Mitigating over-smoothing and over-squashing using augmentations of Forman-Ricci curvature

L Fesser, M Weber - Learning on Graphs Conference, 2024 - proceedings.mlr.press
Abstract While Graph Neural Networks (GNNs) have been successfully leveraged for
learning on graph-structured data across domains, several potential pitfalls have been …

Augmentations of Forman's Ricci curvature and their applications in community detection

L Fesser, SS de Haro Ivánez, K Devriendt… - Journal of Physics …, 2024 - iopscience.iop.org
The notion of curvature on graphs has recently gained traction in the networks community,
with the Ollivier–Ricci curvature (ORC) in particular being used for several tasks in network …

Curvature-based clustering on graphs

Y Tian, Z Lubberts, M Weber - arXiv preprint arXiv:2307.10155, 2023 - arxiv.org
Unsupervised node clustering (or community detection) is a classical graph learning task. In
this paper, we study algorithms, which exploit the geometry of the graph to identify densely …

Robust large-margin learning in hyperbolic space

M Weber, M Zaheer, AS Rawat… - Advances in Neural …, 2020 - proceedings.neurips.cc
Recently, there has been a surge of interest in representation learning in hyperbolic spaces,
driven by their ability to represent hierarchical data with significantly fewer dimensions than …

Capacity and bias of learned geometric embeddings for directed graphs

M Boratko, D Zhang, N Monath… - Advances in …, 2021 - proceedings.neurips.cc
A wide variety of machine learning tasks such as knowledge base completion, ontology
alignment, and multi-label classification can benefit from incorporating into learning …

Projection-free nonconvex stochastic optimization on Riemannian manifolds

M Weber, S Sra - IMA Journal of Numerical Analysis, 2022 - academic.oup.com
We study stochastic projection-free methods for constrained optimization of smooth functions
on Riemannian manifolds, ie, with additional constraints beyond the parameter domain …

Box embeddings: An open-source library for representation learning using geometric structures

T Chheda, P Goyal, T Tran, D Patel, M Boratko… - arXiv preprint arXiv …, 2021 - arxiv.org
A major factor contributing to the success of modern representation learning is the ease of
performing various vector operations. Recently, objects with geometric structures (eg …

Fmgnn: Fused manifold graph neural network

C Deng, F Xu, J Ding, L Fu, W Zhang… - arXiv preprint arXiv …, 2023 - arxiv.org
Graph representation learning has been widely studied and demonstrated effectiveness in
various graph tasks. Most existing works embed graph data in the Euclidean space, while …

Effective Structural Encodings via Local Curvature Profiles

L Fesser, M Weber - arXiv preprint arXiv:2311.14864, 2023 - arxiv.org
Structural and Positional Encodings can significantly improve the performance of Graph
Neural Networks in downstream tasks. Recent literature has begun to systematically …

Exploiting Data Geometry in Machine Learning

M Weber - Proceedings of the AAAI Conference on Artificial …, 2024 - ojs.aaai.org
A key challenge in Machine Learning (ML) is the identification of geometric structure in high-
dimensional data. Most algorithms assume that data lives in a high-dimensional vector …