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Learning methods of recurrent Spiking Neural Networks based on adjoint equations approach

In artificial Spiking Neural Networks (SNNs) the information processing and transmission are carried out by spike trains in a manner similar to the generic biological neurons. Recently it has been reported that they are computationally more powerful than the conventional neural networks. It is strongly desired to derive efficient learning methods of SNNs. It is, however, much more difficult to analyze and design SNNs due to their intricately discontinuous and implicit nonlinear mechanisms. In this paper, we discuss learning methods of recurrent SNNs constructed with integrate-and-fire type spiking neurons. We have already proposed a learning method of recurrent SNNs such that they possess the desired spike trains with the specified spike emission times. The method is derived based on the sensitivity equations approach. In the learning method, however, computational time required for learning increases extremely as the number of neurons in SNNs increases. In this paper, we propose two efficient learning methods of recurrent SNNs based on the adjoint equations approach. We compare the proposed and existing learning methods from the viewpoint of computational time. It is shown that the proposed methods drastically reduce computational time.