▶Gradient descent
Each parameter moves opposite the local loss gradient.
Training a Neural Network
Forward prediction and backward credit assignment
Training alternates a forward pass that computes a prediction with a backward pass that differentiates the loss and updates every parameter.
watchone idea
→manipulateone example
→leave withone intuition
The essential idea: backpropagation uses the chain rule to assign each weight its share of the prediction error.
One Concept · One Example
What to notice
- The loss quantifies prediction error.
- Gradients propagate from output toward input.
- Learning rate controls update size.
Forward, backward, update
Chain rule
Backpropagation multiplies local derivatives along computational paths.
Train the network from the slides
Follow Charlotte's sample through the forward pass, loss, gradient, and update, while the convergence curve records how loss changes with iteration count.
Training sample from the slidesCharlottex₁ = −2 · x₂ = −1 · ytrue = 1
Input layerx₁−2x₂−1
weighted sum →weighted sum →Outputŷ0.5237
1 · Forward passŷ = 0.5237
2 · Compute loss(1 − ŷ)² = 0.2269
3 · Backprop∂L/∂w₁ = 0.0215
4 · Updatew₁ ← 1.0000
Training convergenceLoss after 0 updates: 0.2269
Neural networks learn by forward evaluation, backpropagated gradients, and repeated parameter updates.