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Interactive 3D/Backpropagation Step-by-Step
Ready - press Run Forward Pass
Backpropagation
3→4→2 network, sigmoid activations, MSE loss
Actions
Target Outputs
What the network should output. Changing these changes the loss.
Target y10.80
Target y20.20
How It Works
Backpropagation applies the chain rule to compute how much each weight contributed to the error. Weights with large gradients contributed more to the mistake.

Formula:
output_delta = (target − output) × σ′(output)
hidden_delta = Σ(w × output_delta) × σ′(hidden)
grad_w = from_activation × to_delta
Legend
Idle neuron
Active neuron (high activation)
Positive weight (forward)
Negative weight (forward)
Large gradient (backward)
Small gradient (backward)

Backpropagation Step-by-Step - Interactive Visualization

Backpropagation is the algorithm that makes neural network training possible. After a forward pass produces a prediction, backprop computes how much each weight contributed to the error - by flowing error signals backwards through the chain rule. This visualization shows the real gradient values on every edge of a 3-layer network.

  • See the forward pass: activations computed left-to-right through each layer
  • See the backward pass: error gradients flow right-to-left via the chain rule
  • Gradient magnitudes shown on edges: larger = that weight contributed more to the error
  • Change target outputs to see how the gradient signals change
  • Understand vanishing gradients: why deep networks can have near-zero gradients in early layers
  • The mathematical foundation of SGD, Adam, and every modern neural network optimizer

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.