Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model
Authors: Jack Kendall
Summary
arXiv:2605. 21568v1 Announce Type: new 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.
Relevance
Read next because Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model overlaps with experiment "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)". Matching terms: model. Source: arxiv cs.LG (Machine Learning).
Abstract
arXiv:2605.21568v1 Announce Type: new 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.