# About me

Praise the sun! I am currently a Research Associate at the University of Cambridge, working in Pietro Lio’s group on Geometric Deep Learning and Graph Neural Networks. Previously, I was a postdoctoral ML Researcher at Twitter Cortex working with Michael Bronstein. I finished my PhD in Mathematics at UCL with a thesis on analysis of singularity formation of rotationally symmetric Ricci Flows. I am now interested in investigating Deep Learning through the lens of Differential Geometry and Physics, with emphasis on graph structured data.

My current lines of research include: (i) Understanding how information flows in Graph Neural Networks and the associated phenomenon of over-squashing. I characterize the role played by the graph structure in the propagation of messages across “distant” nodes via local quantities such as curvature and global quantities such as access and commute time - our first step in this direction got an ICLR honorable mention. A more recent work generalizes our analysis and proves that over-squashing occurs among nodes at high effective resistance. (ii) Investigating how Graph Neural Networks “use” the underlying graph topology and to what extent we need to rely on the same input graph to exchange messages across layers. This direction falls into the field of graph-rewiring, which I believe to be a promising area to analyse limitations of GNNs both in terms of expressivity and over-squashing, and an approach that has already been taken by more expressive GNNs – albeit a little indirectly. Understanding the role played by the input topology to propagate information and whether we can in fact decouple the computational graph from the latter is also key to fully assess the potential capabilities of graph transformers, and more generally to develop new frameworks that are both expressive and more resilent to issues arising from the underlying graph topology. (iii) Studying Graph Neural Networks as multi-particles dynamics - our work explains how the common “channel-mixing” module can be interpreted as a pairwise potential and how by interacting with the graph Laplacian spectrum it learns to generate attractive or repulsive forces via its positive and neagtive eigenvalues respectively.

**Contact**: fd405 (at) cam (dot) ac (dot) uk

## News

#### 2023

- June 2023: I’ll be giving a talk in Berlin at the CECAM/Psi-k conference
- April: Our new framework for message-passing with delay got accepted at ICML23
- April: Our new theoretical work on over-squashing got accepted at ICML23
- March: reviewer for ICML23
- February: new paper out!

#### 2022

- December: Invited panelist at LoG tutorial on Graph-rewiring and Fairness
- December: Keynote speaker at Neurips 2022 Workshop: New Frontiers on Graph Learning
- August: LoGaG reading group, invited talk
- August: MML seminar at UCLA, invited talk
- August: Stanford GNN Reading Group, invited talk
- August: I gave a long talk at the Hammers and Nails 2022 Workshop in Tel Aviv
- July: I have taught at the First Italian School in Geometric Deep Learning
- July: I have been a mentor at the LOGML22 - our project is about graph-rewiring using geometric exploration policies
- June: I have reviewed for NeurIPS 2022
- May: I have coauthored a blogpost with Michael Bronstein and Cristian Bodnar on a recent about cellular sheaf theory for tackling heterophily in GNNs
- April: Our work on understanding over-squashing in GNNs through graph curvature has got an Outstanding Paper Honorable Mention at ICLR 2022!
- April: Aleksa Gordić made a great video about our paper on bottlenecks and over-squashing in GNNs. This is highly recommended to anyone interested in understanding our work in quite some detail!
- March: I gave a talk at the Dagsthul seminar Graph Embeddings: Theory meets Practice
- January: I have been invited to write my opinion on future perspetives of GNNs in a blogpost authored by Michael Bronstein and Petar Veličković, featuring many prominent researchers in the field.