A live feed-forward network training by backpropagation in real time. Sphere colour = neuron activation, edge colour/width = connection weight sign & magnitude. The floor grid shows the learned decision boundary over the training data.
a = f( Σ wᵢxᵢ + b ) where f is the selected
activation (ReLU / tanh / sigmoid). The output neuron always uses a sigmoid so its value reads as
a class probability ŷ ∈ (0,1).
L = (1/n) Σ (ŷ − y)² by full-batch
gradient descent: for every layer, the error signal is propagated backward via the chain rule
δˡ = (Wˡ⁺¹)ᵀδˡ⁺¹ ⊙ f′(zˡ), then weights update as
W ← W − η · δ·aᵀ with learning rate η set by the slider.
L(x,y) = x² + y² + 0.3·sin(3x)cos(3y) so you can see how η trades off convergence
speed against overshoot/divergence — the same dynamic driving the network above.