Equilibrium propagation (EP) is an alternative to backpropagation (BP) that
allows the training of deep neural networks with local learning rules. It thus
provides a compelling framework for training neuromorphic systems and
understanding learning in neurobiology. However, EP requires infinitesimal
teaching signals, thereby limiting its applicability in noisy physical systems.
Moreover, the algorithm requires separate temporal phases and has not been
applied to large-scale problems. Here we address these issues by extending EP
to holomorphic networks. We show analytically that this extension naturally
leads to exact gradients even for finite-amplitude teaching signals.
Importantly, the gradient can be computed as the first Fourier coefficient from
finite neuronal activity oscillations in continuous time without requiring
separate phases. Further, we demonstrate in numerical simulations that our
approach permits robust estimation of gradients in the presence of noise and
that deeper models benefit from the finite teaching signals. Finally, we
establish the first benchmark for EP on the ImageNet 32x32 dataset and show
that it matches the performance of an equivalent network trained with BP. Our
work provides analytical insights that enable scaling EP to large-scale
problems and establishes a formal framework for how oscillations could support
learning in biological and neuromorphic systems.

该研究工作介绍了平衡传播 (EP) 在训练神经网络方面的应用，扩展了基于此的算法到全纯网络，能精确计算梯度，进而支持更深层数的模型训练，并在 ImageNet 数据集上与 BP 算法进行了对比，具有重要意义。