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Recurrent neural networks (RNNs) are brain-inspired models widely used in machine learning for analyzing sequential data.
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Recurrent neural networks are universal approximators
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Recurrent neural networks as versatile tools of neuroscience research
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A proposal on machine learning via dynamical systems
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Bruno Cessac and Manuel Samuelides · 2007
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Differential Equations Driven by Rough Paths
Terry J Lyons, Michael Caruana, and Thierry Lévy · 2007
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Fluctuation relations for diffusion processes
Raphaël Chetrite and Krzysztof Gawedzki · 2008
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Memory traces in dynamical systems
Surya Ganguli, Dongsung Huh, and Haim Sompolinsky · 2008
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Kernel methods in machine learning
Thomas Hofmann, Bernhard Schölkopf, and Alexander J Smola · 2008
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Support Vector Machines
Ingo Steinwart and Andreas Christmann · 2008
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Nonlinear and stochastic methods in neurosciences
Jonathan Touboul · 2008
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Neural ordinary differential equations
Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 2018
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Echo state networks are universal
Lyudmila Grigoryeva and Juan-Pablo Ortega · 2018
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Stochastic training of residual networks: a differential equation viewpoint
Qi Sun, Yunzhe Tao, and Qiang Du · 2018
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Deep learning as optimal control problems: Models and numerical methods
Martin Benning, Elena Celledoni, Matthias J Ehrhardt, Brynjulf Owren, and Carola-Bibiane Schönlieb · 2019
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Linear response in neuronal networks: from neurons dynamics to collective response
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AntisymmetricRNN: A dynamical system view on recurrent neural networks
Bo Chang, Minmin Chen, Eldad Haber, and Ed H Chi · 2019
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Symplectic recurrent neural networks
Zhengdao Chen, Jianyu Zhang, Martin Arjovsky, and Léon Bottou · 2019
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GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series
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Machine learning from a continuous viewpoint
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Kernels for sequentially ordered data
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Learning stochastic differential equations using RNN with log signature features
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Recurrent neural networks in the eye of differential equations
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Latent ordinary differential equations for irregularly-sampled time series
Yulia Rubanova, Ricky TQ Chen, and David K Duvenaud · 2019
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Recent advances in physical reservoir computing: A review
Gouhei Tanaka, Toshiyuki Yamane, Jean Benoit Héroux, Ryosho Nakane, Naoki Kanazawa, Seiji Takeda, Hidetoshi Numata, Daiju Nakano, and Akira Hirose · 2019
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The recurrent neural tangent kernel
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Mathematical foundation of nonequilibrium fluctuation–dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients
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Lipschitz recurrent neural networks
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Adaptive Euler–Maruyama method for SDEs with nonglobally Lipschitz drift
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