Turing Computation with Recurrent Artificial Neural Networks
This work addresses the foundational problem of bridging symbolic computation and neural networks for researchers in machine learning and dynamical systems, though it appears incremental as it builds on prior results.
The authors tackled the problem of mapping Turing Machines to Recurrent Artificial Neural Networks by providing a novel and parsimonious constructive method based on Nonlinear Dynamical Automata, resulting in a simple and elegant architecture that enables direct programming without training and potential integration with training approaches like Neural Turing Machines.
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.