相关论文: Persistent reachability homology in machine learni…

Artificial intelligence-assisted drug design is revolutionizing the pharmaceutical industry. Effective molecular features are crucial for accurate machine learning predictions, and advanced mathematics plays a key role in designing these…

Self-supervised learning has gradually emerged as a powerful technique for graph representation learning. However, transferable, generalizable, and robust representation learning on graph data still remains a challenge for pre-training…

We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…

The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…

To improve human-preference alignment training, current research has developed numerous preference datasets consisting of preference pairs labeled as "preferred" or "dispreferred". These preference pairs are typically used to encode human…

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…

We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree $i\geq 2$. To extend them to higher degrees, we introduce the notion of…

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…

The training of neural networks is usually monitored with a validation (holdout) set to estimate the generalization of the model. This is done instead of measuring intrinsic properties of the model to determine whether it is learning…

We consider the parametric reachability problem (PRP) for families of networks described by vertex-replacement (VR) graph grammars, where network nodes run replicas of finite-state processes that communicate via binary handshaking. We show…

The social contagion literature makes a distinction between simple (independent cascade or bond percolation processes that pass infections through edges) and complex contagions (bootstrap percolation or threshold processes that require…

Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…

Graphical forecasting models learn the structure of time series data via projecting onto a graph, with recent techniques capturing spatial-temporal associations between variables via edge weights. Hierarchical variants offer a distinct…

Representational limits of message-passing graph neural networks (MP-GNNs), e.g., in terms of the Weisfeiler-Leman (WL) test for isomorphism, are well understood. Augmenting these graph models with topological features via persistent…

Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…

Hypergraphs serve as an effective model for depicting complex connections in various real-world scenarios, from social to biological networks. The development of Hypergraph Neural Networks (HGNNs) has emerged as a valuable method to manage…

Photosensitivity refers to a neurophysiological condition in which the brain generates epileptic discharges known as Photoparoxysmal Responses (PPR) in response to light flashes.In severe cases, these PPR can lead to epileptic seizures. The…

Graph Neural Networks (GNNs) have become the de-facto standard tool for modeling relational data. However, while many real-world graphs are directed, the majority of today's GNN models discard this information altogether by simply making…

Heterogeneous graph neural networks have seen rapid progress in web applications such as social networks, knowledge graphs, and recommendation systems, driven by the inherent heterogeneity of web data. However, existing methods typically…

Parkinson's disease (PD) is a debilitating neurodegenerative disease that has severe impacts on an individual's quality of life. Compared with structural and functional MRI-based biomarkers for the disease, electroencephalography (EEG) can…