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

arXiv cs.LG / 5/1/2026

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Key Points

  • EigenDecomposition (ED) is a key building block in many computer vision workloads, but it is often too slow when applied to mini-batches of matrices in deep neural networks.
  • The paper extends prior work by proposing a batch-efficient Divide-and-Conquer approach for ED aimed at larger matrices than the earlier QR-based method (which was for dim < 32).
  • The approach targets performance improvements for mini-batches where matrix dimensions are still relatively small (up to under 64).
  • Numerical experiments indicate the proposed ED method can be significantly faster than PyTorch’s SVD implementation for those mini-batch sizes.
  • The contribution is positioned as an efficient algorithmic alternative to standard SVD-based pipelines when ED needs to be computed repeatedly across batches.

Abstract

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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