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

Neural SDEs are continuous-time generative models for sequential data. State-of-the-art
performance for irregular time series generation has been previously obtained by training …

Neural SDEs combine many of the best qualities of both RNNs and SDEs, and as such are a
natural choice for modelling many types of temporal dynamics. They offer memory efficiency …

Many machine learning approaches for decision making, such as reinforcement learning,
rely on simulators or predictive models to forecast the time-evolution of quantities of interest …

This article provides a concise overview of some of the recent advances in the application of
rough path theory to machine learning. Controlled differential equations (CDEs) are …

Inferring the causal structure underlying stochastic dynamical systems from observational
data holds great promise in domains ranging from science and health to finance. Such …

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach
to modeling the dynamics of a latent state, which is observed at discrete-time points via a …

We develop a provably convergent kernel-based solver for path-dependent PDEs (PPDEs).
Our numerical scheme leverages signature kernels, a recently introduced class of kernels …

These notes expound the recent use of the signature transform and rough path theory in
data science and machine learning. We develop the core theory of the signature from first …