The thesis was supervised by Prof. Dr. Nihat Ay, head of the institute. Prof. Giovanni Pistone of the de Castro Statistics Initiative at the Collegio Carlo Alberto in Turin joined the defence via Zoom as second examiner; his contributions to probability and mathematical statistics include work in information geometry and algebraic statistics. Chair Sabine Le Borne. magna cum laude. The PhD project was conducted within the DFG Priority Programme “The Active Self” (SPP 2134). In addition to corresponding financial support from the DFG, Jesse also received support from VISOR, the VISTA School of Graduate Research.
Jesse joined the institute in 2020 after Mathematics at the University of Cambridge and Liberal Arts and Sciences at University College Utrecht. His research lies in information geometry and Bayesian networks, with applications in machine learning and the cognitive sciences. Early papers addressed the natural gradient in overparametrised systems: when the natural parameter gradient, obtained by multiplying the ordinary gradient by the inverse Gram matrix of the metric, pushes forward to the natural gradient on the model, and which invariance properties it has. In a sole-authored paper he studied the Bures–Wasserstein geometry of positive-definite Hermitian matrices and their trace-one subset. For Bayesian networks, he derived global conditions, in terms of d-separation, and local conditions under which a recognition network, as used in variational autoencoders and Helmholtz machines, can model the true posterior distribution of a generative model exactly. His more recent work concerns the Fisher–Rao gradient of the evidence lower bound (ELBO) and a concise mathematical description of active inference in discrete time, which he presented on the Active Inference Institute podcast in 2025.
Jesse and Nihat Ay have published five joint papers: “Parametrisation independence of the natural gradient in overparametrised systems” (GSI 2021), “Invariance properties of the natural gradient in overparametrised systems” (Information Geometry, 2023, with Johannes Müller), “Inversion of Bayesian networks” (International Journal of Approximate Reasoning, 2024, with Peter van Hintum), “A concise mathematical description of active inference in discrete time” (Journal of Mathematical Psychology, 2025, with Carlotta Langer) and “On the natural gradient of the evidence lower bound” (Journal of Machine Learning Research, 2025, with Adwait Datar). In the summer term 2026, Jesse also taught exercise classes for Machine Learning I and co-organised the course Causal Machine Learning. Jesse will remain at the institute until beginning of next year and will be finalizing some research projects.
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