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Feed-forward Spiking neural networks allow us to process time data naturally without the additional complexity of a recurrent neural network. So what is the benefit of Recurrent Spiking Neural Networks over Feed-forward Spiking Neural Networks?

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In non-recurrent feedforward SNN, the duration of each spike's effect on the network is limited. For example, if LIF neuron is used, then the potentiated or inhibited potential due to the input spike will be exponentially decayed over time and eventually disappeared. However, if you use the recurrent SNN, theoretically the effect of input spikes can last for arbitrarily long.

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