There have been many implementations of Einstein's summation. numpy's numpy.einsum is the least efficient one as it only runs in single thread on CPU. PyTorch's torch.einsum works for both CPU and CUDA tensors. However, since there is no virtual CUDA memory, torch.einsum will run out of CUDA memory for large tensors.

This code aims at implementing a memory-efficient einsum function using PyTorch as the backend. This code also uses the opt_einsum package to optimizes the contraction path to achieve the minimal FLOPS.


from opt_einsum_torch import EinsumPlanner
import torch

# Some huge tensors
arr1, arr2 = ..., ...
ee = EinsumPlanner(torch.device('cuda:0'), cuda_mem_limit=0.9)
result = ee.einsum('ijk,jkl->il', arr1, arr2)

The resulting tensor result will be a PyTorch CPU tensor. You could convert it into numpy array by simply calling result.numpy().

Future works

  • Support multiple GPUs.
  • Memory efficient einsum kernels.
  • CUDA data transfer profilers.
GitHub - hhaoyan/opt-einsum-torch at pythonawesome.com
Memory-efficient optimum einsum using opt_einsum planning and PyTorch kernels. - GitHub - hhaoyan/opt-einsum-torch at pythonawesome.com