Computational capabilities of recurrent NARX neural networks

By Hava T. Siegelmann, Bill G. Horne, C. Lee Giles. 1997

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Citations in the corpus

Sequential parameter optimization (2005, background): “In time series modeling, a nonlinear autoregressive exogenous model (NARX) Siegelmann et al. (1997)”
Echo state networks are universal (2018, background): “Another strand of interesting literature that we will not explore in this work has to with the Turing computability capabilities of the systems of the type that we just introduced; recent relevant works in this direction are [Kili 96, Sieg 97, Cabe 15, Cabe 16], and references therein.”
Advanced Methods for Time Series Prediction Using Recurrent Neural Networks (2011, methodology): “RNNs are computationally more powerful than feed-forward networks (Siegelmann et al, 1997), and valuable approximation results were obtained for dynamical systems (Seidl & Lorenz, 2001).”
Long-term time series prediction with the NARX network: An empirical evaluation (2008, methodology): “The resulting connectionist architecture is then called a NARX network [10,32], a powerful class of dynamical models which has been shown to be computationally equivalent to Turing machines [38].”
A Connectionist Cognitive Model for Temporal Synchronisation and Learning (2007, background): “Nonlinear Auto Regressive with eXogenous inputs (NARX) networks ( Siegelmann, Horne, & Giles 1995 ) are based on a recurrent multi-layer architecture where recurrent links are allowed only from output to input neurons.”
The use of NARX neural networks to predict chaotic time series (2008, background): “However, some difficulties and limitations remain nevertheless of current actuality and cause researches for new NN models and learning techniques to be conducted[4][5][7][8].”
Learning and Representing Temporal Knowledge in Recurrent Networks (2011, unknown): “The construction of such principled, integrated models can provide an enriched understanding of the techniques and tools used in Neural Computation, Cognitive Science and Artiﬁcial Intelligence (AI).”
Neural networks for the prediction and forecasting of water resource variables: a review of modelling issues and applications (2000, background): “The inclusion of inputs at explicit time lags, resulting in NARX recurrent networks, has been found to considerably improve performance in such cases (Lin et al., 1996; Siegelmann et al., 1997).”
Sequence Learning (2001, background): “Finally, some recurrent architectures, such as fully recurrent and NARX networks, are Turing equivalent [56] [57] [55].”
Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability (2001, methodology): “A solution to that problem might be NARMA models and nonlinear autoregressive moving average models with exogenous inputs (NARMAX) (Siegelmann et al. 1997) realised by recurrent neural networks.”