Abstract: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 applied. We end by deriving an explicit layer-wise Hamiltonian recurrence relation governing inference for stationary solutions of both deep Fitzhugh-Nagumo networks and deep Energy-Based Models.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.21568 [cs.LG] |
| (or arXiv:2605.21568v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.21568 arXiv-issued DOI via DataCite (pending registration) |
From: Jack Kendall [view email]
[v1]
Wed, 20 May 2026 17:42:19 UTC (327 KB)
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