21 citations · 96 across the 15 of their papers we have counts for
3 papers · 1 filter
Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability
Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia +1
We study a particular group law on formal power series in non-commuting variables induced by their interpretation as linear forms on a suitable graded connected word Hopf algebra.…
The geometry of controlled rough paths
Mazyar Ghani Varzaneh, Sebastian Riedel, Alexander Schmeding +1
We prove that the spaces of controlled (branched) rough paths of arbitrary order form a continuous field of Banach spaces. This structure has many similarities to an (infinite-dime…
Stability of Deep Neural Networks via discrete rough paths
Christian Bayer, Peter K. Friz, Nikolas Tapia
Using rough path techniques, we provide a priori estimates for the output of Deep Residual Neural Networks in terms of both the input data and the (trained) network weights. As tra…