We improve the results by Siegelmann & Sontag (1995) by providing a novel and parsimonious constructive mapping between Turing Machines and Recurrent Artificial Neural Networks, based on recent developments of Nonlinear Dynamical Automata. The architecture of the resulting R-ANNs is simple and elegant, stemming from its transparent relation with the underlying NDAs. These characteristics yield promise for developments in machine learning methods and symbolic computation with continuous time dynamical systems. A framework is provided to directly program the R-ANNs from Turing Machine descriptions, in absence of network training. At the same time, the network can potentially be trained to perform algorithmic tasks, with exciting possibilities in the integration of approaches akin to Google DeepMind's Neural Turing Machines.
翻译:我们改进了Siegelmann & Sontag(1995年)的成果,根据非线性动态自动自闭器的最新发展,在图灵机和经常性人工神经网络之间提供了一种新颖和令人厌恶的建设性绘图,由此形成的R-ANN的架构简便而优雅,因为它与基本的NDAs具有透明的关系。这些特征为机器学习方法的发展和以连续的时间动态系统进行象征性的计算带来了希望。在没有网络培训的情况下,为图灵机描述的R-ANNs提供了直接编程的框架。与此同时,网络有可能接受培训,以完成算法任务,在整合与谷歌深明的神经图样机类似的方法方面有着令人兴奋的可能性。