Veronica graduated with a BSc in Mathematics from the University of Genoa in 2022, where she also completed her MSc in Applied Mathematics. In her Master’s thesis, she examined algorithms for the reconstruction of images from limited-angle computed tomography data. She has always been drawn to mathematical analysis, and during her Master’s studies, she developed a strong interest in its applications, particularly in inverse problems and mathematical imaging.

In her free time, she enjoys reading, spending time outdoors, hiking, and her favourite sport is skiing.

Project title:
Measure reconstruction problems in machine learning and inverse problems

Supervisor(s):
Yury Korolev, Chris Budd

Project description:
A wide class of tasks in machine learning and inverse problems can be reformulated as optimization problems over spaces of probability measures. This formulation is particularly valuable because it often reveals structural properties, such as convexity, that are not apparent in classical formulations, thereby enabling deeper analysis. Optimal transport theory is especially important in this context: it provides a way of measuring distances between probability distributions and, in doing so, equips the space of probability measures with a natural geometry and variational structure. This makes it possible to work directly at the level of probability measures, offering theoretical insights and motivating new algorithms.

Applications include image reconstruction from indirect measurements in inverse problems and the study of training dynamics in neural networks. Further applications arise in deep learning. For instance, Transformers, the architecture underlying generative AI models such as ChatGPT, can be viewed as mappings on the space of probability measures. This viewpoint makes it possible to analyse their behaviour using tools from optimal transport and offers new ways to understand how such models operate.

Building on these ideas, my project investigates novel applications of measure theory and optimal transport across diverse settings in machine learning and inverse problems.