Backpropagation
Understand how neural networks learn through the backpropagation algorithm.
What is Backpropagation?#
Backpropagation is the algorithm that makes neural networks learn. It calculates how much each weight contributed to the error and adjusts accordingly.
The Core Idea
Calculate the gradient of the loss with respect to each weight, then update weights in the direction that reduces loss.
The Learning Process#
Forward Pass
Input flows through network, producing a prediction
Calculate Loss
Compare prediction to actual label
Backward Pass
Calculate gradients using chain rule
Update Weights
Adjust weights to reduce loss
The Chain Rule#
Backprop uses the chain rule from calculus:
∂Loss/∂w = ∂Loss/∂output × ∂output/∂w
For deeper networks, chain through all layers:
∂Loss/∂w1 = ∂Loss/∂y × ∂y/∂h2 × ∂h2/∂h1 × ∂h1/∂w1
PyTorch Autograd#
PyTorch handles backprop automatically:
import torch
import torch.nn as nn
# Define model
model = nn.Linear(10, 1)
criterion = nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)
# Training step
optimizer.zero_grad() # Clear old gradients
output = model(input) # Forward pass
loss = criterion(output, target) # Calculate loss
loss.backward() # Backward pass (compute gradients)
optimizer.step() # Update weights
Gradient Flow Problems#
- Vanishing gradients: Use ReLU, skip connections
- Exploding gradients: Use gradient clipping
- Dead neurons: Use Leaky ReLU
- Sigmoid/tanh in deep networks
- Large weight initializations
- Standard ReLU with negative inputs
Key Takeaways#
Remember
Backpropagation = chain rule + gradient descent. Modern frameworks handle it automatically, but understanding the concept helps debug training issues.
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