Tensor shapes and dimensions in PyTorch - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the shape of the tensor after this operation?

Consider the following PyTorch code snippet. What is the shape of the tensor y after running this code?

PyTorch

import torch
x = torch.randn(4, 3, 2)
y = x.permute(1, 0, 2)

A (3, 4, 2)

B (4, 2, 3)

C (2, 3, 4)

D (3, 2, 4)

💡 Hint

Remember that permute rearranges the dimensions in the order you specify.

The original tensor x has shape (4, 3, 2). The permute(1, 0, 2) swaps the first and second dimensions, so the new shape is (3, 4, 2).

❓ Model Choice

intermediate

Choosing the correct input shape for a CNN

You want to build a convolutional neural network (CNN) in PyTorch to classify color images of size 64x64 pixels. Which input tensor shape should you use for a batch of 16 images?

A (64, 64, 3, 16)

B (16, 64, 64, 3)

C (16, 3, 64, 64)

D (3, 16, 64, 64)

💡 Hint

PyTorch expects image tensors in the format (batch_size, channels, height, width).

PyTorch convolution layers expect input tensors shaped as (batch_size, channels, height, width). For 16 images with 3 color channels and 64x64 pixels, the shape is (16, 3, 64, 64).

❓ Hyperparameter

advanced

Effect of batch size on tensor shape during training

If you change the batch size from 32 to 64 in a training loop, how does the shape of the input tensor to the model change?

A The tensor shape remains unchanged

B All dimensions double

C The last dimension doubles, others stay the same

D The first dimension doubles, other dimensions stay the same

💡 Hint

Batch size affects the number of samples processed at once, which is the first dimension.

The batch size corresponds to the first dimension of the input tensor. Increasing batch size from 32 to 64 doubles this dimension, while other dimensions (channels, height, width) remain unchanged.

🔧 Debug

advanced

Why does this tensor reshape cause an error?

Given a tensor t with shape (2, 3, 4), why does the following code raise an error?

t.view(3, 7)

PyTorch

import torch
t = torch.randn(2, 3, 4)
t_reshaped = t.view(3, 7)

A Because view cannot change the number of dimensions

B Because the total number of elements does not match between original and new shape

C Because 3 and 8 are not valid dimensions for any tensor

D Because the tensor must be contiguous before calling view

💡 Hint

Check the total number of elements before and after reshape.

The original tensor has 2*3*4 = 24 elements. The requested shape (3, 7) requires 3*7 = 21 elements, which does not match. PyTorch's `view()` requires the total number of elements to be the same.

🧠 Conceptual

expert

Understanding broadcasting with tensor shapes

You have two tensors: a with shape (5, 1, 4) and b with shape (1, 3, 4). What will be the shape of the result when you add a + b in PyTorch?

A (5, 3, 4)

B (5, 1, 4)

C (1, 3, 4)

D (5, 3)

💡 Hint

Broadcasting expands dimensions of size 1 to match the other tensor's size.

Broadcasting rules expand dimensions with size 1 to match the other tensor's size. Here, (5,1,4) and (1,3,4) broadcast to (5,3,4).

Practice

1. What does the shape of a PyTorch tensor represent?

easy

A. The number of elements in each dimension of the tensor

B. The data type of the tensor elements

C. The device where the tensor is stored

D. The memory size of the tensor in bytes

Solution

1. Step 1: Understand tensor shape meaning

   The shape of a tensor tells how many elements are in each dimension, like rows and columns in a matrix.

2. Step 2: Differentiate from other properties

   Data type, device, and memory size are different properties and not related to shape.

3. Final Answer:

   The number of elements in each dimension of the tensor -> Option A

4. Quick Check:

   Tensor shape = elements per dimension [OK]

Hint: Shape = counts of elements per dimension [OK]

Common Mistakes:

• Confusing shape with data type
• Thinking shape shows memory size
• Mixing shape with device location

2. Which of the following is the correct way to get the shape of a tensor t in PyTorch?

easy

A. shape(t)

B. t.shape()

C. t.size()

D. t.get_shape()

Solution

1. Step 1: Recall PyTorch shape methods

   In PyTorch, t.size() returns the shape of the tensor as a tuple-like object.

