Tensor operations (add, mul, matmul) in PyTorch - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of element-wise addition and multiplication

What is the output of the following PyTorch code?

PyTorch

import torch

a = torch.tensor([1, 2, 3])
b = torch.tensor([4, 5, 6])
add_result = a + b
mul_result = a * b
print(add_result.tolist(), mul_result.tolist())

A [5, 7, 9] [5, 7, 9]

B [4, 7, 9] [4, 10, 18]

C [5, 7, 9] [4, 10, 18]

D [5, 7, 9] [1, 2, 3]

💡 Hint

Remember that + and * between tensors perform element-wise operations.

The + operator adds corresponding elements: 1+4=5, 2+5=7, 3+6=9. The * operator multiplies element-wise: 1*4=4, 2*5=10, 3*6=18.

❓ Model Choice

intermediate

Choosing the correct operation for matrix multiplication

Which PyTorch operation correctly performs matrix multiplication between two 2D tensors?

A torch.matmul(a, b)

B torch.mul(a, b)

C torch.add(a, b)

D a + b

💡 Hint

Matrix multiplication is not element-wise addition or multiplication.

torch.matmul performs matrix multiplication. torch.add and + do element-wise addition. torch.mul does element-wise multiplication.

🔧 Debug

advanced

Identify the error in tensor multiplication

What error will the following code raise?

PyTorch

import torch

a = torch.tensor([1, 2, 3])
b = torch.tensor([[4, 5, 6], [7, 8, 9]])
result = a * b
print(result)

A ValueError: operands could not be broadcast together with shapes (3,) (2,3)

B No error, outputs element-wise multiplication

C TypeError: unsupported operand type(s) for *: 'list' and 'Tensor'

D RuntimeError: The size of tensor a (3) must match the size of tensor b (2) at non-singleton dimension 0

💡 Hint

Check if the shapes of the tensors are compatible for element-wise multiplication.

No error. Tensor a has shape (3,) and tensor b has shape (2,3). The shapes are broadcastable: PyTorch pads a on the left to (1,3), and the leading dimension 1 broadcasts to 2, resulting in element-wise multiplication with output shape (2,3): tensor([[4,10,18],[14,16,27]]).

❓ Metrics

advanced

Calculate output shape after matrix multiplication

Given two tensors a and b with shapes (4, 3) and (3, 5), what is the shape of torch.matmul(a, b)?

A (4, 5)

B (3, 3)

C (5, 4)

D (4, 3)

💡 Hint

Matrix multiplication shape rule: (m, n) x (n, p) = (m, p).

The inner dimensions 3 match. The output shape is (4, 5).

🧠 Conceptual

expert

Difference between torch.mul and torch.matmul

Which statement correctly describes the difference between torch.mul and torch.matmul?

A torch.mul performs matrix multiplication; torch.matmul performs element-wise multiplication.

B Both perform element-wise multiplication but torch.matmul supports broadcasting.

C Both perform matrix multiplication but torch.mul is faster.

D torch.mul performs element-wise multiplication; torch.matmul performs matrix multiplication following linear algebra rules.

💡 Hint

Think about how each function treats tensor dimensions and multiplication rules.

torch.mul multiplies each element of one tensor by the corresponding element of another tensor (element-wise). torch.matmul performs matrix multiplication, combining rows and columns as in linear algebra.