Forward, Backward, Update
Key concept: One training step is three phases: run the network forward, propagate gradients backward, then update every parameter with θ ← θ − η∇θ.
This demo runs the full training loop on a small 2→3→3→2 multilayer network (ReLU, 29 parameters) learning to classify the four XOR corners — the same problem Demos 4 and 6 introduce. One click advances exactly one phase.
Forward lights up the activation values layer by layer with a travelling dot. Backward draws the gradient bands ∂ℒ/∂H², ∂ℒ/∂H¹, ∂ℒ/∂X flowing the opposite way, with a bar under each parameter block showing the size of its gradient. Update applies θ ← θ − η∇θ and adds a new point to the loss curve. Click through repeatedly (or let it auto-run) and the network reaches 4/4 correct in about 60 steps.
What to look for: watch the hidden-layer columns H¹ and H² — early on they mix the two classes together, but after enough update steps they separate cleanly into red and blue columns. That separation is the network discovering a feature map like the one Demo 4 hands over by hand.
Interaction is easiest on a laptop/desktop screen. On a small screen, you can also open the demo in its own tab at full size.