The inference half is not the whole prize. Backpropagation needs a von Neumann machine: it stores every activation on the forward pass and replays them backwards. Equilibrium propagation does not. You let the system settle freely, then nudge the output gently toward the target and let it settle again, and the difference between the two equilibria gives you the gradient. Everything is local, there is no tape, and there is no backward pass. Scellier and Bengio titled the original paper as a bridge between energy-based models and backpropagation for exactly this reason, and there are now hardware demonstrations in analog, Ising, oscillator and memristive devices. So the learning rule that lost the lottery is the one the new substrate runs for free. In this lab you will prove the estimate correct on a case where the exact answer is available in closed form.