Supervised learning in multilayer spiking neural networks with inner products of spike trains

Recent advances in neurosciences have revealed that neural information in the brain is encoded through precisely timed spike trains, not only through the neural firing rate. This paper presents a new supervised, multi-spike learning algorithm for multilayer spiking neural networks, which can implement the complex spatio-temporal pattern learning of spike trains. The proposed algorithm firstly defines inner product operators to mathematically describe and manipulate spike trains, and then solves the problems of error function construction and backpropagation among multiple output spikes during learning. The algorithm is successfully applied to different temporal tasks, such as learning sequences of spikes and nonlinear pattern classification problems. The experimental results show that the proposed algorithm has higher learning accuracy and efficiency than the Multi-ReSuMe learning algorithm. It is effective for solving complex spatio-temporal pattern learning problems.