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🧠 Training a Neural Network: Forward and Backpropagation

🟢 Forward Propagation (Forward Pass)​

Forward propagation is how a neural network takes input and produces an output by passing data through layers.

🔍 How it works:​

  1. Take input data (e.g., features like a, b, c)
  2. Multiply each input by a weight, add a bias
  3. Apply an activation function (like sigmoid, ReLU)
  4. Pass the result forward to the next layer
  5. At the final layer, output a prediction (like spam/not spam)

📦 Analogy:​

Think of it like a smoothie blender:

  • Ingredients = input data
  • Blending = math through layers
  • Smoothie = output prediction

🔴 Backpropagation (Backward Pass)​

Backpropagation is how the network learns from its mistakes. It works backward from the output to update the weights.

🔍 How it works:​

  1. After forward pass, compare the prediction with the correct label using a loss function

    Example: "The model predicted 0.8 but the real label was 1"

  2. Compute the error (cost or loss)

  3. Use derivatives to calculate how much each weight contributed to the error

  4. Update the weights using gradient descent to reduce the error next time

📦 Analogy:​

Like throwing a ball at a target:

  • You throw it (forward pass)
  • See where it landed (loss)
  • Adjust your aim (backpropagation)
  • Try again with improvement (gradient descent)

🔁 The Full Training Loop:​

  1. Forward Propagation: Make prediction
  2. Loss Function: Measure how wrong it was
  3. Backpropagation: Calculate how to fix weights
  4. Gradient Descent: Update weights
  5. Repeat until the model learns

🧠 Why It Matters​

This loop — forward pass + backward pass — is how deep learning models learn over time.

  • Forward pass is inference
  • Backward pass is learning

Together, they train models to recognize patterns, minimize error, and improve performance.