Equilibrium propagation (EP) is a compelling alternative to the backpropagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight symmetry and infinitesimal equilibrium perturbations, i.e., nudges, to estimate unbiased gradients efficiently. Both requirements are challenging to implement in physical systems. Yet, whether and how weight asymmetry affects its applicability is unknown because, in practice, it may be masked by biases introduced through the finite nudge. To address this question, we study generalized EP, which can be formulated without weight symmetry, and analytically isolate the two sources of bias. For complex-differentiable non-symmetric networks, we show that the finite nudge does not pose a problem, as exact derivatives can still be estimated via a Cauchy integral. In contrast, weight asymmetry introduces bias resulting in low task performance due to poor alignment of EP's neuronal error vectors compared to BP. To mitigate this issue, we present a new homeostatic objective that directly penalizes functional asymmetries of the Jacobian at the network's fixed point. This homeostatic objective dramatically improves the network's ability to solve complex tasks such as ImageNet 32x32. Our results lay the theoretical groundwork for studying and mitigating the adverse effects of imperfections of physical networks on learning algorithms that rely on the substrate's relaxation dynamics.

通过研究广义平衡传播（generalized EP），我们发现权重的非对称性会导致平衡传播算法与反向传播算法的性能比较低，因此我们提出了一种新的恒定目标函数，用于惩罚网络在固定点的雅可比矩阵的功能不对称性，这显著提高了网络解决复杂任务的能力，例如ImageNet 32x32。

通过雅可比稳态改进非对称权重的均衡传播