2. Step 2: Check other options

   t.shape is an attribute, not a method, so t.shape() is incorrect. shape(t) and t.get_shape() are not valid PyTorch syntax.

3. Final Answer:

   t.size() -> Option C

4. Quick Check:

   Use t.size() to get shape [OK]

Hint: Use t.size() method to get shape [OK]

Common Mistakes:

• Calling t.shape() as a method
• Using non-existent functions like shape(t)
• Trying t.get_shape() which is invalid

3. What is the shape of the tensor created by torch.randn(3, 4, 5)?

medium

A. (3, 5, 4)

B. (3, 4, 5)

C. (5, 3, 4)

D. (4, 5, 3)

Solution

1. Step 1: Understand torch.randn arguments

   The arguments (3, 4, 5) specify the size of each dimension in order: first dimension 3, second 4, third 5.

2. Step 2: Confirm shape matches arguments

   The tensor shape matches exactly the arguments given, so the shape is (3, 4, 5).

3. Final Answer:

   (3, 4, 5) -> Option B

4. Quick Check:

   Shape matches input sizes (3,4,5) [OK]

Hint: Shape matches torch.randn arguments order [OK]

Common Mistakes:

• Mixing up dimension order
• Assuming shape is reversed
• Confusing shape with total elements

4. Consider this code snippet:

import torch
t = torch.randn(2, 3)
print(t.shape())

What error will this code produce?

medium

A. TypeError: 'torch.Size' object is not callable

B. AttributeError: 'Tensor' object has no attribute 'shape'

C. SyntaxError: invalid syntax

D. No error, prints (2, 3)

Solution

1. Step 1: Identify usage of t.shape()

   In PyTorch, t.shape is an attribute, not a method, so calling t.shape() tries to call a non-callable object.

2. Step 2: Understand error type

   This causes a TypeError saying the 'torch.Size' object is not callable.

3. Final Answer:

   TypeError: 'torch.Size' object is not callable -> Option A

4. Quick Check:

   t.shape is attribute, not method [OK]

Hint: t.shape is attribute, don't add () [OK]

Common Mistakes:

• Calling t.shape() instead of t.shape
• Expecting no error from t.shape()
• Confusing AttributeError with TypeError

5. You have a tensor x with shape (10, 5, 3). You want to reshape it to a 2D tensor with 5 rows and keep the total number of elements the same. Which of the following shapes is valid for the reshaped tensor?

hard

A. (5, 15)

B. (5, 10, 3)

C. (5, 5, 6)

D. (5, 30)

Solution

1. Step 1: Calculate total elements in original tensor

   Original shape is (10, 5, 3), so total elements = 10 * 5 * 3 = 150.

2. Step 2: Check which new shape keeps total elements and has 5 rows

   We want 5 rows, so first dimension = 5. The second dimension must satisfy 5 * ? = 150, so ? = 30. Check options:
   - A: (5, 15) -> 5*15=75 invalid total elements
   - B: (5, 10, 3) -> 5*10*3=150 valid but has 3 dims, not 2
   - C: (5, 30) -> 5*30=150 valid
   - D: (5, 5, 6) -> 5*5*6=150 valid but 3 dims

3. Step 3: Confirm valid shape with 5 rows and total elements

   (5, 30) is (5, 30) which matches 5 rows and total elements 150. (5, 15) is incorrect because 5*15=75, less than 150.

4. Final Answer:

   (5, 30) -> Option D

5. Quick Check:

   5 * 30 = 150 elements [OK]

Hint: Total elements must stay same; multiply dims to check [OK]

Common Mistakes:

• Ignoring total element count when reshaping
• Choosing shape with wrong total elements
• Confusing number of dimensions required