Linear (fully connected) layers in PyTorch - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output shape of a linear layer

Given the following PyTorch code, what is the shape of the output tensor after passing input through the linear layer?

PyTorch

import torch
import torch.nn as nn

input_tensor = torch.randn(10, 5)  # batch size 10, input features 5
linear_layer = nn.Linear(5, 3)  # input features 5, output features 3
output = linear_layer(input_tensor)
print(output.shape)

A torch.Size([5, 3])

B torch.Size([10, 3])

C torch.Size([3, 10])

D torch.Size([10, 5])

💡 Hint

Remember the linear layer transforms the last dimension from input features to output features, keeping batch size the same.

The input tensor has shape (10, 5). The linear layer maps 5 input features to 3 output features. The batch size (10) remains unchanged, so output shape is (10, 3).

❓ Model Choice

intermediate

Choosing the correct linear layer for input-output sizes

You have input data with 20 features and want to output predictions with 4 values per example. Which PyTorch linear layer correctly matches this?

A nn.Linear(20, 4)

B nn.Linear(4, 20)

C nn.Linear(20, 20)

D nn.Linear(4, 4)

💡 Hint

The first argument is input features, the second is output features.

The linear layer should take 20 input features and produce 4 output features, so nn.Linear(20, 4) is correct.

❓ Hyperparameter

advanced

Effect of changing output features in a linear layer

If you increase the output features of a linear layer from 10 to 50, which of the following is true?

A The batch size of input must be reduced.

B The number of learnable parameters decreases.

C The number of learnable parameters increases.

D The number of learnable parameters stays the same.

💡 Hint

Learnable parameters depend on input and output features.

The number of parameters in a linear layer is input_features * output_features + output_features (bias). Increasing output features increases parameters.

🔧 Debug

advanced

Identifying error in linear layer input size mismatch

What error will this code raise when running the forward pass?

PyTorch

import torch
import torch.nn as nn

linear = nn.Linear(8, 4)
input_tensor = torch.randn(5, 10)
output = linear(input_tensor)

A RuntimeError: size mismatch for input features

B TypeError: input must be a tensor

C ValueError: output size must be positive

D No error, runs successfully

💡 Hint

Check if input tensor's last dimension matches linear layer's input features.

The linear layer expects input features of size 8, but input tensor has size 10 in last dimension, causing a RuntimeError.

🧠 Conceptual

expert

Why use bias in linear layers?

Which statement best explains the role of the bias term in a linear (fully connected) layer?

A Bias is used to increase the batch size during training.

B Bias reduces the number of parameters to prevent overfitting.

C Bias normalizes the input features before multiplication.

D Bias allows the model to shift the output independently of the input, enabling better fitting of data.

💡 Hint

Think about what happens if bias is zero.

Bias adds a constant term to the output, allowing the model to fit data that does not pass through the origin.

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