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Log Signatures and Neural Controlled Differential Equations

Presented by: 
James Morrill University of Oxford
Date: 
Tuesday 16th March 2021 - 14:00 to 14:25
Venue: 
INI Seminar Room 1
Session Title: 
Log Signatures and Controlled Differential Equations
Session Chair: 
Harald Oberhauser
Abstract: 
Neural Ordinary Differential Equations are the continuous time extension of residual networks. They combine two dominant modelling paradigms in Neural Networks and Differential Equations and result in a host of benefits over a standard neural net. However, being ODEs, their solution trajectory is uniquely defined by the initial state of the system. In the case of sequential data (e.g. a time series), it is imperative that the solution trajectory can be updated based on incoming data. In this talk we describe the Neural Controlled Differential Equation - which can be thought as ODE extension to an RNN - and depends continuously on the incoming data. We give experiments that demonstrate state-of-the-art performance across a range of modelling tasks, and go on to describe the application areas the model is expected to be of most utility.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons