper/2610.00983/) (2026)
- [OSFP4: Joint Optimization of Diagonal Smoothing and Block Scales for NVFP4 Quantization](https://mlsanity.com/paper/2610.08231/) (2026)
- [WUSPruner: Second-Moment-Optimal Transforms for Structured Pruning](https://mlsanity.com/paper/2610.15394/) (2026)
- [SpectrumQuant: Spectrum Alignment for LLM Quantization](https://mlsanity.com/paper/2610.20303/) (2026)

## Abstract (arXiv)

Quantizing LLM weights and activations is a standard approach for efficient deployment, but a few extreme outliers can stretch the dynamic range and amplify low-bit quantization errors. Prior transform-based mitigations (e.g., Hadamard rotations) are fixed and data-agnostic, and their optimality for quantization has remained unclear. We derive closed-form optimal linear blockwise transforms for joint weight-activation quantization under standard RTN AbsMax-scaled block quantizers, covering both integer and floating-point formats. The resulting construction, WUSH, combines a Hadamard backbone with a data-dependent second-moment component to form a non-orthogonal transform that is provably near-optimal for FP and INT quantizers under mild assumptions while admitting an efficient fused GPU implementation. Empirically, WUSH improves W4A4 accuracy over the strongest Hadamard-based baselines (e.g., on Llama-3.1-8B-Instruct in MXFP4, it gains +2.8 average points with RTN and +0.7 with GPTQ) while delivering up to 5.8× per-layer throughput over BF16 via FP4 MatMul. Source code is available at https://github.com/IST-DASLab/WUSH.