DL Layers, Neurons and Dimensions

Synopsis


   Layer    - (5, 10) means 5 input Features 10 neurons. 
   Neuron   - Single Scalar Output Per Neuron. Uses Wx Matrix and Bias.
   ReLU     - Rectified Linear Unit: (x > 0? x : 0)

DL 2 Hidden Layers

User: Munian A (munian.alagan@gmail.com)
Created: 3/28/2025 22:02

Prompt: Explain DL input layer, hidden layers, neurons, Activation Functions

Explain what is the responsibility of single neuron -- does it produce single scalar value or vector ? Explain with a simple working pytorch code.

Response:

Great question! Let's break it down step by step.

Understanding the Transformation of Each Neuron:

  1. Input Layer:

    • Suppose we have 5 input features per data point (row).
    • So, the input to the first hidden layer has a shape of .

  2. First Hidden Layer:

    • Suppose this layer has 10 neurons.
    • Each neuron has a weight vector of shape and a bias of shape .
    • The input to each neuron is a dot product of the input feature vector with its weight vector plus bias.
    • Each neuron produces a single scalar value (which is then passed through an activation function).
    • Since we have 10 neurons, the output of the first hidden layer is of shape .

  3. Second Hidden Layer:

    • Suppose this layer has 6 neurons.
    • Each neuron in this layer takes input from all 10 neurons of the previous layer.
    • So, the weight vector for each neuron has shape , and bias has shape .
    • Each neuron again produces a single scalar value, and since we have 6 neurons, the output shape is .

  4. Output Layer:

    • Suppose we are classifying into 3 classes.
    • The final layer has 3 neurons.
    • Each neuron takes input from all 6 neurons of the second hidden layer.
    • So, each neuron has a weight vector of shape and bias of shape .
    • The output shape is , which represents the logits for the 3 classes.

Does Each Neuron Contribute to a Single Number?

Yes! Each neuron processes the entire input it receives and outputs a single scalar value. This value is placed at a fixed position in the output vector, and each neuron contributes separately to the formation of the next layer's input.

Simple Working PyTorch Code

Below is a simple PyTorch example demonstrating these transformations:

import torch
import torch.nn as nn
import torch.nn.functional as F

# Define a simple neural network
class SimpleNN(nn.Module):
    def __init__(self):
        super(SimpleNN, self).__init__()
        self.fc1 = nn.Linear(5, 10)  # First hidden layer (5 -> 10)
        self.fc2 = nn.Linear(10, 6)  # Second hidden layer (10 -> 6)
        self.fc3 = nn.Linear(6, 3)   # Output layer (6 -> 3)

    def forward(self, x):
        x = F.relu(self.fc1(x))  # Activation for first hidden layer
        x = F.relu(self.fc2(x))  # Activation for second hidden layer
        x = self.fc3(x)          # No activation here; logits output
        return x

# Simulating input
batch_size = 4  # Assume we process 4 samples at a time
input_data = torch.randn(batch_size, 5)  # Random input tensor with 5 features

# Create model and pass input through it
model = SimpleNN()
output = model(input_data)

print("Input shape:", input_data.shape)  # (4, 5)
print("Output shape after first hidden layer:", F.relu(model.fc1(input_data)).shape)  # (4, 10)
print("Output shape after second hidden layer:", F.relu(model.fc2(F.relu(model.fc1(input_data)))).shape)  # (4, 6)
print("Final output shape:", output.shape)  # (4, 3)

Explanation of Code:

  • We define a simple neural network with 2 hidden layers and an output layer.
  • nn.Linear(a, b) defines a fully connected layer with weights of shape (b, a).
  • We use ReLU activation (F.relu()) for the hidden layers.
  • The output layer provides raw logits (not yet passed through softmax).
  • We simulate a batch of 4 samples, each with 5 features, and pass it through the network.

