Broadcasting in PyTorch - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to add a tensor and a scalar using broadcasting.

PyTorch

import torch

a = torch.tensor([1, 2, 3])
b = 5
result = a [1] b
print(result)

Drag options to blanks, or click blank then click option'

A/

B-

C*

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication instead of addition.

Trying to add without an operator.

Adding a tensor and a scalar uses broadcasting, so + correctly adds 5 to each element.

2fill in blank

medium

Complete the code to multiply a 2D tensor by a 1D tensor using broadcasting.

PyTorch

import torch

a = torch.tensor([[1, 2, 3], [4, 5, 6]])
b = torch.tensor([1, 0, 1])
result = a [1] b
print(result)

Drag options to blanks, or click blank then click option'

A*

B+

C-

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of multiplication.

Trying to multiply tensors with incompatible shapes without broadcasting.

Multiplying a 2D tensor by a 1D tensor broadcasts the 1D tensor across rows, so * is the correct operator.

3fill in blank

hard

Fix the error in the code by completing the broadcasting operation correctly.

PyTorch

import torch

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

Drag options to blanks, or click blank then click option'

A+

B*

C-

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication which causes shape mismatch.

Trying to add tensors with incompatible shapes without broadcasting.

Adding a (2,3) tensor and a (2,) tensor broadcasts the smaller tensor across columns, so + works correctly.

4fill in blank

hard

Fill both blanks to create a tensor of shape (3, 4) by broadcasting a (3, 1) tensor with a (1, 4) tensor.

PyTorch

import torch

a = torch.tensor([[1], [2], [3]])  # shape (3, 1)
b = torch.tensor([[4, 5, 6, 7]])  # shape (1, 4)
result = a [1] b
print(result.shape)  # should print torch.Size([2])

Drag options to blanks, or click blank then click option'

A*

B+

C(3, 4)

D(4, 3)

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of multiplication.

Confusing the output shape dimensions.

Multiplying tensors with shapes (3,1) and (1,4) broadcasts to (3,4). The shape printed is (3, 4).

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps each word to its length if the length is greater than 3.

PyTorch

words = ['apple', 'bat', 'carrot', 'dog']
lengths = { [1]: [2] for word in words if len(word) [3] 3 }
print(lengths)

Drag options to blanks, or click blank then click option'

Aword

Blen(word)

C>

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong comparison operator.

Swapping key and value in the dictionary comprehension.

The dictionary comprehension maps each word to its len(word) only if the length is greater than 3.

Practice

1. What does broadcasting in PyTorch allow you to do?

easy

A. Perform operations on tensors of different shapes by expanding smaller ones

B. Convert tensors to numpy arrays automatically

C. Change the data type of tensors during operations

D. Split tensors into smaller chunks for parallel processing

Solution

1. Step 1: Understand broadcasting concept

   Broadcasting allows PyTorch to perform element-wise operations on tensors with different shapes by expanding the smaller tensor to match the larger one.

2. Step 2: Compare options with definition

   Only Perform operations on tensors of different shapes by expanding smaller ones correctly describes this behavior. Other options describe unrelated tensor operations.

3. Final Answer:

   Perform operations on tensors of different shapes by expanding smaller ones -> Option A

4. Quick Check:

   Broadcasting = expanding smaller tensor shapes [OK]

Hint: Broadcasting expands smaller tensor shapes to match larger ones [OK]

Common Mistakes:

• Confusing broadcasting with data type conversion
• Thinking broadcasting splits tensors
• Assuming broadcasting changes tensor storage

2. Which of the following PyTorch code snippets correctly uses broadcasting to add a tensor of shape (3, 1) to a tensor of shape (3, 4)?

easy

A. x = torch.randn(3, 1)
y = torch.randn(3, 4)
z = y + x.T

B. x = torch.randn(3, 1)
y = torch.randn(4, 3)
z = x + y

C. x = torch.randn(1, 3)
y = torch.randn(3, 4)
z = x + y

D. x = torch.randn(3, 1)
y = torch.randn(3, 4)
z = x + y

Solution

1. Step 1: Check tensor shapes for broadcasting compatibility

   Tensor x has shape (3,1) and y has shape (3,4). Broadcasting works from right to left: 1 and 4 are compatible (1 can expand to 4), and 3 and 3 match.

