Motivated by the paradigm of reservoir computing, we consider randomly initialized
controlled ResNets defined as Euler-discretizations of neural controlled differential …

Signatory is a library for calculating and performing functionality related to the signature and
logsignature transforms. The focus is on machine learning, and as such includes features …

Vector space models for symbolic processing that encode symbols by random vectors have
been proposed in cognitive science and connectionist communities under the names Vector …

This work studies approximation based on single-hidden-layer feedforward and recurrent
neural networks with randomly generated internal weights. These methods, in which only …

We consider a stochastic volatility model where the dynamics of the volatility are described
by a linear function of the (time extended) signature of a primary process which is supposed …

We consider asset price models whose dynamics are described by linear functions of the
(time extended) signature of a primary underlying process, which can range from a (market …

Several problems in stochastic analysis are defined through their geometry, and preserving
that geometric structure is essential to generating meaningful predictions. Nevertheless, how …

Fluids exist universally in nature and technology. Among the many types of fluid flows is the
well-known vortex shedding, which takes place when a fluid flows past a bluff body. Diverse …

We introduce so-called functional input neural networks defined on a possibly infinite
dimensional weighted space with values also in a possibly infinite dimensional output …

Reservoir computing approximation and generalization bounds are proved for a new
concept class of input/output systems that extends the so-called generalized Barron …