A Basic Compositional Model for Spiking Neural Networks
A Basic Compositional Model for Spiking Neural Networks
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DOI：
10.1007/978-3-031-15629-8_22
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发表时间：
2018-08
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影响因子：
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通讯作者：
N. Lynch;Cameron Musco
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作者：
N. Lynch;Cameron Musco
我们提出了一个正式的，数学基础的建模和推理的行为ofsynchronous，随机尖峰神经网络（SNNs），这已被广泛应用于神经计算的研究。我们的方法遵循在并发理论领域建立的范例。我们的SNN模型是基于神经元的有向图，分为输入，输出和内部神经元。我们在这里关注基本的SNN，其中神经元的唯一状态是指示神经元当前是否正在激发的布尔值。我们还定义了SNN的外部行为，在其外部发射模式的概率分布方面。我们在SNN上定义了两个操作符：复合操作符，它支持将SNN建模为较小SNN的组合，以及隐藏操作符，它将SNN的一些输出行为重新分类为内部行为。我们证明的结果表明，使用这些运营商建立的网络的外部行为是如何与其组件网络的外部行为。最后，我们定义了一个由SNN解决的问题的概念，并展示了合成和隐藏算子如何影响网络解决的问题。我们用三个例子来说明我们的定义：一个由门构成的布尔电路，一个由赢家通吃网络和过滤器网络构成的注意网络，以及一个涉及以循环方式组合两个网络的玩具例子。
We present a formal, mathematical foundation for modeling and reasoning about the behavior ofsynchronous, stochastic Spiking Neural Networks (SNNs), which have been widely used in studies of neural computation. Our approach follows paradigms established in the field of concurrency theory.Our SNN model is based on directed graphs of neurons, classified as input, output, and internal neurons. We focus here on basic SNNs, in which a neuron’s only state is a Boolean value indicating whether or not the neuron is currently firing. We also define theexternal behaviorof an SNN, in terms of probability distributions on its external firing patterns. We define two operators on SNNs: acomposition operator, which supports modeling of SNNs as combinations of smaller SNNs, and ahiding operator, which reclassifies some output behavior of an SNN as internal. We prove results showing how the external behavior of a network built using these operators is related to the external behavior of its component networks. Finally, we definition the notion of aproblemto be solved by an SNN, and show how the composition and hiding operators affect the problems that are solved by the networks.We illustrate our definitions with three examples: a Boolean circuit constructed from gates, anAttentionnetwork constructed from aWinner-Take-Allnetwork and aFilternetwork, and a toy example involving combining two networks in a cyclic fashion.