Expected Output:

Input shape: torch.Size([4, 5])
Output shape after first hidden layer: torch.Size([4, 10])
Output shape after second hidden layer: torch.Size([4, 6])
Final output shape: torch.Size([4, 3])

Let me know if you need further clarification! 🚀

Prompt: Enhance this code with epochs, optimizer and loss functions

Response:

Here's an enhanced version of your PyTorch code that includes:

  • Training loop for N epochs
  • Loss computation using CrossEntropyLoss (for multi-class classification)
  • Optimizer (Adam)
  • Dataset simulation with random input and labels
  • Tracking of loss during training
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim

# Define the Neural Network
class SimpleNN(nn.Module):
    def __init__(self):
        super(SimpleNN, self).__init__()
        self.fc1 = nn.Linear(5, 10)  # First hidden layer (5 -> 10)
        self.fc2 = nn.Linear(10, 6)  # Second hidden layer (10 -> 6)
        self.fc3 = nn.Linear(6, 3)   # Output layer (6 -> 3)

    def forward(self, x):
        x = F.relu(self.fc1(x))  # Activation for first hidden layer
        x = F.relu(self.fc2(x))  # Activation for second hidden layer
        x = self.fc3(x)          # No activation (logits output)
        return x

# Hyperparameters
num_epochs = 20
batch_size = 8
learning_rate = 0.01

# Simulated dataset (random inputs and labels)
num_samples = 100  # Assume we have 100 samples
X = torch.randn(num_samples, 5)  # 100 samples, 5 features each
y = torch.randint(0, 3, (num_samples,))  # 100 labels in range [0,2] (3 classes)

# Model, loss function, optimizer
model = SimpleNN()
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=learning_rate)

# Training loop
for epoch in range(num_epochs):
    total_loss = 0.0
    for i in range(0, num_samples, batch_size):
        inputs = X[i:i + batch_size]
        labels = y[i:i + batch_size]

        # Forward pass
        outputs = model(inputs)
        loss = criterion(outputs, labels)

        # Backward pass and optimization
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()

        total_loss += loss.item()

    # Print epoch loss
    print(f"Epoch [{epoch + 1}/{num_epochs}], Loss: {total_loss / (num_samples // batch_size):.4f}")

print("Training Complete!")

Enhancements:

✅ Training loop with num_epochs
✅ Mini-batch training with batch_size
✅ CrossEntropyLoss (since it's a classification problem)
✅ Adam optimizer for efficient learning
✅ Prints loss per epoch for tracking training progress

This code will train the model using random data—replace X and y with real data for actual training. 🚀 Let me know if you need further improvements!

Prompt: Above code does not translate logit to class values ?

In the above code the final output layer produces raw logit values, but in the input we have fixed class labels. Above code does not directly use softmax function to translate logit values to class values -- still above code works implicitly finding the loss ? please clarify.

Response:

Great observation! The reason the code works without explicitly applying Softmax is because of how CrossEntropyLoss works in PyTorch.

🔹 Why Doesn't the Code Need Softmax?

In PyTorch, nn.CrossEntropyLoss() expects raw logits as input (not probabilities). Internally, it applies Softmax and Negative Log-Likelihood (NLL) loss in one step.

So, when the model outputs raw logits, CrossEntropyLoss automatically:

  1. Applies the Softmax function to convert logits into probabilities.
  2. Computes the negative log-likelihood loss using the correct class label.

Thus, the code implicitly handles the softmax transformation during loss computation.

🔹 What Happens Internally?

For each sample, the model outputs raw logits (before Softmax), e.g.:

Logits from final layer:  [2.0, -1.0, 0.5]  # Example output

Softmax converts this into probabilities:

Probabilities:  [0.71, 0.04, 0.25]  # Softmax applied internally

If the actual class label is 0, the loss for this sample would be:

Loss = -log(0.71) = 0.34  # Negative log probability of the correct class

CrossEntropyLoss does this automatically for all training samples.

🔹 What If We Manually Applied Softmax?

If we modified the model to apply F.softmax(output, dim=1), we should NOT use CrossEntropyLoss. Instead, we would need to use nn.NLLLoss() (Negative Log-Likelihood Loss) because CrossEntropyLoss already applies Softmax internally.

output = F.softmax(model(inputs), dim=1)  # Applying softmax manually
loss = nn.NLLLoss()(torch.log(output), labels)  # Log applied before NLLLoss

However, this is unnecessary because CrossEntropyLoss already does both steps.

🔹 Conclusion

✅ Raw logits are passed to CrossEntropyLoss, and it automatically applies Softmax.
✅ No need to explicitly apply Softmax before computing loss.
✅ If Softmax was applied manually, we’d have to change the loss function accordingly.

This design is efficient because it avoids redundant calculations and improves numerical stability. Let me know if you need further clarification! 🚀

Prompt:

What is the best way to visualize this deep learning layers transformation which clearly depicts the input , output dimensions and data flow ?

