An interactive demonstration of equilibrium propagation training a tiny network with one clamped input, two hidden neurons, and one output. Each training step runs a free relaxation and a weakly-clamped nudged relaxation toward a target, then updates each weight by a local contrastive Hebbian rule. The network diagram shows weights as colored edges and free-phase activations as node fills; small deltas show how the target nudge shifts each hidden neuron. A loss sparkline falls as the free-phase output converges to the target.

Edge color = weight sign (+ / ), thickness = magnitude. Node fill = free-phase activation. Δ = shift under the nudge (the target propagating backward).
Equilibrium propagation networkInput, two hidden, one output, trained by two relaxations. x=1 Δ +0.00 Δ +0.00 Δ +0.00 input hidden output (dashed = target)
Free-phase loss per training step
Output ŷ
0.50
Target y
0.80
Loss
0.00
0.80
0.60