  Equilibrium Propagation (EP) is a biologically plausible local learning
algorithm initially developed for convergent recurrent neural networks (RNNs),
where weight updates rely solely on the connecting neuron states across two
phases. The gradient calculations in EP have been shown to approximate the
gradients computed by Backpropagation Through Time (BPTT) when an
infinitesimally small nudge factor is used. This property makes EP a powerful
candidate for training Spiking Neural Networks (SNNs), which are commonly
trained by BPTT. However, in the spiking domain, previous studies on EP have
been limited to architectures involving few linear layers. In this work, for
the first time we provide a formulation for training convolutional spiking
convergent RNNs using EP, bridging the gap between spiking and non-spiking
convergent RNNs. We demonstrate that for spiking convergent RNNs, there is a
mismatch in the maximum pooling and its inverse operation, leading to
inaccurate gradient estimation in EP. Substituting this with average pooling
resolves this issue and enables accurate gradient estimation for spiking
convergent RNNs. We also highlight the memory efficiency of EP compared to
BPTT. In the regime of SNNs trained by EP, our experimental results indicate
state-of-the-art performance on the MNIST and FashionMNIST datasets, with test
errors of 0.97% and 8.89%, respectively. These results are comparable to those
of convergent RNNs and SNNs trained by BPTT. These findings underscore EP as an
optimal choice for on-chip training and a biologically-plausible method for
computing error gradients.
