title: Framing RNN as a kernel method: A neural ODE approach
abstract: 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.
authors: Adeline Fermanian Pierre Marion Jean-Philippe Vert Gérard Biau
hIndex: Jean-Philippe Vert 62