Linear (fully connected) layers in PyTorch - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a linear (fully connected) layer in a neural network?

A linear layer connects every input neuron to every output neuron with a weight. It performs a weighted sum of inputs plus a bias, producing outputs.

beginner

How do you create a linear layer in PyTorch?

Use torch.nn.Linear(input_size, output_size). For example, torch.nn.Linear(10, 5) creates a layer with 10 inputs and 5 outputs.

beginner

What are the learnable parameters in a linear layer?

The weights matrix and the bias vector. Weights connect inputs to outputs, and bias shifts the output values.

intermediate

What is the shape of the weight matrix in a linear layer with input size 8 and output size 3?

The weight matrix shape is (3, 8). It has one row per output and one column per input.

beginner

Why do we add a bias term in a linear layer?

Bias allows the model to shift the output up or down, helping it fit data better by not forcing the output to pass through zero.

What does a linear layer do in a neural network?

A Reduces the size of the input data by half

B Computes a weighted sum of inputs plus bias

C Applies a non-linear activation function

D Normalizes the input data

A linear layer multiplies inputs by weights and adds bias to produce outputs.

In PyTorch, which class creates a linear layer?

A torch.nn.ReLU

B torch.nn.Conv2d

C torch.nn.Linear

D torch.nn.BatchNorm1d

torch.nn.Linear creates a fully connected linear layer.

If a linear layer has input size 4 and output size 2, what is the shape of its weight matrix?

A (4, 2)

B (2, 2)

C (4, 4)

D (2, 4)

Weight matrix shape is (output_size, input_size), so (2, 4).

What is the role of the bias in a linear layer?

A To shift the output values

B To reduce overfitting

C To normalize the output

D To scale the inputs

Bias shifts the output values, allowing more flexible fitting.

Which of these is NOT true about linear layers?

A They apply a non-linear activation by default

B They include weights and bias parameters

C They connect every input to every output

D They perform a matrix multiplication

Linear layers do NOT apply non-linear activation by default.

Explain how a linear (fully connected) layer transforms input data in a neural network.

Think about multiplying inputs by weights and adding bias.

Describe how you would implement a linear layer in PyTorch and what parameters it needs.

Focus on the class name and constructor arguments.

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