# Karatsuba Matrix Multiplication and its Efficient Custom Hardware Implementations

arXiv: https://arxiv.org/abs/2501.08889 · HTML: https://mlsanity.com/paper/2501.08889/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 15 Jan 2025.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [In-Datacenter Performance Analysis of a Tensor Processing Unit](https://mlsanity.com/paper/1704.04760/) (2017)
- [TPU v4: An Optically Reconfigurable Supercomputer for Machine Learning with Hardware Support for Embeddings](https://mlsanity.com/paper/2304.01433/) (2023)
- [Fast Algorithms for Convolutional Neural Networks](https://mlsanity.com/paper/1509.09308/) (2015)
- [BISMO: A Scalable Bit-Serial Matrix Multiplication Overlay for Reconfigurable Computing](https://mlsanity.com/paper/1806.08862/) (2018)
- [WinoCNN: Kernel Sharing Winograd Systolic Array for Efficient Convolutional Neural Network Acceleration on FPGAs](https://mlsanity.com/paper/2107.04244/) (2021)
- [Fast Inner-Product Algorithms and Architectures for Deep Neural Network Accelerators](https://mlsanity.com/paper/2311.12224/) (2023)

## Abstract (arXiv)

While the Karatsuba algorithm reduces the complexity of large integer multiplication, the extra additions required minimize its benefits for smaller integers of more commonly-used bitwidths. In this work, we propose the extension of the scalar Karatsuba multiplication algorithm to matrix multiplication, showing how this maintains the reduction in multiplication complexity of the original Karatsuba algorithm while reducing the complexity of the extra additions. Furthermore, we propose new matrix multiplication hardware architectures for efficiently exploiting this extension of the Karatsuba algorithm in custom hardware. We show that the proposed algorithm and hardware architectures can provide real area or execution time improvements for integer matrix multiplication compared to scalar Karatsuba or conventional matrix multiplication algorithms, while also supporting implementation through proven systolic array and conventional multiplier architectures at the core. We provide a complexity analysis of the algorithm and architectures and evaluate the proposed designs both in isolation and in an end-to-end deep learning accelerator system compared to baseline designs and prior state-of-the-art works implemented on the same type of compute platform, demonstrating their ability to increase the performance-per-area of matrix multiplication hardware.