Semi-supervised learning (SSL) is the problem of finding missing labels from a partially labelled data set. The heuristic one uses is that “similar feature vectors should have similar labels”. The notion of similarity between feature vectors explored in this talk comes from a graph-based geometry where an edge is placed between feature vectors that are closer than some connectivity radius. A...
This talk presents results on scaling laws in hypergraph and multi-operator learning. Scaling considerations simultaneously guide both the theoretical foundations and the practical design of modern learning systems. The first part shows how a large-data asymptotic analysis identifies connectivity-scaling regimes in which semi-supervised learning on hypergraphs is effective and stable. This...
The fractional graph Laplacian, defined as a fractional power of the standard graph Laplacian, is one of the most popular tools for modeling non‑local diffusion on graphs. However, it is known to induce dynamics that, in some cases, are incompatible with the topology of the original network. To address this limitation, a regularized fractional Laplacian obtained through a combination of the...
Subdiffusion on networks can occur where overcrowding is present. It is studied through time-fractional diffusion equations, and admits an explicit solution through the Mittag-Leffler function. We give a representation of subdiffusion as a superposition of classical diffusion processes with subordination to a different timescale. Memory arises in subdiffusion, while the classical diffusion...
