Both Gradient Descent and Backpropagation are key techniques in training neural networks, but they serve different purposes. Let’s break it down:
πΉ 1. What is Gradient Descent?
Gradient Descent is an optimization algorithm used to minimize the loss function by adjusting the model's weights.
π Key Idea:
- It calculates the gradient (slope) of the loss function with respect to each weight.
- It updates the weights in the direction that reduces the loss.
- Repeats until the model converges (i.e., loss stops decreasing).
π Mathematical Formula:
Where:
- W = weight
- Ξ± (alpha) = learning rate
- ∂L/∂W = gradient (derivative of loss function)
π Types of Gradient Descent:
πΉ 2. What is Backpropagation?
Backpropagation (Backprop) is an algorithm used to compute gradients efficiently in a neural network.
π Key Idea:
- It propagates errors backward from the output layer to the input layer.
- Uses Chain Rule of Differentiation to compute gradients for each layer’s weights.
- Works together with Gradient Descent to update weights.
π Steps in Backpropagation:
1️⃣ Forward Pass: Compute predictions using current weights.
2️⃣ Compute Loss: Compare predictions with actual values.
3️⃣ Backward Pass: Calculate gradients of loss w.r.t each weight (using the chain rule).
4️⃣ Update Weights: Apply Gradient Descent to adjust weights.
5️⃣ Repeat Until Convergence! π
πΉ 3. Key Differences
πΉ 4. Analogy: A Hiker in a Mountain π️
Imagine a hiker trying to reach the lowest valley (minimize loss).
✅ Backpropagation: Like a guide, it calculates the best path down at each step.
✅ Gradient Descent: Like walking in that direction, adjusting the steps carefully.
Backprop tells you which way to go, and Gradient Descent moves you in that direction.
πΉ 5. Example Code in Python
Let’s train a simple neural network using Gradient Descent + Backpropagation in TensorFlow:
π Here’s what happens internally:
1️⃣ Forward pass → Compute output.
2️⃣ Compute loss → Measure how far predictions are from actual values.
3️⃣ Backpropagation → Compute gradients.
4️⃣ Gradient Descent → Update weights.
5️⃣ Repeat for 10 epochs!
πΉ 6. Summary
✅ Gradient Descent = Optimizes weights using computed gradients.
✅ Backpropagation = Efficiently calculates those gradients for each weight.
✅ They work together to train deep learning models efficiently!
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