Energy Function in Analog Neural Circuits for Equilibrium Propagation Algorithm Implementation

The Equilibrium Propagation (EqProp) algorithm offers a promising approach for training analog neural networks by estimating error gradients without the need for a separate computational circuit. Existing EqProp methods simplify gradient estimation through local gradient evaluations for individual components, which may incompletely represent circuit interdependencies and lead to unstable convergence. This work introduces a revised gradient estimation approach that defines the energy function based on conventional electrical power. The proposed method accounts for the interdependent relationships among all circuit components and reflects the actual behavior of analog neural circuits more accurately. As a result, it improves learning stability and robustness. The existing method shows an average error rate of 7dB after 100 epochs for the XOR task with an 80% failure rate. In contrast, the proposed method achieves an average error rate of −6dB for the same number of epochs. These findings highlight the potential of the proposed approach to improve convergence stability and accuracy in nonlinear resistive networks, as demonstrated on the XOR task, while motivating further investigation into more complex network architectures.