Original Contribution: Approximation of dynamical systems by continuous time recurrent neural networks
By Ken-ichi Funahashi, Yuichi Nakamura. 1993
Subfields: Model Architectures, Statistical Learning Theory
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Model Architectures
- Christopher R'e
- Tri Dao
- Atri Rudra
- Albert Gu
- Karan Goel
- Khaled Kamal Saab
- Patrick Kidger
- Haitao Zhao
In Statistical Learning Theory
- Patrick Kidger
- Terry Lyons
- Tamara G. Kolda
- Randall D. Beer
- Stefanos P. Zafeiriou
- Christopher R'e
- Surya Ganguli
- George Trigeorgis
Citations in the corpus
- Evolutionary Robotics: A New Scientific Tool for Studying Cognition (2005, background): “This class of DSs also has the advantage of being universal, in the sense that it has been formally proved that any sufficiently smooth DS can be approximated to any desired degree of accuracy by a CTRNN with a sufficient number of nodes [ 18 ].”
- An overview of reservoir computing: theory, applications and implementations (2007, background): “RNNs have been shown to be Turing equivalent [25] for common activation functions, can approximate arbitrary finite state automata [33] and are universal approximators [ 10 ].”
- Neural Controlled Differential Equations for Irregular Time Series (2020, background): “Indeed the connection between RNNs and dynamical systems is well-known [1, 2, 3, 4].”
- Liquid Time-constant Networks (2020, methodology): “Time Series Predictions We evaluated the performance of LTCs realized by the proposed Fused ODE solver against the state-of-the-art discretized RNNs, LSTMs (Hochreiter and Schmidhuber 1997), CT-RNNs (ODE-RNNs) (Funahashi and Nakamura 1993; Rubanova, Chen, and Duvenaud 2019), continuoustime gated rec”
- Neuroevolution: from architectures to learning (2008, background): “While being one of the simplest nonlinear, continuous dynamic network models, CTRNNs are universal dynamic approximators [24].”
- The Dynamics of Active Categorical Perception in an Evolved Model Agent (2003, background): “They are relatively computationally and analytically tractable, have a straightforward neurobiological interpretation that captures some of the key features of nerve cells, and are universal approximators of smooth dynamics (Funahashi & Nakamura, 1993; Kimura & Nakano, 1998).”