Title: Extending Equilibrium Propagation to Non-Conservative Dynamics

Abstract:

Equilibrium Propagation (EP) is a learning methodology inspired by physics, which leverages the stationary states of dynamical systems for both inference and training. Originally, this approach was restricted to conservative systems—specifically, those whose dynamics are derived from an energy function. However, given their widespread utility, it is crucial to adapt EP for non-conservative systems characterized by non-reciprocal interactions. Prior efforts to generalize EP to these contexts were unable to calculate the precise gradient of the cost function.

In this work, we introduce a framework that expands EP to encompass any non-conservative system, including feedforward networks. We maintain the core principle of equilibrium propagation: the simultaneous use of stationary states for inference and learning. To ensure the exact computation of the cost function’s gradient, we adjust the dynamics during the learning phase by incorporating a term proportional to the non-reciprocal component of the interactions. Furthermore, this algorithm can be formulated variationally, where learning dynamics are generated by an energy function defined within an augmented state space. Our numerical experiments demonstrate that this proposed method outperforms earlier proposals in both performance and learning speed.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC