A Delay Learning Algorithm Based on Spike Train Kernels for Spiking Neurons

Neuroscience research confirms that the synaptic delays are not constant, but can be modulated. This paper proposes a supervised delay learning algorithm for spiking neurons with temporal encoding, in which both the weight and delay of a synaptic connection can be adjusted to enhance the learning performance. The proposed algorithm firstly defines spike train kernels to transform discrete spike trains during the learning phase into continuous analog signals so that common mathematical operations can be performed on them, and then deduces the supervised learning rules of synaptic weights and delays by gradient descent method. The proposed algorithm is successfully applied to various spike train learning tasks, and the effects of parameters of synaptic delays are analyzed in detail. Experimental results show that the network with dynamic delays achieves higher learning accuracy and less learning epochs than the network with static delays. The delay learning algorithm is further validated on a practical example of an image classification problem. The results again show that it can achieve a good classification performance with a proper receptive field. Therefore, the synaptic delay learning is significant for practical applications and theoretical researches of spiking neural networks.