A New Algorithm Of Spiking Neural Networks Involving Derivative Of State Function

Spiking neural networks (SNNs) are more biologically plausible and are often referred to as the third generation of neural networks. SNNs have experienced an increasingly large amount of research attention. Information processing with classical neural networks based on the frequency of spike emission may lose information, which leads to the investigation of spiking neural networks. In SNNs, the real world information is interpreted as spike time, which makes SNNs have a possibility to fast decode information and have a special advantage to process temporal problems. A spiking neuron receives input vector of spike times, and activates a state function by increasing the time until the value of the state function reaches certain threshold value at a firing time. And the firing time is the output of the spiking neuron. SNNs have been applied extensively and successfully for practical application such as auto-associator, pattern recognition, classification and clustering.The numerous potential advantages of SNNs have been widely discussed, such as com-putational complexity, learnability and temporal data processing. However, the computational power of SNNs is still hard to control, so that efficient network models and algorithms remain to be discovered. From the view of mathematics people, we propose a modified spiking neu-ron and give a corresponding learning algorithm. The single modified spiking neuron can solve the problems solved by usual neural networks with hidden layer. Furthermore, we propose a one-layer modified spiking neural network using the modified neuron as the building block. In addition, we give the proof of the key formula in the learning algorithm of SNNs. The main results of this dissertation can be summarized as follows:1. In Chapter2, we propose, and investigate the performance of, a modified spiking neuron, of which the output is a linear combination of the firing time ta and the derivative x’(ta). An advantage of the modified spiking neuron is shown by the fact that the XOR problem can be solved by a single modified spiking neuron, but not by the classical spiking perceptron or the usual feedforward perceptron. Furthermore, somehow surprising advantage of the modified spiking neuron is that the performance of the single modified spiking neuron is comparable to a usual spiking neural network with a hidden layer for solving some benchmark problems. 2. In Chapter3, we propose, and investigate the performance of, a modifide one-layer spiking neural network using the modified neuron as the building block. It is shown by numerical experiments that a modified one-layer spiking neural network using same or fewer encod-ing neurons is almost as good as a usual spiking neural network with a hidden layer for performing classification on real-world data.3. In Chapter4, we prove a key formula in the learning algorithm of spiking neural network, without the help of the linearity assumption between the state function and the time around the firing time.