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：我们描述了层阶概念如何在三种分层神经网络中得到表征。其目标是支持在仅获得概念部分信息且网络中部分神经元可能失效时对这些概念的识别。我们的失效模型涉及初始随机失效。这三种网络类型为：高连通性的前馈网络、低连通性的前馈网络，以及具有低连通性、同时包含前向边和层内"侧向"边的分层网络。为实现容错性，所有表征均对每个概念使用多个代表性神经元。我们展示了这三种网络架构下识别的实现机制，并量化了正确识别概率如何依赖于多个参数，包括代表神经元数量及神经元失效概率。我们还探讨了在这三类网络中学习这些表征的潜在方法。对于前馈网络，其学习算法与文献[4]中的方法类似；而对于含有侧向边的网络，算法则主要受到装配演算工作[3,6,7]的启发。