Approximation of Dynamical Systems by Continuous Time Recurrent Neural Networks -- Extension to Non-autonomous Systems, and Approximate Extended Conditions

By Nakamura Yuichi, Nakagawa Masahiro. 2009

191 citations recorded by the source corpus.

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Citations in the corpus

Phased LSTM: Accelerating Recurrent Network Training for Long or Event-based Sequences (2016, background): “Although early work such as [25, 10, 4] has realized the resulting limitations and suggested continuous-time dynamical systems approaches towards RNNs, the great majority of modern RNN implementations uses fixed time steps.”
Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting (2019, neutral): “Recurrent Neural Networks (RNN’s) [10] have been popular in”
The Secret Sharer: Measuring Unintended Neural Network Memorization & Extracting Secrets (2018, unknown): “The majority of this paper considers the latter choice, which traditionally give superior accuracy [3, 19, 52].”
An overview of reservoir computing: theory, applications and implementations (2007, unknown): “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].”
Reservoir computing approaches to recurrent neural network training (2009, unknown): “First, it can be shown that under fairly mild and general assumptions, such RNNs are universal approximators of dynamical systems [7].”
Neural Networks Fail to Learn Periodic Functions and How to Fix It (2020, unknown): “4 “Universal Extrapolation Theorem” In contrast to the well-known universal approximation theorems [19, 8, 12] that qualifies a neural network on a bounded region, we prove a theorem that we refer to as the universal extrapolation theorem, which focuses on the behavior of a neural network with Snake”
Action Recognition in Video Sequences using Deep Bi-Directional LSTM With CNN Features (2018, methodology): “RNNs are introduced for analyzing hidden sequential patterns in both temporal sequential and spatial sequential data [26].”
Training Excitatory-Inhibitory Recurrent Neural Networks for Cognitive Tasks: A Simple and Flexible Framework (2016, unknown): “…models and the wider class of continuous-time dynamical systems: the units of an RNN can be interpreted as the temporal or ensemble average of one or more co-tuned spiking neurons [13], while any nonlinear dynamical system can be approximated by an RNN with a sufficient number of units [14, 15].”
Automated adaptive inference of phenomenological dynamical models (2015, unknown): “Importantly, both classes are complete and are able to represent any smooth, nonlinear dynamics with a sufﬁcient number of (hidden) dynamical variables 30,32,33 .”
Distributed Containment Maneuvering of Multiple Marine Vessels via Neurodynamics-Based Output Feedback (2017, background): “The ESN takes the universal approximation property [28], [33] in the sense that, for any given real continuous function f(ξ),R → R on a sufficiently large compact set Ω and arbitrary positive number ε∗, there exists an ESN in the form of (2) such that”