Vanilla spiking neurons in Spiking Neural Networks (SNNs) use charge-fire-reset neuronal dynamics, which can only be simulated serially and can hardly learn long-time dependencies. We find that when removing reset, the neuronal dynamics can be reformulated in a non-iterative form and parallelized. By rewriting neuronal dynamics without reset to a general formulation, we propose the Parallel Spiking Neuron (PSN), which generates hidden states that are independent of their predecessors, resulting in parallelizable neuronal dynamics and extremely high simulation speed. The weights of inputs in the PSN are fully connected, which maximizes the utilization of temporal information. To avoid the use of future inputs for step-by-step inference, the weights of the PSN can be masked, resulting in the masked PSN. By sharing weights across time-steps based on the masked PSN, the sliding PSN is proposed to handle sequences of varying 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 the best of our knowledge, this is the first study about parallelizing spiking neurons and can be a cornerstone for the spiking deep learning research.

Vanilla spiking neurons in Spiking Neural Networks (SNNs) use charge-fire-reset neuronal dynamics, which can only be simulated serially and can hardly learn long-time dependencies. We find that when removing reset, the neuronal dynamics can be reformulated in a non-iterative form and parallelized. By rewriting neuronal dynamics without reset to a general formulation, we propose the Parallel Spiking Neuron (PSN), which generates hidden states that are independent of their predecessors, resulting in parallelizable neuronal dynamics and extremely high simulation speed. The weights of inputs in the PSN are fully connected, which maximizes the utilization of temporal information. To avoid the use of future inputs for step-by-step inference, the weights of the PSN can be masked, resulting in the masked PSN.

To learn useful dynamics on long time scales, neurons must use plasticity rules that account for long-term, circuit-wide effects of synaptic changes. In other words, neural circuits must solve a credit assignment problem to appropriately assign responsibility for global network behavior to individual circuit components. Furthermore, biological constraints demand that plasticity rules are spatially and temporally local; that is, synaptic changes can depend only on variables accessible to the pre- and postsynaptic neurons. While artificial intelligence offers a computational solution for credit assignment, namely backpropagation through time (BPTT), this solution is wildly biologically implausible. It requires both nonlocal computations and unlimited memory capacity, as any synaptic change is a complicated function of the entire history of network activity. Similar nonlocality issues plague other approaches such as FORCE (Sussillo et al. 2009). Overall, we are still missing a model for learning in recurrent circuits that both works computationally and uses only local updates. Leveraging recent advances in machine learning on approximating gradients for BPTT, we derive biologically plausible plasticity rules that enable recurrent networks to accurately learn long-term dependencies in sequential data. The solution takes the form of neurons with segregated voltage compartments, with several synaptic sub-populations that have different functional properties. The network operates in distinct phases during which each synaptic sub-population is updated by its own local plasticity rule. Our results provide new insights into the potential roles of segregated dendritic compartments, branch-specific inhibition, and global circuit phases in learning.