Status:
Personal website:
+44 1865 273525
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Research interests:
Applications of rough analysis to deep learning
Further details:
A mathematician who enjoys martial arts, ice skating and scuba diving. My supervisor is Terry Lyons.
I am the maintainer for the Signatory project.
Miscellaneous pieces of work:
- Interpolating PDE solutions using feedforward neural networks (i.e. Numerical PDE super-resolution)
- Limits of Fisher–KPP equations, branching Brownian motion and a spatial lambda-Fleming–Viot model for population expansion (gosh what a mouthful)
- Polynomial Approximation of Holomorphic Functions (my Master's Dissertation)
Teaching:
TA for C8.2 Stochastic Analysis and PDEs
(Hilary Term 2019)
TA for C4.1 Further Functional Analysis
(Michaelmas Term 2018)
Tutor for C8.2 Stochastic Analysis and PDEs
(Trinity Term 2018)
Major / recent publications:
Publications
Deep Signature Transforms
Patric Bonnier*, Patrick Kidger*, Imanol Perez Arribas*, Cristopher Salvi*, Terry Lyons
*Equal contribution
Neural Information Processing Systems (2019)
arXiv:1905.08494
Preprints
Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU
Patrick Kidger, Terry Lyons
arXiv:2001.00706
The degree-$(n+1)$ polynomials are the most difficult $C^{\,n + 1}$ functions to uniformly approximate with degree-$n$ polynomials.
Patrick Kidger
arXiv:2001.00668
Universal Approximation with Deep Narrow Networks
Patrick Kidger, Terry Lyons
arXiv:1905.08539