Response:

Great question! The best way to visualize deep learning transformations (input, output dimensions, and data flow) depends on the level of detail you want. Here are some effective approaches:

1️⃣ Summary Table Representation (Text-Based)

A simple tabular format helps clarify input-output transformations:

Layer Input Shape Weight Shape Output Shape Activation
Input (batch_size, 5) - (batch_size, 5) -
FC1 (Hidden) (batch_size, 5) (10, 5) (batch_size, 10) ReLU
FC2 (Hidden) (batch_size, 10) (6, 10) (batch_size, 6) ReLU
Output Layer (batch_size, 6) (3, 6) (batch_size, 3) (Logits)

This method clearly shows dimensions at each step.

2️⃣ PyTorch summary() (Automatic Model Summary)

For a PyTorch model, you can use torchsummary:

from torchsummary import summary

model = SimpleNN()
summary(model, (5,))

This will print a detailed architecture with input/output sizes.

3️⃣ Tensor Flow Diagram (Graph-Based)

A simple block diagram makes it visually appealing:

(Input: batch_size x 5) ───► [FC1: 10 neurons] ───► ReLU ───► 
[FC2: 6 neurons] ───► ReLU ───► [Output: 3 logits]

Each arrow shows data flow.

4️⃣ PyTorch Hooks (Real-Time Tensors Inspection)

If you want to see real values flowing through the model, you can register hooks:

def print_shape(module, input, output):
    print(f"{module.__class__.__name__}: Input {input[0].shape}, Output {output.shape}")

for layer in model.children():
    layer.register_forward_hook(print_shape)

# Pass sample input
X_sample = torch.randn(4, 5)
model(X_sample)

This prints real-time input/output shapes as data passes through.

5️⃣ Netron (Best Interactive Visualizer)

For a fully interactive view, use Netron:

torch.onnx.export(model, torch.randn(1, 5), "model.onnx")
  • Open model.onnx in Netron.
  • See neurons, connections, activations, etc.

Best Approach?

  • For quick overview → Table or summary()
  • For debugging dimensions → PyTorch hooks
  • For deep inspection → Netron

Powered by ChatGPT Exporter

Another Response Variation From Deepseek

Visualizing the Data Flow

        Input (1,5) → [fc1: (5,4)] → (1,4) → ReLU → 
        [fc2: (4,3)] → (1,3) → ReLU → 
        [fc3: (3,3)] → (1,3) → Softmax → Output

Each neuron in a layer processes all outputs from the previous layer and emits exactly one value that gets fed to all neurons in the next layer.

Enhanced PyTorch Code with Training Loop

Here's an enhanced version of your code that includes:

  • A complete training loop with multiple epochs
  • Loss function (CrossEntropyLoss for classification)
  • Optimizer (Adam)
  • Data generation (synthetic dataset)
  • Training and validation steps
  • Accuracy calculation
import torch
import torch.nn as nn
import torch.nn.functional as F
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
import matplotlib.pyplot as plt

# Set random seeds for reproducibility
torch.manual_seed(42)

class SimpleNN(nn.Module):
    def __init__(self):
        super(SimpleNN, self).__init__()
        self.fc1 = nn.Linear(5, 4)  # First hidden layer: 5 in, 4 out
        self.fc2 = nn.Linear(4, 3)  # Second hidden layer: 4 in, 3 out
        self.fc3 = nn.Linear(3, 3)  # Output layer: 3 in, 3 out (classes)
        
    def forward(self, x):
        # First hidden layer with ReLU activation
        x = F.relu(self.fc1(x))
        
        # Second hidden layer with ReLU activation
        x = F.relu(self.fc2(x))
        
        # Output layer (no activation here, CrossEntropyLoss includes softmax)
        x = self.fc3(x)
        return x

# Generate synthetic dataset
X, y = make_classification(n_samples=1000, n_features=5, n_classes=3, 
                          n_informative=3, random_state=42)

# Split into train and validation sets
X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=42)

# Convert to PyTorch tensors
X_train = torch.FloatTensor(X_train)
y_train = torch.LongTensor(y_train)
X_val = torch.FloatTensor(X_val)
y_val = torch.LongTensor(y_val)

# Create a network instance
model = SimpleNN()

# Define loss function and optimizer
criterion = nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(model.parameters(), lr=0.01)

# Training parameters
epochs = 100
batch_size = 32
train_losses = []
val_losses = []
train_accuracies = []
val_accuracies = []

# Training loop
for epoch in range(epochs):
    model.train()
    epoch_train_loss = 0
    correct_train = 0
    total_train = 0
    
    # Mini-batch training
    for i in range(0, len(X_train), batch_size):
        # Get batch
        batch_X = X_train[i:i+batch_size]
        batch_y = y_train[i:i+batch_size]
        
        # Zero gradients
        optimizer.zero_grad()
        
        # Forward pass
        outputs = model(batch_X)
        loss = criterion(outputs, batch_y)
        
        # Backward pass and optimize
        loss.backward()
        optimizer.step()
        
        # Track metrics
        epoch_train_loss += loss.item()
        _, predicted = torch.max(outputs.data, 1)
        total_train += batch_y.size(0)
        correct_train += (predicted == batch_y).sum().item()
    
    # Calculate training metrics
    train_loss = epoch_train_loss / (len(X_train) / batch_size)
    train_accuracy = correct_train / total_train
    train_losses.append(train_loss)
    train_accuracies.append(train_accuracy)
    
    # Validation
    model.eval()
    with torch.no_grad():
        val_outputs = model(X_val)
        val_loss = criterion(val_outputs, y_val)
        _, val_predicted = torch.max(val_outputs.data, 1)
        val_accuracy = (val_predicted == y_val).sum().item() / len(y_val)
        
        val_losses.append(val_loss.item())
        val_accuracies.append(val_accuracy)
    
    # Print progress
    if (epoch+1) % 10 == 0:
        print(f'Epoch [{epoch+1}/{epochs}], '
              f'Train Loss: {train_loss:.4f}, Val Loss: {val_loss.item():.4f}, '
              f'Train Acc: {train_accuracy:.4f}, Val Acc: {val_accuracy:.4f}')

# Plot training history
plt.figure(figsize=(12, 5))
plt.subplot(1, 2, 1)
plt.plot(train_losses, label='Train Loss')
plt.plot(val_losses, label='Val Loss')
plt.title('Loss over epochs')
plt.legend()

plt.subplot(1, 2, 2)
plt.plot(train_accuracies, label='Train Accuracy')
plt.plot(val_accuracies, label='Val Accuracy')
plt.title('Accuracy over epochs')
plt.legend()
plt.show()

# Final evaluation
model.eval()
with torch.no_grad():
    # Test on validation set
    outputs = model(X_val)
    _, predicted = torch.max(outputs.data, 1)
    final_accuracy = (predicted == y_val).sum().item() / len(y_val)
    print(f'\nFinal Validation Accuracy: {final_accuracy:.4f}')

Key Enhancements:

  1. Complete Training Loop:

    • Added proper epoch-based training
    • Included batch processing for better memory efficiency

  2. Loss Function:

    • Used CrossEntropyLoss (which combines log-softmax and negative log likelihood)
    • Note: Removed explicit softmax from model since CrossEntropyLoss includes it

  3. Optimization:

    • Added Adam optimizer with learning rate
    • Proper gradient zeroing and backpropagation

  4. Evaluation Metrics:

    • Tracked both training and validation loss
    • Calculated accuracy for both sets
    • Added visualization of training progress

  5. Data Handling:

    • Generated synthetic classification data
    • Split into training and validation sets
    • Converted to PyTorch tensors

  6. Model Evaluation:

    • Final accuracy calculation
    • Proper model.eval() context for validation

This code provides a complete framework for training and evaluating your neural network, with all the essential components of a deep learning pipeline.

Interactive Graph
Table Of Contents
DL Layers, Neurons and Dimensions
Synopsis
Prompt: Explain DL input layer, hidden layers, neurons, Activation Functions
Response:
Understanding the Transformation of Each Neuron:
Does Each Neuron Contribute to a Single Number?
Simple Working PyTorch Code
Explanation of Code:
Expected Output:
Prompt: Enhance this code with epochs, optimizer and loss functions
Response:
Enhancements:
Prompt: Above code does not translate logit to class values ?
Response:
🔹 Why Doesn't the Code Need Softmax?
🔹 What Happens Internally?
🔹 What If We Manually Applied Softmax?
🔹 Conclusion
Prompt:
Response:
1️⃣ Summary Table Representation (Text-Based)
2️⃣ PyTorch summary() (Automatic Model Summary)
3️⃣ Tensor Flow Diagram (Graph-Based)
4️⃣ PyTorch Hooks (Real-Time Tensors Inspection)
5️⃣ Netron (Best Interactive Visualizer)
Best Approach?
Another Response Variation From Deepseek
Visualizing the Data Flow
Enhanced PyTorch Code with Training Loop
Key Enhancements: