# A Short Note on Batch-efficient Divide-and-Conquer Algorithm for EigenDecomposition

arXiv: https://arxiv.org/abs/2604.27325 · HTML: https://mlsanity.com/paper/2604.27325/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 3 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Builds on (most cited first, 2 of 2)

- [Fast Differentiable Matrix Square Root and Inverse Square Root](https://mlsanity.com/paper/2201.12543/) (2022)
- [Batch-efficient EigenDecomposition for Small and Medium Matrices](https://mlsanity.com/paper/2207.04228/) (2022)

## Abstract (arXiv)

EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in deep neural networks. Our previous work proposed a dedicated QR-based ED algorithm for batched small matrices (dim<32). This short paper targets the limitation and proposes a batch-efficient Divide-and-Conquer based ED algorithm for larger matrices. The numerical test shows that for a mini-batch of matrices whose dimensions are smaller than 64, our method can be much faster than the Pytorch SVD function.