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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.21568 |
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| _version_ | 1866917518088601600 |
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| author | Kendall, Jack |
| author_facet | Kendall, Jack |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21568 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model Kendall, Jack Machine Learning 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. |
| title | Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.21568 |