相关论文: Contraction and Hourglass Persistence for Learning…

In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…

We present a topological framework for analysing neural time series that integrates Transfer Entropy (TE) with directed Persistent Homology (PH) to characterize information flow in spiking neural systems. TE quantifies directional influence…

Persistent homology (PH) studies the topology of data across multiple scales by building nested collections of topological spaces called filtrations, computing homology and returning an algebraic object that can be vizualised as a…

High-accuracy prediction of the physical properties of amorphous materials is challenging in condensed-matter physics. A promising method to achieve this is machine-learning potentials, which is an alternative to computationally demanding…

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological…

Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data. In this work, we demonstrate that PH can be used as a universal framework to identify phases in spin models,…

Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…

Continual learning on graphs tackles the problem of training a graph neural network (GNN) where graph data arrive in a streaming fashion and the model tends to forget knowledge from previous tasks when updating with new data. Traditional…

Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…

Persistent homology is a popular technique in topological data analysis that tracks the lifespans of homological features in a nested sequence of spaces. This data is typically presented in a multi-set called a persistence diagram or a…

Persistent homology, a method from topological data analysis, extracts robust, multi-scale features from data. It produces stable representations of time series by applying varying thresholds to their values (a process known as a…

Convolutional neural networks (CNNs) are a standard tool for computer vision tasks such as image classification. However, typical model architectures may result in the loss of topological information. In specific domains such as…

Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…

In machine-learning-assisted high-throughput defect studies, a defect-aware latent representation of the supercell structure is crucial to the accurate prediction of defect properties. The performance of current graph neural network (GNN)…

Dynamic graphs are prevalent in real-world scenarios, where continuous structural changes induce catastrophic forgetting in graph neural networks (GNNs). While continual learning has been extended to dynamic graphs, existing methods…

Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (box) product of graphs and the effect on their outputs on the…

We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…

Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations. We propose a novel framework that integrates persistent homology features with stability…

We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is acyclic, as well as along any subgraph of this directed graph. This method…

Graph Neural Networks (GNNs) have been highly successful for the node classification task. GNNs typically assume graphs are homophilic, i.e. neighboring nodes are likely to belong to the same class. However, a number of real-world graphs…