Linear (fully connected) layers in PyTorch

Introduction

A linear layer connects every input to every output with a weight, helping the model learn simple relationships between data.

When you want to transform input features into output features in a neural network.

When building a simple classifier that needs to combine all input information.

When you want to reduce or expand the size of data features in a model.

When connecting layers in a deep learning model to learn patterns.

When you want to predict continuous values from input features.

Syntax

PyTorch

torch.nn.Linear(in_features, out_features, bias=True)

in_features is the number of input values per data point.

out_features is the number of output values the layer produces.

Examples

Creates a linear layer that takes 10 inputs and outputs 5 values.

PyTorch

layer = torch.nn.Linear(10, 5)

Creates a linear layer with 3 inputs and 1 output without adding a bias term.

PyTorch

layer = torch.nn.Linear(3, 1, bias=False)

Sample Model

This code creates a linear layer that transforms 4 input features into 2 output features. It then passes a batch of 3 inputs through the layer and prints the results.

PyTorch

import torch
import torch.nn as nn

# Create a linear layer with 4 inputs and 2 outputs
linear_layer = nn.Linear(4, 2)

# Example input: batch of 3 data points, each with 4 features
input_data = torch.tensor([[1.0, 2.0, 3.0, 4.0],
                           [4.0, 3.0, 2.0, 1.0],
                           [0.5, 0.5, 0.5, 0.5]])

# Pass input through the linear layer
output = linear_layer(input_data)

# Print output shape and values
print(f"Output shape: {output.shape}")
print(f"Output values:\n{output}")

Important Notes

The weights and bias in a linear layer are learned during training.

The output shape is always (batch_size, out_features).

You can access the weights with layer.weight and bias with layer.bias.

Summary

Linear layers connect every input to every output with weights and optional bias.

They transform input features into output features in neural networks.

They are simple but powerful building blocks for many models.

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