Tensor operations (add, mul, matmul) in PyTorch - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the add operation do on tensors in PyTorch?

The add operation adds corresponding elements of two tensors of the same shape, producing a new tensor with the summed values.

intermediate

Explain the difference between mul and matmul in PyTorch tensor operations.

mul performs element-wise multiplication between two tensors of the same shape, multiplying each element individually. matmul performs matrix multiplication, combining rows and columns according to linear algebra rules.

intermediate

What shape requirements must tensors meet to use matmul in PyTorch?

For matmul, the inner dimensions must match: if tensor A is shape (m, n), tensor B must be shape (n, p). The result will have shape (m, p).

advanced

How does broadcasting work with add or mul in PyTorch?

Broadcasting lets PyTorch automatically expand smaller tensors to match the shape of larger tensors when performing add or mul, as long as their shapes are compatible.

beginner

Write a PyTorch code snippet to multiply two tensors element-wise and then add another tensor.

import torch

x = torch.tensor([1, 2, 3])
y = torch.tensor([4, 5, 6])
z = torch.tensor([7, 8, 9])

result = x.mul(y).add(z)  # element-wise multiply x and y, then add z
print(result)  # tensor([11, 18, 27])

What does torch.matmul(A, B) compute if A is (2, 3) and B is (3, 4)?

A Matrix multiplication resulting in shape (2, 4)

B Element-wise multiplication resulting in shape (2, 3)

C Element-wise addition resulting in shape (2, 3)

D Matrix multiplication resulting in shape (3, 3)

matmul multiplies matrices where inner dimensions match. Here, 3 matches 3, so output shape is (2, 4).

Which operation multiplies tensors element by element?

A matmul

B add

C mul

D dot

mul performs element-wise multiplication between tensors.

If tensor A is shape (5,) and tensor B is shape (1,), what happens when you do A + B in PyTorch?

A Error due to shape mismatch

B Broadcasting adds B to each element of A

C Result is shape (1,)

D Result is shape (5, 1)

PyTorch broadcasts the smaller tensor B to match A's shape and adds element-wise.

What is the output of torch.add(torch.tensor([1,2]), torch.tensor([3,4]))?

A tensor([4, 6])

B tensor([3, 6])

C tensor([1, 2, 3, 4])

D Error

Element-wise addition sums corresponding elements: 1+3=4, 2+4=6.

Which PyTorch function would you use to perform matrix multiplication?

A torch.mul

B torch.add

C torch.sum

D torch.matmul

torch.matmul performs matrix multiplication.

Describe how add, mul, and matmul differ when working with tensors in PyTorch.

Think about how each operation combines tensor elements and their shape rules.

Explain what broadcasting means in the context of tensor operations like add and mul in PyTorch.

Imagine adding a small tensor to a bigger one without manually reshaping.