In this paper we address the issue of automatically learning parameters of spiking neural networks. Biological neurons are formalized as timed automata and synaptical connections are represented as shared channels among these automata. Such a formalism allows us to take into account several time-related aspects, such as the influence of past inputs in the computation of the potential value of each neuron, or the presence of the refractory period, a lapse of time immediately following the spike emission in which the neuron cannot emit. The proposed model is then formally validated: more precisely, we ensure that some relevant properties expressed as temporal logical formulae hold in the model. Once the validation step is accomplished, we take advantage of the proposed model to write an algorithm for learning synaptical weight values such that an expected behavior can be displayed. The technique we present takes inspiration from supervised learning ones: we compare the effective output of the network to the expected one and backpropagate proper corrective actions in the network. We develop several case studies including a mutual inhibition network.

中文翻译：

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尖峰神经网络建模为定时自动机：带有参数学习

在本文中，我们解决了自动学习尖峰神经网络参数的问题。生物学神经元形式化为定时自动机，突触连接表示为这些自动机之间的共享通道。这种形式主义使我们可以考虑几个与时间有关的方面，例如过去输入对每个神经元电位值的计算的影响，或存在不应期，在尖峰发射后立即经过的时间神经元无法发射。然后，对所提出的模型进行正式验证：更准确地说，我们确保模型中包含以时间逻辑公式表示的一些相关属性。验证步骤完成后，我们利用提出的模型编写用于学习突触权重值的算法，以便可以显示预期的行为。我们提出的技术从有监督的学习中汲取了灵感：我们将网络的有效输出与预期的进行比较，然后反向传播网络中的适当纠正措施。我们开发了包括互斥网络在内的几个案例研究。