本文为荷兰阿姆斯特丹大学（作者：Olaf Booij）的硕士论文，共67页。

提出了一种新的基于梯度下降法的脉冲神经网络的有监督学习规则，该规则适用于多层结构的神经网络。所有现有的SNN学习规则都限制了脉冲神经元只触发一次。然而，我们的算法是专门设计来处理发出多个脉冲的神经元，充分利用了脉冲神经元的能力。SNN非常适合于时域数据的处理，因为它们是动态的，并且根据我们的学习规则，它们现在可以用于时态模式的分类任务。我们通过将该算法成功地应用于唇读任务中来证明这一点，唇读任务涉及到口语视频片段的分类。我们还证明了单层SNN的计算能力甚至比假设的更大，通过证明，它可以计算异或函数，这是与传统神经网络不同的。

A novel supervised learning-rule is derivedfor Spiking Neural Networks (SNNs) using the gradient descent method, which canbe applied on networks with a multi-layered architecture. All existinglearning-rules for SNNs limit the spiking neurons to fire only once. Ouralgorithm however is specially designed to cope with neurons that fire multiplespikes, taking full advantage of the capabilities of spiking neurons. SNNs arewell-suited for the processing of temporal data, because of their dynamicnature, and with our learning rule they can now be used for classificationtasks on temporal patterns. We show this by successfully applying the algorithmon a task of lipreading, which involves the classification of video-fragmentsof spoken words. We also show that the computational power of a one-layered SNNis even greater than was assumed, by showing that it can compute theExclusive-OR function, as opposed to conventional neural networks.

1. 引言
2. 脉冲神经网络概述
3. 单层SNN学习算法
4. 多层网络
5. 标准唇语
6. 讨论与结论

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