将平衡传播拓展至神经元扩散网络，建立能量模型与哈密顿网络的等价关系。
Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model
- 用自伴随算子处理菲茨休-纳古莫夫神经网络的稳态解
- 证明深度残差结构下存在空间哈密顿量，可支持反向传播
- 推导出层间哈密顿递推公式，适用于两类深度模型
本文将平衡传播框架拓展至斜梯度系统，揭示深度能量模型与哈密顿神经网络之间的等价性。以扩散耦合的菲茨休-纳古莫夫神经元网络为典型范例，我们证明其稳态解由自伴随算子描述，因此可应用平衡传播进行信用分配。对于具有深度残差网络拓扑的菲茨休-纳古莫夫网络，其稳态解具备（空间）哈密顿量结构，因而可采用哈密顿回声反向传播方法。最后，我们推导出控制深度菲茨休-纳古莫夫网络与深度能量模型稳态解推理的显式层间哈密顿递推关系。
原文摘要 · Abstract (English)
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.
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