Papers › Framing RNN as a kernel method: A neural ODE approach

Framing RNN as a kernel method: A neural ODE approach

2 Jun 2021NeurIPS 2021 12arXiv:2106.01202archive 2025-07-28

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

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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