We describe how hierarchical concepts can be represented in three types of layered neural networks. The aim is to support recognition of the concepts when partial information about the concepts is presented, and also when some of the neurons in the network might fail. Our failure model involves initial random failures. The three types of networks are: feed-forward networks with high connectivity, feed-forward networks with low connectivity, and layered networks with low connectivity and with both forward edges and "lateral" edges within layers. In order to achieve fault-tolerance, the representations all use multiple representative neurons for each concept. We show how recognition can work in all three of these settings, and quantify how the probability of correct recognition depends on several parameters, including the number of representatives and the neuron failure probability. We also discuss how these representations might be learned, in all three types of networks. For the feed-forward networks, the learning algorithms are similar to ones used in [4], whereas for networks with lateral edges, the algorithms are generally inspired by work on the assembly calculus [3, 6, 7].

翻译：我们描述了层级概念如何在三类分层神经网络中得以表征，旨在支持在仅呈现概念部分信息以及网络中部分神经元可能失效时对概念的识别。我们的失效模型涉及初始随机失效。这三类网络分别是：高连接度的前馈网络、低连接度的前馈网络，以及具有低连接度、同时包含前向边和层内"侧向"边的分层网络。为实现容错性，所有表征均采用每个概念对应多个代表神经元的方式。我们展示了在这三种网络设置中识别如何实现，并量化了正确识别概率如何依赖于包括代表神经元数量和神经元失效概率在内的多个参数。我们还讨论了在这三类网络中这些表征的学习可能性。对于前馈网络，学习算法与文献[4]中的方法类似；而对于包含侧向边的网络，算法则主要受装配计算相关工作[3,6,7]的启发。