Linear (fully connected) layers in PyTorch - Model Pipeline Trace

Model Pipeline - Linear (fully connected) layers

This pipeline shows how data moves through a simple neural network with linear layers. Linear layers connect every input to every output, like a full team passing a ball to every player.

Data Flow - 5 Stages

1Input Data

1000 rows x 10 columns→Raw input features representing 10 measurements per example→1000 rows x 10 columns

[[0.5, 1.2, -0.3, ..., 0.7], [1.0, -0.5, 0.0, ..., 1.1], ...]

↓

2Linear Layer 1

1000 rows x 10 columns→Multiply inputs by weights matrix (10x5) and add bias (5)→1000 rows x 5 columns

[[0.1, -0.2, 0.3, 0.0, 0.5], [0.4, 0.1, -0.1, 0.2, 0.3], ...]

↓

3Activation (ReLU)

1000 rows x 5 columns→Apply ReLU to keep positive values, zero out negatives→1000 rows x 5 columns

[[0.1, 0.0, 0.3, 0.0, 0.5], [0.4, 0.1, 0.0, 0.2, 0.3], ...]

↓

4Linear Layer 2

1000 rows x 5 columns→Multiply by weights matrix (5x3) and add bias (3)→1000 rows x 3 columns

[[0.2, -0.1, 0.4], [0.5, 0.0, 0.1], ...]

↓

5Output

1000 rows x 3 columns→Final scores for 3 classes→1000 rows x 3 columns

[[2.1, 0.5, -1.0], [1.5, 0.7, 0.3], ...]

Training Trace - Epoch by Epoch

Loss
1.2 |*       
0.9 | *      
0.7 |  *     
0.55|   *    
0.45|    *   
    +---------
     1 2 3 4 5 Epochs

Epoch	Loss ↓	Accuracy ↑	Observation
1	1.2	0.45	Loss starts high, accuracy low as model begins learning
2	0.9	0.60	Loss decreases, accuracy improves as weights adjust
3	0.7	0.72	Model learns better patterns, accuracy rises
4	0.55	0.80	Loss continues to drop, accuracy nearing good performance
5	0.45	0.85	Training converges with lower loss and higher accuracy

Prediction Trace - 5 Layers

Layer 1: Input Sample

Layer 2: Linear Layer 1

Layer 3: ReLU Activation

Layer 4: Linear Layer 2

Layer 5: Output Scores

Model Quiz - 3 Questions

What does the first linear layer do to the input data?

A It normalizes the input data

B It multiplies inputs by weights and adds bias to reduce dimensions

C It applies a non-linear activation function

D It splits data into training and testing sets

Key Insight

Linear layers connect every input to every output, allowing the model to learn weighted sums of features. Adding activation functions like ReLU introduces non-linearity, helping the model learn complex patterns. Training shows loss going down and accuracy going up, meaning the model is learning well.

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