2. Step 2: Verify each option's shapes and operations

   x = torch.randn(3, 1) y = torch.randn(3, 4) z = x + y adds (3,1) + (3,4) correctly. x = torch.randn(3, 1) y = torch.randn(4, 3) z = x + y has incompatible shapes (3,1) + (4,3). x = torch.randn(1, 3) y = torch.randn(3, 4) z = x + y has (1,3) + (3,4) which is incompatible. x = torch.randn(3, 1) y = torch.randn(3, 4) z = y + x.T transposes x to (1,3), making addition incompatible.

3. Final Answer:

   x = torch.randn(3, 1)\ny = torch.randn(3, 4)\nz = x + y -> Option D

4. Quick Check:

   Broadcasting matches trailing dims: 1 and 4 compatible [OK]

Hint: Broadcasting matches shapes from right; 1 can expand to 4 [OK]

Common Mistakes:

• Mixing up tensor shapes and their order
• Assuming transpose always helps broadcasting
• Ignoring dimension order in broadcasting

3. What is the output shape of the following PyTorch code?

import torch
x = torch.randn(2, 3, 1)
y = torch.randn(1, 3, 4)
z = x + y
print(z.shape)

medium

A. torch.Size([2, 3, 4])

B. torch.Size([2, 3, 1])

C. torch.Size([1, 3, 4])

D. RuntimeError due to incompatible shapes

Solution

1. Step 1: Analyze shapes for broadcasting

   x shape is (2,3,1), y shape is (1,3,4). Broadcasting compares dimensions from right: 1 and 4 compatible (1 expands to 4), 3 and 3 match, 2 and 1 compatible (1 expands to 2).

2. Step 2: Determine resulting shape

   Broadcasted shape is (2,3,4) because dimensions expand to the maximum compatible size.

3. Final Answer:

   torch.Size([2, 3, 4]) -> Option A

4. Quick Check:

   Broadcasted shape = max dims per axis [OK]

Hint: Broadcast shape picks max size per dimension from right [OK]

Common Mistakes:

• Ignoring leading dimension broadcasting
• Assuming shapes must be identical
• Thinking 1 cannot expand to larger size

4. Consider this PyTorch code snippet:

import torch
x = torch.randn(4, 1)
y = torch.randn(3, 4)
z = x + y

What is the error and how to fix it?

medium

A. RuntimeError due to shape mismatch; fix by reshaping y to (4,1)

B. RuntimeError due to shape mismatch; fix by reshaping x to (3,1)

C. RuntimeError due to shape mismatch; fix by reshaping x to (1,4)

D. No error; code runs fine

Solution

1. Step 1: Check tensor shapes and broadcasting rules

   x shape is (4,1), y shape is (3,4). Broadcasting compares from right: 1 and 4 compatible (1 expands to 4), 4 and 3 incompatible. So addition fails.

2. Step 2: Fix shapes for broadcasting

   Reshape x to (3,1) so shapes become (3,1) and (3,4). Now 1 and 4 compatible (1 expands to 4), 3 and 3 match. Addition works.

3. Final Answer:

   RuntimeError due to shape mismatch; fix by reshaping x to (3,1) -> Option B

4. Quick Check:

   Broadcast dims must be compatible from right [OK]

Hint: Match trailing dims; reshape smaller tensor to align [OK]

Common Mistakes:

• Trying to reshape y incorrectly
• Ignoring dimension order in broadcasting
• Assuming transpose fixes all shape errors

5. You have a tensor a of shape (5, 1, 3) and a tensor b of shape (1, 4, 1). You want to add them using broadcasting and then compute the mean over the last dimension. Which code snippet correctly does this?

hard

A. c = a + b.T
result = c.mean(dim=2)

B. c = a + b
result = c.mean(dim=1)

C. c = a + b
result = c.mean(dim=2)

D. c = a + b
result = c.mean(dim=0)

Solution

1. Step 1: Verify broadcasting shapes

   a shape: (5,1,3), b shape: (1,4,1). Broadcasting compares dims from right: 3 and 1 compatible (1 expands to 3), 1 and 4 compatible (1 expands to 4), 5 and 1 compatible (1 expands to 5). Result shape is (5,4,3).

2. Step 2: Compute mean over last dimension

   The last dimension is dim=2 (0-based indexing). So mean(dim=2) computes mean over size 3 dimension, resulting in shape (5,4).

3. Final Answer:

   c = a + b\nresult = c.mean(dim=2) -> Option C

4. Quick Check:

   Broadcast shapes then mean over last dim (2) [OK]

Hint: Broadcast shapes, then mean over last dimension (dim=2) [OK]

Common Mistakes:

• Using wrong dimension for mean
• Transposing b unnecessarily
• Confusing dimension indices