Imperial College London

Dr Cristopher Salvi

Faculty of Natural SciencesDepartment of Mathematics








808Weeks BuildingSouth Kensington Campus





I am a Lecturer (Assistant Professor) in Mathematics and Machine Learning at Imperial College London (Imperial-X). Prior to this, I was a Chapman Fellow in Mathematics and I obtained my PhD from the University of Oxford under the supervision of Prof. Terry Lyons.

LinkedIn / GitHub / Google Scholar

Research Interests

My research focuses on rough analysis, differential equations and deep learning. Examples of projects I am currently working on include:

  • Scaling laws of randomly initialised neural networks.
  • Neural diff. equations, diffusion models and SSMs.
  • Signature kernels for time series.
  • Autodifferentiable (stochastic) numerics.

Selected Publications

  1. A structure theorem for streamed information (J. Algebra 23) 
  2. Training neural SDEs with sig. kernel scores (NeurIPS 23) 
  3. Signature kernels as infinite limits of cResNets (ICML 23)
  4. Neural SPDEs for spatio-temporal signals (NeurIPS 22)
  5. Neural RDEs for long time series (ICML 21)
  6. Bayesian Gaussian Processes on sequential data (ICML 21) 
  7. Distribution regression on sequential data (AISTATS 21)
  8. Signature kernels are solutions to Goursat PDEs (SIAM 21)
  9. Higher order sig. kernel mean embeddings (NeurIPS 21)
  10. Deep signature transforms (NeurIPS 19)