6 papers · 1 filter
Riemannian Metric Matching for Scalable Geometric Modeling of Distributions
Jacob Bamberger, Adam Gosztolai, Pierre Vandergheynst +2
High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly wit…
Diffusion Processes on Implicit Manifolds
Victor Kawasaki-Borruat, Clara Grotehans, Pierre Vandergheynst +1
High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples an…
Geometry-Induced Diffusion on Graphs: A Learnable Weighted Laplacian for Spectral GNNs
Mia Zosso, Ali Hariri, Victor Kawasaki-Borruat +2
Long-range graph tasks are challenging for Graph Neural Networks (GNNs): global mechanisms such as attention or rewiring schemes can be computationally expensive, while deep local…
Carré du champ flow matching: better quality-generalisation tradeoff in generative models
Jacob Bamberger, Iolo Jones, Dennis Duncan +3
Deep generative models often face a fundamental tradeoff: high sample quality can come at the cost of memorisation, where the model reproduces training data rather than generalisin…
Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks
Ali Hariri, Álvaro Arroyo, Alessio Gravina +6
ChebNet, one of the earliest spectral GNNs, has largely been overshadowed by Message Passing Neural Networks (MPNNs), which gained popularity for their simplicity and effectiveness…
On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning
Álvaro Arroyo, Alessio Gravina, Benjamin Gutteridge +5
Graph Neural Networks (GNNs) are models that leverage the graph structure to transmit information between nodes, typically through the message-passing operation. While widely succe…