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Framing RNN as a kernel method: A neural ODE approach

Adeline Fermanian · Pierre Marion · Jean-Philippe Vert · Gérard Biau

Keywords: [ Kernel Methods ] [ Deep Learning ] [ Theory ]


Building on the interpretation of a recurrent neural network (RNN) as a continuous-time neural differential equation, we show, under appropriate conditions, that the solution of a RNN can be viewed as a linear function of a specific feature set of the input sequence, known as the signature. This connection allows us to frame a RNN as a kernel method in a suitable reproducing kernel Hilbert space. As a consequence, we obtain theoretical guarantees on generalization and stability for a large class of recurrent networks. Our results are illustrated on simulated datasets.

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