Supervised Learning In Spiking Neural Networks With Inner Product Of Spike Trains

Motivated by recent advances in neurosciences, neural information is encoded in the brain through the precisely timed spike trains, not only through the neural firing rate. The third generation of artificial neural network based on precise spike timing coding schemes, namely the spiking neural networks, are shown very suitable for implementation of the brain neural signal processing problem and effective tools for the processing of complex spatio-temporal information. However,due to their intricately discontinuous and implicit nonlinear mechanisms, the formulation of efficient supervised learning algorithms for spiking neural networks is difficult, which has become an important problem in the research area.In this paper, firstly we introduce the general framework of supervised learning algorithms for spiking neural networks, and analysis their performance evaluations including spike trains learning ability, offline and online processing ability, the locality of learning mechanism and the applicability to network structure. We survey the advance of the research on supervised learning algorithms, which can be divided into three categories according to the difference of their methods: gradient descent rule, synaptic plasticity rule, and spike trains convolution rule. We also discuss the advantages and disadvantages of these algorithms and prospect the problems in current research.Furthermore, based on the inner product of spike trains, we propose a new supervised learning algorithm for spiking neurons with temporal encoding. The learning rule for synapses is developed by constructing the multiple spikes error function using the inner product of spike trains, and its learning rate is adaptively adjusted according to the actual firing rate of spike neurons during learning. The proposed algorithm is successfully applied to various spike trains learning tasks, in which the desired spike trains are encoded by Poisson process or linear method. The effect of different learning rate, different number of synaptic inputs, different length of the desired output spike trains, different firing rates of the input and desired spike trains and different kernels on the performance of the learning algorithm is also analyzed. The experiment results show that our proposed method has higher learning accuracy and flexibility than the existing learning methods, so it is effectivefor solving complex spatio-temporal pattern learning problems.Finally we extend the proposed algorithm for the multilayer feedforward spiking neural networks and propose a new supervised multi-spike learning algorithm for multilayer feedforward spiking neural networks based on the inner product of spike trains. The proposed algorithm is applied to classification tasks with classic benchmarks, Wisconsin Breast Cancer dataset to verify the ability of solving nonlinear pattern classification problems. The data of Wisconsin Breast Cancer dataset are encoded with linear spike trains coding scheme and we analyze the training results and the impact of number of neurons in hidden layer on the classification accuracy. The experimental results show that the proposed algorithm can effectively solve the nonlinear classification problem and has certain value for practical operation.