Linear (fully connected) layers in PyTorch - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a linear layer with 10 inputs and 5 outputs.

PyTorch

import torch.nn as nn

layer = nn.Linear([1], 5)

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

A10

B15

C5

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using the output size as the input size.

Confusing input and output sizes.

The first argument to nn.Linear is the number of input features. Here, it should be 10.

2fill in blank

medium

Complete the code to pass input data through the linear layer.

PyTorch

import torch
import torch.nn as nn

layer = nn.Linear(4, 2)
input_data = torch.randn(1, 4)
output = layer([1])

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

Atorch.tensor([1, 2, 3, 4])

Blayer

Ctorch.randn(1, 2)

Dinput_data

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the layer itself instead of the input data.

Passing a tensor with wrong shape.

To get the output, we pass the input data to the layer as a function call.

3fill in blank

hard

Fix the error in the code to correctly create a linear layer with 3 inputs and 1 output.

PyTorch

import torch.nn as nn

layer = nn.Linear([1], 1)

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

A1

B3

C4

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using output size as input size.

Using zero or invalid sizes.

The input size must match the number of input features, which is 3 here.

4fill in blank

hard

Fill both blanks to create a linear layer and pass a tensor through it.

PyTorch

import torch
import torch.nn as nn

layer = nn.Linear([1], [2])
input_tensor = torch.randn(2, 3)
output = layer(input_tensor)

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

A3

B2

C1

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping input and output sizes.

Confusing batch size with input features.

The input tensor has shape (2, 3), so input features = 3 and batch size = 2. The layer output size is 2.

5fill in blank

hard

Fill all three blanks to create a linear layer, pass input, and get output shape.

PyTorch

import torch
import torch.nn as nn

layer = nn.Linear([1], [2])
input_tensor = torch.randn(4, [3])
output = layer(input_tensor)
output_shape = output.shape

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

A5

B3

C7

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up input and output sizes.

Using wrong tensor shapes.

The input tensor has shape (4, 3), so input features = 3. The layer outputs 7 features. The input tensor's last dimension is 3.

Practice

1. What does a torch.nn.Linear layer do in a neural network?

easy

A. It connects every input feature to every output feature with weights and optional bias.

B. It applies a convolution operation on the input data.

C. It reduces the input size by pooling.

D. It normalizes the input features to have zero mean and unit variance.

Solution

1. Step 1: Understand the role of Linear layers

   A Linear layer multiplies input features by weights and adds bias to produce output features.

2. Step 2: Compare with other layer types

   Convolution, pooling, and normalization are different operations, not done by Linear layers.

3. Final Answer:

   It connects every input feature to every output feature with weights and optional bias. -> Option A

4. Quick Check:

   Linear layer = weighted sum + bias [OK]

Hint: Linear layers do weighted sums of inputs to outputs [OK]

Common Mistakes:

• Confusing Linear with convolution layers
• Thinking Linear layers do pooling
• Mixing normalization with Linear layers

2. Which of the following is the correct way to create a Linear layer with 10 inputs and 5 outputs in PyTorch?

easy

A. torch.nn.Linear(10, 5)

B. torch.nn.Linear(out_features=10, in_features=5)

C. torch.nn.Linear(in_features=5, out_features=10)

D. torch.nn.Linear(5, 10)

Solution

1. Step 1: Recall Linear layer constructor parameters

   The constructor is torch.nn.Linear(in_features, out_features).

2. Step 2: Match input and output sizes

   We want 10 inputs and 5 outputs, so in_features=10 and out_features=5.

3. Final Answer:

   torch.nn.Linear(10, 5) -> Option A

4. Quick Check:

   Input size first, output size second [OK]

Hint: Remember: Linear(in_features, out_features) [OK]

Common Mistakes:

• Swapping input and output sizes
• Using keyword arguments in wrong order
• Confusing number of features with batch size

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

import torch
layer = torch.nn.Linear(4, 3)
input_tensor = torch.randn(2, 4)
output = layer(input_tensor)
print(output.shape)

medium

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

B. torch.Size([4, 3])

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

D. torch.Size([2, 3])

Solution

1. Step 1: Understand input and layer dimensions

   The input tensor has shape (2, 4), meaning batch size 2 and 4 features per sample. The Linear layer maps 4 inputs to 3 outputs.

2. Step 2: Calculate output shape

   The output shape is (batch size, output features) = (2, 3).

3. Final Answer:

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

4. Quick Check:

   Output shape = (batch, out_features) [OK]

Hint: Output shape = (batch size, out_features) [OK]

Common Mistakes:

• Confusing input and output feature dimensions
• Mixing batch size with feature size
• Expecting output shape to match input shape

4. Identify the error in this PyTorch code snippet:

import torch
layer = torch.nn.Linear(3, 2)
input_tensor = torch.randn(4, 4)
output = layer(input_tensor)

medium

A. Input tensor has wrong batch size.

B. Linear layer input features do not match input tensor features.

C. Output tensor shape is incorrect.

D. Missing activation function after Linear layer.

Solution

1. Step 1: Check Linear layer input features

   The Linear layer expects input features of size 3.

2. Step 2: Check input tensor shape

   The input tensor shape is (4, 4), so each sample has 4 features, which does not match the expected 3.

3. Final Answer:

   Linear layer input features do not match input tensor features. -> Option B

4. Quick Check:

   Input features must match layer's in_features [OK]

Hint: Input feature size must match Linear layer's in_features [OK]

Common Mistakes:

• Confusing batch size with feature size
• Ignoring feature dimension mismatch
• Thinking activation function is mandatory

5. You want to build a simple neural network with one hidden Linear layer that takes 8 input features, has 4 hidden units, and outputs 2 classes. Which PyTorch code correctly defines this model?

hard

A. import torch.nn as nn
model = nn.Sequential(
nn.Linear(8, 2),
nn.ReLU(),
nn.Linear(4, 2)
)

B. import torch.nn as nn
model = nn.Sequential(
nn.Linear(4, 8),
nn.ReLU(),
nn.Linear(2, 4)
)

C. import torch.nn as nn
model = nn.Sequential(
nn.Linear(8, 4),
nn.ReLU(),
nn.Linear(4, 2)
)

D. import torch.nn as nn
model = nn.Sequential(
nn.Linear(2, 4),
nn.ReLU(),
nn.Linear(8, 4)
)

Solution

1. Step 1: Define input to hidden layer

   The first Linear layer should map 8 input features to 4 hidden units: nn.Linear(8, 4).

2. Step 2: Define hidden to output layer

   The second Linear layer should map 4 hidden units to 2 output classes: nn.Linear(4, 2).

3. Step 3: Check activation function placement

   ReLU activation is correctly placed between the two Linear layers.

4. Final Answer:

   Correct model definition with layers: Linear(8,4), ReLU, Linear(4,2) -> Option C

5. Quick Check:

   Input -> hidden -> output sizes match [OK]

Hint: Match layer sizes: input->hidden->output with activation in between [OK]

Common Mistakes:

• Swapping input and output sizes in layers
• Placing activation after output layer
• Using wrong feature sizes in layers