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Second order spiking perceptron and its applications

机译：二阶加标感知器及其应用

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摘要

Based on the usual approximation scheme, we lay a so-called second order spiking network with the renewal process inputs, which employ both first and second order statistical representation, i.e., the means, variances and correlations of the synaptic input. Then we apply an error minimization technique to train the network and derive the corresponding back-propagation learning rule to present a more biologically plausible so-called Second Order Spiking Perceptron. It shows that such perceptron, even a single neuron, is able to perform various complex non-linear tasks like the XOR problem that classical single-layer percep-trons are unable to perform. Among including the second order statistics in computations, such perceptron offers the most important advantage over their predecessors, in that it can train not only the output means but the output variances by introducing the variance term in the error presentation. As a result, we can not only obtain the desired output means but decrease the output noises (variances) by training the networks, and also can reach the trade-off between the output mean error and output variance by the adjustment of the penalty factor in error function, due to a specific learning task.
机译：基于通常的近似方案，我们使用更新过程输入构建了一个所谓的二阶尖峰网络，该网络使用一阶和二阶统计表示，即突触输入的均值，方差和相关性。然后，我们应用错误最小化技术来训练网络，并推导相应的反向传播学习规则，以提出生物学上更合理的所谓的二阶尖峰感知器。它表明，即使是单个神经元，这种感知器也能够执行各种复杂的非线性任务，例如经典单层感知器无法执行的XOR问题。在计算中包括二阶统计量的过程中，这种感知器比它们的前辈具有最重要的优势，因为它不仅可以通过在误差表示中引入方差项来训练输出均值，而且可以训练输出方差。结果，我们不仅可以通过训练网络来获得所需的输出均值，而且可以降低输出噪声（方差），并且可以通过调整惩罚因子来达到输出平均误差和输出方差之间的权衡。错误功能，由于特定的学习任务。

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