Fig. 1: Training the Ising machine with EP.
From: Training an Ising machine with equilibrium propagation
a Illustration of the free phase and nudge phase of the Equilibrium Propagation algorithm applied to an Ising spin system. For both phases, the input is fed to the chip through bias fields (see Section 1 and 1), with a strength that depends on the task. The steady spins states obtained at equilibrium after the free and the nudge phases can be directly measured on the chip to compute the parameters updates. b Annealing schedule used to drive the Ising machine during the two sequential phases of EP. At the end of both phases, the probability of transition between states ends at 0, in the steady state where we measure the states of all the spins. The small bump in the probability during the nudge phase, achieved through reverse annealing, allows the system to be sensitive to the nudge signal applied to the output neurons. c Binary activations - such as spins - in a dynamical neural network trained with EP can cause the vanishing gradient issue if the input of the neuron is only weakly modified between the free and the nudge phase. d Schematic of the D-Wave chip used with the specific Chimera architecture where spins are arranged as small 4 × 4 fully connected square lattices and laterally coupled to 2 neighbors. The spins σi are represented as horizontal and vertical lines, whereas the couplings Jij are represented as plain circles for intra-cluster coupling and dotted bridges for cluster-to-cluster coupling.
