Vanilla spiking neurons in Spiking Neural Networks (SNNs) use charge-fire-reset neuronal dynamics, which can only be simulated in serial and can hardly learn long-time dependencies. We find that when removing reset, the neuronal dynamics are reformulated in a non-iterative form and can be parallelized. By rewriting neuronal dynamics without resetting to a general formulation, we propose the Parallel Spiking Neuron (PSN), which uses dense connections between time-steps to maximize the utilization of temporal information. To avoid the use of future inputs for low-latency inference, we add masks on the weights and obtain the masked PSN. By sharing weights across time-steps, the sliding PSN is proposed with the ability to deal with sequences with variant lengths. We evaluate the PSN family on simulation speed and temporal/static data classification, and the results show the overwhelming advantage of the PSN family in efficiency and accuracy. To our best knowledge, this is the first research about parallelizing spiking neurons and can be a cornerstone for the spiking deep learning community. Our codes are available at \url{https://github.com/fangwei123456/Parallel-Spiking-Neuron}.

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