**Project Heads**

*Christian Bayer, Peter Friz*

**Project Members**

Nikolas Tapia (TU / WIAS)

**Project Duration**

01.01.2019 – 31.12.2020

**Located at**

TU Berlin / WIAS

**Project Webpages**

**Selected Publications
**

**P. K. Friz**, M. Hairer,*A Course on Rough Paths*. 2nd ed. Universitext (2020). Springer.- C. Bellingeri, A. Djurdjevac,
**P. K. Friz**,**N. Tapia**.*Transport and continuity equations with (very) rough noise*. (2020). arXiv 2002.10432 [math.AP] - J. Diehl, K. Ebrahimi-Fard,
**N. Tapia**.*Time-warping invariants of multidimensional time series*. Acta Appl. Math (2020). doi: 10.1007/s10440-020-00333-x - E. Celledoni, P. E. Lystad,
**N. Tapia**.*Signatures in Shape Analysis: an Efficient Approach to Motion Identification*. (2019) In*Geometric Science of Information. GSI 2019. Lecture Notes in Computer Science vol. 11712*. F. Nielsen, F. Barbaresco eds. doi: 10.1007/978-3-030-26980-7_3 **N. Tapia**, L. Zambotti.*The geometry of the space of branched Rough Paths*. Proc. London Math. Soc.**121**no. 2 (2020) pp. 220–251. doi: 10.1112/plms.12311**C. Bayer**,**P. K. Friz**,**N. Tapia**.*Robustness of Residual Networks via Rough Path techniques*. (2020) In preparation.

**Selected Pictures
**

The weights are taken by an actual trained network from He et al.

One can observe that since the weights turn out to have high 1-variation, our analysis yield sharper control for higher values of p.

The picture shows that even in this case choosing p>1 can improve a priori bounds.

One observes that due to the high variability of the trained weights, a priori knowledge of the deviation is better if we are allowed to choose p>1.

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