Giuseppe Alessio D’Inverno
Giuseppe Alessio D’Inverno is a Postdoctoral Researcher at the Laboratoires Mathématiques d’Orsay, Université Paris-Saclay, since February 2026. He previously served as a Postdoctoral Researcher in the MathLab Group at SISSA in Trieste from 2024 to early 2026. He earned his PhD in Information Engineering & Science from the University of Siena in 2024, focusing his thesis on the theoretical properties of Graph Neural Networks.
His primary research interests encompass the mathematical foundations of deep learning, graph representation learning, numerical modeling for PDEs, and physics-informed neural networks. Throughout his career, he has conducted research stays at international institutions such as Concordia University, the Montréal Institute for Learning Algorithms (MILA), and EPFL.
In addition to his research, he has extensive teaching experience, serving as a lecturer for doctoral courses and as a teaching assistant for undergraduate subjects. He has also co-supervised several Master’s and Bachelor’s theses in applied mathematics and data science.
Project
Information Propagation through neural networks can be interpreted as the separation of different input signal trajectories as they propagate through the network layers.
Two regimes typically arise in Information Propagation, depending on the weight and bias initialization: in the chaotic regime, even small input differences are amplified, leading to instability and poor noise robustness, while in the ordered regime, all inputs are mapped to similar outputs, suppressing Information Propagation.
[1] revealed that in MLPs and CNNs the boundary between chaotic and ordered regime is fractal, showing that the choice of the weight and bias initialization is crucial. The project will extend this analysis to GNNs, answering to the following research questions:
- is there a link between Information Propagation and message passing/network propagation?
- how is Information Propagation characterized w.r.t. different graph distance metrics?
A key aspect of this study is examining how the notion of different metrics for distance between graphs affects Information Propagation, leveraging standard results in graph theory associated to such metrics. The observed insights may be used to create links with the existing literature in randomly initialized MP-GNNs and closely related architectures (e.g. Graph Echo State Networks). Additional comparisons between MP-GNNs and energy-based GNNs may be conducted, to investigate whether IP behaves differently.
References
[1] D’Inverno et al. (2025). Revisiting Deep Information Propagation: Fractal Frontier and Finite-size Effects. arXiv preprint arXiv:2508.03222.
