Special ACM Seminar

Motivated by the paradigm of reservoir computing, I will consider randomly initialized neural controlled differential equations and show that in the infinite-width limit and under proper rescaling of the vector fields, these neural architectures converge weakly to Gaussian processes indexed on path-space and with covariances satisfying certain PDEs varying according to the choice of activation function. In the special case where the activation function is the identity, the equation reduces to a linear PDE and the limiting kernel agrees with the original signature kernel. 

This is based on joint work with Nicola M. Cirone and Maud Lemercier.