Deep Learning

Backpropagation: How Networks Learn

Follow data forward through the network, compute the loss, then watch gradients flow backward via the chain rule. Step through each phase neuron by neuron.

Walkthrough ProgressStep 1 of 8

Network DiagramForward Pass

Active neuronDead neuron (ReLU=0)Hover neurons to inspect values

Forward Pass

Input Values

These are the four input features the network receives. Each value is fed into the input layer and passed forward without any transformation.

Key Points

Input neurons don't apply any activation; they simply relay their values.
Here: x = [0.5, 0.8, 0.2, 0.9]
In practice these could be pixel values, sensor readings, or normalized features.

Step 1 of 80% complete

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Forward Pass (1–3)

Compute Loss (4)

Backward Pass (5–7)

Weight Update (8)

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Key Insight

Backpropagation is just the chain rule applied recursively. Each layer receives a gradient from the layer above, multiplies it by the local derivative, and passes it further back. No magic, just calculus and matrix multiplication.

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