Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model
In this work, we extend the Equilibrium Propagation framework to skew-gradient systems and show an equivalence between deep Energy-Based Models and Hamiltonian neural networks. We focus on networks of diffusively coupled Fitzhugh-Nagumo neurons as a prototypical example. We show that since stationary solutions of the Fitzhugh-Nagumo model are described by self-adjoint operators, the methods of equilibrium propagation for performing credit assignment can be applied. Furthermore, for Fitzhugh-Nagumo networks with the topology of a deep residual network, we show that the steady state solutions admit a (spatial) Hamiltonian, and thus the methods of Hamiltonian Echo Backpropagation can be appl...
| Authors | Jack Kendall |
|---|---|
| Primary category | cs.LG |
| Published | 20 May 2026 |
| Last updated at source | 20 May 2026 |
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