# High-Rate Quantized Matrix Multiplication I

arXiv: https://arxiv.org/abs/2601.17187 · HTML: https://mlsanity.com/paper/2601.17187/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 23 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [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)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [EDEN: Communication-Efficient and Robust Distributed Mean Estimation for Federated Learning](https://mlsanity.com/paper/2108.08842/) (2021)
- [QJL: 1-Bit Quantized JL Transform for KV Cache Quantization with Zero Overhead](https://mlsanity.com/paper/2406.03482/) (2024)
- [FP4 All the Way: Fully Quantized Training of LLMs](https://mlsanity.com/paper/2505.19115/) (2025)
- [Four Over Six: More Accurate NVFP4 Quantization with Adaptive Block Scaling](https://mlsanity.com/paper/2512.02010/) (2025)
- [NestQuant: Nested Lattice Quantization for Matrix Products and LLMs](https://mlsanity.com/paper/2502.09720/) (2025)
- [Block Rotation is All You Need for MXFP4 Quantization](https://mlsanity.com/paper/2511.04214/) (2025)
- [WUSH: Near-Optimal Adaptive Transforms for LLM Quantization](https://mlsanity.com/paper/2512.00956/) (2025)
- [Optimal Quantization for Matrix Multiplication](https://mlsanity.com/paper/2410.13780/) (2024)

## Built on by (most cited first, 7 of 7)

- [High-Rate Quantized Matrix Multiplication II](https://mlsanity.com/paper/2605.13768/) (2026)
- [Contraction-Gauge Preconditioning for Quantized Matrix Multiplication](https://mlsanity.com/paper/2607.18745/) (2026)
- [A Nuclear-Norm Lower Bound for Dithered Scalar Quantization of Matrix Products](https://mlsanity.com/paper/2609.05641/) (2026)
- [Fast Matrix Multiplication in fp8: Certified Coefficient Optimization and Measured Error](https://mlsanity.com/paper/2609.26077/) (2026)
- [Transforms for LLM Quantization: The Great Inversion and Format Co-Design](https://mlsanity.com/paper/2608.25188/) (2026)
- [A Note on Scaling in Randomly Rotated Quantization and Its Connection to the CDEF +1 Pythagorean Relation](https://mlsanity.com/paper/2609.08759/) (2026)
- [WaterKron and FlipFlop Hessian: Information-Theoretically Grounded Quantization with Kronecker-factored Hessians](https://mlsanity.com/paper/2609.14706/) (2026)

## Abstract (arXiv)

This paper investigates the problem of quantized matrix multiplication (MatMul), which has become crucial for the efficient deployment of large language models (LLMs). We consider a Generic MatMul setting, where both matrices must be quantized (weight+activation quantization) without specific apriori (calibration) statistical information about the factors. We review the fundamental information-theoretic tradeoff between quantization rate and distortion (high-rate theory), and contrast those with the performance of popular quantization schemes (absmax INT and floating-point (FP)), for which we also derive accurate heuristic approximations. Part II of this paper studies the weight-only quantization setup where second-order statistics of the activation matrices are available at the encoder.