My up-to-date information can be found on my personal website .
I am currently working on the ERS Project neuroIC002 "Recurrence and stochasticity for neuro-inspired computation" under the guidance of Prof. Holger Rauhut and in collaboration with physicists and neuroscientists from Forschungszentrum Jülich. The aim of the seed fund is to explore the effect of recurrence and stochasticity in the performance of biological neural networks in comparison to the widely-studied deterministic feed-forward artificial neural networks.
Historically, my mathematical research has looked at the interplay between stochastic analysis (more particularly within the framework of the theories of rough paths and regularity structures) and differential geometry.
Research papers:
- Boutaib, Y. The accessibility problem for geometric rough differential equations.
- Boutaib, Y.; Bartolomaeus, W.; Nestler, S.; Rauhut, H. Path classification by stochastic linear recurrent neural networks. Adv. Contin. Discrete Models 2022, Paper No. 13, 29 pp.
- Boutaib, Y.; Lyons, T. A new definition of rough paths on manifolds. To appear in Annales de la Faculté des Sciences de Toulouse.
- Boutaib, Y. On Lipschitz maps and the Hölder regularity of flows. Rev. Roumaine Math. Pures Appli. 65 (2020), no. 2, 129-175.
- Boutaib, Y.; Gyurko, L.G.; Lyons, T.; Yang, D. Dimension-free Euler estimates of rough differential equations. Rev. Roumaine Math. Pures Appli. 59 (2014), no. 1, 25-53.
Recorded talks:
- A short review of rough paths on manifolds (GPSD Mannheim 2021, Stochastic analysis session).
- Path classification with continuous-time linear stochastic RNNs (GPSD Mannheim 2021, Statistical learning and computational statistics session).
Unpublished notes:
- Azzali, S.; Boutaib, Y.; Frabetti, A.; Paycha, S. Direct connections on groupoids and their jet prolongations.
Extended abstract:
- Boutaib, Y. The role of recurrence and stochasticity in learning streaming data. Mathematisches Forschungsinstitut Oberwolfach Report No. 55/2021, Applied Harmonic Analysis and Data Science, DOI: 10.4171/OWR/2021/55.
- Boutaib, Y. Geometric Structure of the reachability set. Mathematisches Forschungsinstitut Oberwolfach Report No. 41/2012, Rough Paths and PDEs, DOI: 10.4171/OWR/2012/41.
DPhil thesis:
- Boutaib, Y. Lipschitz geometry and rough paths. University of Oxford (2016).