Dot Product of Tensors with Different Shapes in PyTorch
p=torch.randn(2,3)
q=torch.randn(3,4,5)


I want to perform dot product, to obtain a result of shape (2,4,5).

How can this be done with PyTorch?

Two solutions for multi-dimensional matrix multiplications:


Use Tensor.reshape() to get 2-D tensors and use torch.mm();
Use directly torch.einsum().


Demonstration:

import torch

p=torch.randn(2,3)
q=torch.randn(3,4,5)

# Solution 1: Reshaping to use 2-dimensional torch.mm()
res1 = torch.mm(p, q.resize(3, 4 * 5)).resize_(2, 4, 5)
print(res1.shape)
# torch.Size([2, 4, 5])

# Solution 2: Using explicit torch.einsum()
res2 = torch.einsum("ab,bcd-&gt;acd", (p, q))
print(res2.shape)
# torch.Size([2, 4, 5])

# Checking if results are equal:
print((res1 == res2).all())
# tensor(1, dtype=torch.uint8)

