# A Nonlinear Hash-based Optimization Method for SpMV on GPUs

arXiv: https://arxiv.org/abs/2504.08860 · HTML: https://mlsanity.com/paper/2504.08860/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Builds on (most cited first, 4 of 4)

- [Continual Learning in the Frequency Domain](https://mlsanity.com/paper/2410.06645/) (2024)
- [CSR5: An Efficient Storage Format for Cross-Platform Sparse Matrix-Vector Multiplication](https://mlsanity.com/paper/1503.05032/) (2015)
- [Gensor: A Graph-based Construction Tensor Compilation Method for Deep Learning](https://mlsanity.com/paper/2502.11407/) (2025)
- [Entropy Maximization in Sparse Matrix by Vector Multiplication (maxE SpMV)](https://mlsanity.com/paper/2308.00106/) (2023)

## Abstract (arXiv)

Sparse matrix-vector multiplication (SpMV) is a fundamental operation with a wide range of applications in scientific computing and artificial intelligence. However, the large scale and sparsity of sparse matrix often make it a performance bottleneck. In this paper, we highlight the effectiveness of hash-based techniques in optimizing sparse matrix reordering, introducing the Hash-based Partition (HBP) format, a lightweight SpMV approach. HBP retains the performance benefits of the 2D-partitioning method while leveraging the hash transformation's ability to group similar elements, thereby accelerating the pre-processing phase of sparse matrix reordering. Additionally, we achieve parallel load balancing across matrix blocks through a competitive method. Our experiments, conducted on both Nvidia Jetson AGX Orin and Nvidia RTX 4090, show that in the pre-processing step, our method offers an average speedup of 3.53 times compared to the sorting approach and 3.67 times compared to the dynamic programming method employed in Regu2D. Furthermore, in SpMV, our method achieves a maximum speedup of 3.32 times on Orin and 3.01 times on RTX4090 against the CSR format in sparse matrices from the University of Florida Sparse Matrix Collection.