Much of studies on neural computation are based on network models of static neurons that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete pulses called spikes. Research in spike-based computation has been impeded by the lack of efficient supervised learning algorithm for spiking networks. Here, we present a gradient descent method for optimizing spiking network models by introducing a differentiable formulation of spiking networks and deriving the exact gradient calculation. For demonstration, we trained recurrent spiking networks on two dynamic tasks: one that requires optimizing fast (~millisecond) spike-based interactions for efficient encoding of information, and a delayed memory XOR task over extended duration (~second). The results show that our method indeed optimizes the spiking network dynamics on the time scale of individual spikes as well as behavioral time scales. In conclusion, our result offers a general purpose supervised learning algorithm for spiking neural networks, thus advancing further investigations on spike-based computation.

本研究提出了一种利用可微分脉冲神经网络模型的梯度下降方法，解决以往基于静态神经元的网络模型无法处理脉冲信号信息处理的问题。实验结果表明该方法可以优化脉冲神经网络的动态行为与行为时间的关系，并为基于脉冲信号的神经计算提供了通用的监督学习算法。

脉冲神经网络的梯度下降