# A method of using RSVD in residual calculation of LowBit GEMM

arXiv: https://arxiv.org/abs/2409.18772 · HTML: https://mlsanity.com/paper/2409.18772/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 27 Sep 2024.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [In-Datacenter Performance Analysis of a Tensor Processing Unit](https://mlsanity.com/paper/1704.04760/) (2017)
- [Towards Accurate Binary Convolutional Neural Network](https://mlsanity.com/paper/1711.11294/) (2017)
- [LUT-GEMM: Quantized Matrix Multiplication based on LUTs for Efficient Inference in Large-Scale Generative Language Models](https://mlsanity.com/paper/2206.09557/) (2022)
- [Data-Free Network Quantization With Adversarial Knowledge Distillation](https://mlsanity.com/paper/2005.04136/) (2020)
- [Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition](https://mlsanity.com/paper/1504.05477/) (2015)
- [VS-Quant: Per-vector Scaled Quantization for Accurate Low-Precision Neural Network Inference](https://mlsanity.com/paper/2102.04503/) (2021)
- [IntraQ: Learning Synthetic Images with Intra-Class Heterogeneity for Zero-Shot Network Quantization](https://mlsanity.com/paper/2111.09136/) (2021)
- [Low-Rank Modeling and Its Applications in Image Analysis](https://mlsanity.com/paper/1401.3409/) (2014)
- [Rethinking Data-Free Quantization as a Zero-Sum Game](https://mlsanity.com/paper/2302.09572/) (2023)

## Abstract (arXiv)

The advancements of hardware technology in recent years has brought many possibilities for low-precision applications. However, the use of low precision can introduce significant computational errors, posing a considerable challenge to maintaining the computational accuracy. We propose low-rank residuals quantized matrix multiplication(LRQMM) method which introduces low-rank approximation in residual compensation for dense low precision quantization matrix multiplication. It can bring several times accuracy improvement with only BLAS-2 level extra time overhead. Moreover, LRQMM is a completely data-free quantization method that does not require additional data for pre-training. And it only works with low precision GEMM operator, which is easy to couple with other methods. Through experimentation, LRQMM can reduce the error of direct quantized matrix multiplication by 1~2 orders of magnitude, when dealing with larger matrix sizes, the computational speed is only reduced by approximately 20%. In deep learning networks, LRQMM-4bit achieves 61.8% ImageNet Top-1 accuracy in Resnet-50, while the Direct Quant accuracy is only 8.3%.