# Fast Kronecker Matrix-Matrix Multiplication on GPUs

arXiv: https://arxiv.org/abs/2401.10187 · HTML: https://mlsanity.com/paper/2401.10187/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2024.

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

- [Efficient and Private Marginal Reconstruction with Local Non-Negativity](https://mlsanity.com/paper/2410.01091/) (2024)
- [LSR-Adapt: Ultra-Efficient Parameter Tuning with Matrix Low Separation Rank Kernel Adaptation](https://mlsanity.com/paper/2502.13568/) (2025)

## Abstract (arXiv)

Kronecker Matrix-Matrix Multiplication (Kron-Matmul) is the multiplication of a matrix with the Kronecker Product of several smaller matrices. Kron-Matmul is a core operation for many scientific and machine learning computations. State-of-the-art Kron-Matmul implementations utilize existing tensor algebra operations, such as matrix multiplication, transpose, and tensor matrix multiplication. However, this design choice prevents several Kron-Matmul specific optimizations, thus, leaving significant performance on the table. To address this issue, we present FastKron, an efficient technique for Kron-Matmul on single and multiple GPUs. FastKron is independent of linear algebra operations enabling several new optimizations for Kron-Matmul. Thus, it performs up to 40.7x and 7.85x faster than existing implementations on 1 and 16 GPUs respectively.