Neuromodulated Equilibrium Learning

Equilibrium Propagation (EP) is a biologically motivated alternative to backpropagation but requires free and nudged equilibrium phases, raising questions about the biological plausibility of phase-separated learning. We introduce Neuromodulated Equilibrium Learning (NEL), a single-equilibrium reward-based framework inspired by Attention-Gated Brain Propagation and neuromodulatory signaling. After reaching a free equilibrium, NEL propagates a reward-dependent modulatory signal derived from the selected action through reciprocal feedback connections to drive local synaptic updates, eliminating both the reward-nudged equilibrium and contrastive update. We evaluate NEL on MNIST, Fashion-MNIST, and CIFAR-10 using multilayer perceptrons and convolutional networks. NEL approaches reward-based Equilibrium Propagation (REP) in shallow architectures, with gaps of 0.67 and 1.20 percentage points on MNIST and one-hidden-layer Fashion-MNIST, while larger gaps emerge in deeper and convolutional networks. A direct cost feedback control using the full supervised output error does not systematically improve over NEL, indicating that sparse reward information alone does not explain the remaining gap to REP. These results show that effective reward-driven learning can arise from a single free equilibrium while motivating further investigation of the computations provided by reward-nudged dynamics.