Mitigating over-smoothing and over-squashing using augmentations of Forman-Ricci curvature
Abstract While Graph Neural Networks (GNNs) have been successfully leveraged for
learning on graph-structured data across domains, several potential pitfalls have been …
learning on graph-structured data across domains, several potential pitfalls have been …
Augmentations of Forman's Ricci curvature and their applications in community detection
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 …
with the Ollivier–Ricci curvature (ORC) in particular being used for several tasks in network …
Curvature-based clustering on graphs
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 …
this paper, we study algorithms, which exploit the geometry of the graph to identify densely …
Robust large-margin learning in hyperbolic space
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 …
driven by their ability to represent hierarchical data with significantly fewer dimensions than …
Capacity and bias of learned geometric embeddings for directed graphs
A wide variety of machine learning tasks such as knowledge base completion, ontology
alignment, and multi-label classification can benefit from incorporating into learning …
alignment, and multi-label classification can benefit from incorporating into learning …
Projection-free nonconvex stochastic optimization on Riemannian manifolds
We study stochastic projection-free methods for constrained optimization of smooth functions
on Riemannian manifolds, ie, with additional constraints beyond the parameter domain …
on Riemannian manifolds, ie, with additional constraints beyond the parameter domain …
Box embeddings: An open-source library for representation learning using geometric structures
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 …
performing various vector operations. Recently, objects with geometric structures (eg …
Fmgnn: Fused manifold graph neural network
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 …
various graph tasks. Most existing works embed graph data in the Euclidean space, while …
Effective Structural Encodings via Local Curvature Profiles
Structural and Positional Encodings can significantly improve the performance of Graph
Neural Networks in downstream tasks. Recent literature has begun to systematically …
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 …
dimensional data. Most algorithms assume that data lives in a high-dimensional vector …