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Found 7 papers, 4 papers with code
Stability of Deep Neural Networks via discrete rough paths
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.
Unified Signature Cumulants and Generalized Magnus Expansions
The signature of a path can be described as its full non-commutative exponential.
Probability 60L10, 60L90, 60E10, 60G44, 60G48, 60G51, 60J76
The moving frame method for iterated-integrals: orthogonal invariants
Geometric features, robust to noise, of curves in Euclidean space are of great interest for various applications such as machine learning and image analysis.
Differential Geometry Algebraic Geometry 60L10, 14L24
Generalized iterated-sums signatures
We explore the algebraic properties of a generalized version of the iterated-sums signature, inspired by previous work of F.~Kir\'aly and H.~Oberhauser.
Tropical time series, iterated-sums signatures and quasisymmetric functions
Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings.
Signatures in Shape Analysis: an Efficient Approach to Motion Identification
Signatures provide a succinct description of certain features of paths in a reparametrization invariant way.
Time-warping invariants of multidimensional time series
We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric functions in the mathematics literature.
