Supervised Learning Algorithms Of Recurrent Spiking Neural Networks Based On STDP

In recent years,spiking neural networks(SNNs)have attracted more and more attention of researchers due to their wider research and application in the field of intelligent computing.Although the early development of the SNN is inspired by the traditional artificial neural network(ANN),it is fundamentally different from the ANN.The SNN has more powerful computing power,which is very suitable for the processing of complex spatiotemporal patterns.On the one hand,the SNN uses precisely timed spike train to encode information,while the ANN uses spike rate to encode information.The processing of information by the human brain is real-time,so it is obvious that the SNN with temporal code is more biologically authentic compared with the traditional artificial neural network.On the other hand,the cerebral cortex network is not a simple feedforward structure.Neurons in the brain are connected recurrently and interact through action potentials.Therefore,compared with the feedforward structure of the SNN,the recurrent spiking neural network(RSNN)with feedback connection can better simulate the information processing process of the brain.Because the neural information of the SNN is expressed in the form of spike train,the internal state variables and error functions of the neurons no longer satisfy the continuously differentiable nature,which makes the learning algorithm of the ANN not directly applicable to the SNN.In addition,recurrent spiking neural networks have more complex dynamics characteristics because of feedback connections,which makes it more difficult to build learning algorithms for RSNNs.Based on the above background,this paper proposes two supervised learning algorithms that can be used to train RSNNs.Firstly,the mapping of the Integrate-and-Fire neuron model to the ReLU neuron model is derived,which solves the discontinuity of variables in the derivation of the learning rules.This mapping provides the basis of applying the supervised learning algorithm of the traditional recurrent neural network to the recurrent spiking neural network.Secondly,combined with the spike-timing dependent plasticity(STDP)learning rules,this paper proposes the supervised learning algorithm based on BP-STDP(Backpropagation-Spike-Timing Dependent Plasticity)for recurrent spiking neural networks by deducing the traditional learning algorithm-BPTT(Backpropagation Through Time)in traditional recurrent neural networks.For the convenience of description,the algorithm is abbreviated as BP-STDP algorithm.The validity of the BP-STDP algorithm is verified by spike train learning task,and the influence of different parameters on the learning effect is analyzed by comparing with the FOLLOW algorithm.At the same time,the classification experiments on the Iris dataset and the WBC dataset verify the processing ability of the BP-STDP algorithm and the FOLLOW algorithm for non-linear pattern classification problems.Finally,based on the BP-STDP algorithm,this paper proposes a supervised learning algorithm based on FA-STDP(Feedback Alignment-Spike-Timing Dependent Plasticity)for recurrent spiking neural networks by introducing a feedback alignment(FA)mechanism in the backpropagation process.For convenience of description,it is abbreviated as FA-STDP algorithm.In the experiment,the effectiveness of the algorithm is verified by the spike train learning task,and the influence of different parameters on the learning effect is analyzed by comparing with the BP-STDP algorithm.Besides,the classification experiments on the Iris and WBC datasets verify the processing ability of the FA-STDP algorithm for non-linear pattern classification problems,which compares with the classification effect of the BP-STDP algorithm at the same time.