References

Améndola, C. and Schmitz, L. (2025). Learning Barycenters from Signature Matrices, preprint arXiv:2509.07815.

Améndola, C.; Friz, P. and Sturmfels, B. (2019). Varieties of signature tensors. Forum of Mathematics, Sigma 7.

Améndola, C.; Lotter, F. and Schmitz, L. (2026). Signature Varieties of Splines, preprint arXiv:2602.13011, arXiv:2602.13011 [math.AG].

Améndola, C.; Riffo, G. and Schmitz, L. (2026+). Signature varieties of membranes, in preparation.

Chen, K.-T. (1957). Integration of paths, geometric invariants and a generalized Baker–Hausdorff formula. Annals of Mathematics 65, 163–178.

Chen, K.-T. (1977). Iterated path integrals. Bulletin of the American Mathematical Society 83, 831–879.

Chevyrev, I. and Kormilitzin, A. (2026). A Primer on the Signature Method in Machine Learning. In: Signature Methods in Finance: An Introduction with Computational Applications (Springer Nature Switzerland, Cham); pp. 3–64.

Chevyrev, I.; Nanda, V. and Oberhauser, H. (2018). Persistence paths and signature features in topological data analysis. IEEE transactions on pattern analysis and machine intelligence 42, 192–202.

Clausel, M.; Diehl, J.; Mignot, R.; Schmitz, L.; Sugiura, N. and Usevich, K. (2024). The Barycenter in Free Nilpotent Lie Groups and Its Application to Iterated-Integrals Signatures. SIAM Journal on Applied Algebra and Geometry 8, 519–552.

Cuchiero, C.; Gazzani, G.; Möller, J. and Svaluto-Ferro, S. (2026). Signature-Based Models in Finance. In: Signature Methods in Finance: An Introduction with Computational Applications (Springer Nature Switzerland, Cham); pp. 227–264.

Friz, P. K. and Victoir, N. B. (2010). Multidimensional stochastic processes as rough paths: theory and applications. Vol. 120 (Cambridge University Press).

Friz, P. K. and Hairer, M. (2020). A Course on Rough Paths (Springer).

Lotter, F. and Schmitz, L. (2026). Signature matrices of membranes. Algebraic Statistics 17, 75–99.

Lyons, T. J.; Caruana, M. and Lévy, T. (2007). Differential equations driven by rough paths: Ecole d'Eté de Probabilités de Saint-Flour XXXIV-2004 (Springer).

Lyons, T. J. (1998). Differential equations driven by rough signals. Revista Matemática Iberoamericana 14, 215–310.

Lyons, T. J. and Qian, Z. (2002). System Control and Rough Paths (Oxford University Press).

Pfeffer, M.; Seigal, A. and Sturmfels, B. (2019). Learning paths from signature tensors. SIAM Journal on Matrix Analysis and Applications 40, 394–416.

Schmitz, L. (2025). An Efficient Algorithm for Tensor Learning, preprint arXiv:2512.14218, arXiv:2512.14218 [math.RA].