提出高效分解大矩阵的分治算法，提升批量计算速度。
A Short Note on Batch-efficient Divide-and-Conquer Algorithm for EigenDecomposition
- 采用分治策略优化批量矩阵特征分解
- 对维度小于64的矩阵，速度远超PyTorch SVD
- 适合深度学习中批量小矩阵运算场景
特征分解（ED）是众多计算机视觉算法的核心。其主要瓶颈在于计算成本高，尤其在深度神经网络的矩阵小批量处理中更为突出。此前工作提出基于QR的批量小矩阵（维度<32）特征分解算法。本文针对此局限，提出一种面向更大矩阵的批处理高效分治特征分解算法。数值实验表明，当矩阵维度小于64时，该方法相较于PyTorch的SVD函数具有显著加速优势。
原文摘要 · Abstract (English)
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.
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