Ben Walker

Abstract

Many real-world systems evolve continuously, yet most machine learning models interpret time series as discrete sequences. Continuous-time approaches instead treat time series as samples from an underlying input path, a formulation that naturally accommodates irregularly sampled or oversampled data. Among these, Neural Controlled Differential Equations (NCDEs) are a maximally expressive class of models that parametrise a vector field using a neural network and evolve their hidden state by solving a dynamical system driven by the input path.

This talk presents three contributions that improve the training, scalability, and interpretability of NCDEs. First, building on neural rough differential equations, Log-NCDEs apply the Log-ODE method to efficiently approximate an NCDE's solution during training, improving both computational speed and empirical performance. Second, Linear NCDEs replace the non-linear vector field with a linear one, enabling closed-form solutions and parallel-in-time computation without sacrificing theoretical expressivity. Third, Structured Linear NCDEs use structured linear vector fields to further enhance efficiency while maintaining theoretical expressiveness and empirical performance. Moreover, the linear and structured-linear formulations offer a clearer view of the learned dynamics, improving the interpretability of NCDEs.

Collectively, these methods reduce the time per training step for NCDEs by up to three orders of magnitude while achieving state-of-the-art performance across diverse time series benchmarks.

Our speaker

Benjamin Walker is a Postdoctoral Researcher at the University of Oxford’s Mathematical Institute, supported by the EPSRC DataSig II programme. His research combines applied mathematics and machine learning to build scalable models for continuous-time data. His work is driven by real-world applications in dynamic graphs, healthcare, and finance.

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