Related papers: Persistent reachability homology in machine learni…

Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of…

Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…

Persistent spread measurement is to count the number of distinct elements that persist in each network flow for predefined time periods. It has many practical applications, including detecting long-term stealthy network activities in the…

Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…

Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…

Recently many efforts have been made to incorporate persistence diagrams, one of the major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we…

The human brain can be considered as complex networks, composed of various regions that continuously exchange their information with each other, forming the brain network graph, from which nodes and edges are extracted using resting-state…

Objective: In modern healthcare, accurately predicting diseases is a crucial matter. This study introduces a novel approach using graph neural networks (GNNs) and a Graph Transformer (GT) to predict the incidence of heart failure (HF) on a…

In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…

The comorbidities of hypertension impose a heavy burden on patients and society. Early identification is necessary to prompt intervention, but it remains a challenging task. This study aims to address this challenge by combining joint graph…

Persistent homology (PH) characterizes the shape of brain networks through the persistence features. Group comparison of persistence features from brain networks can be challenging as they are inherently heterogeneous. A recent scale-space…

Tumor segmentation in whole-slide images of histology slides is an important step towards computer-assisted diagnosis. In this work, we propose a tumor segmentation framework based on the novel concept of persistent homology profiles…

(see paper for full abstract) Cut problems and connectivity problems on digraphs are two well-studied classes of problems from the viewpoint of parameterized complexity. After a series of papers over the last decade, we now have (almost)…

In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…

Robustness in complex systems is of significant engineering and economic importance. However, conventional attack-based a posteriori robustness assessments incur prohibitive computational overhead. Recently, deep learning methods, such as…

Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…

Decoupled dataset distillation (DD) compresses large corpora into a few synthetic images by matching a frozen teacher's statistics. However, current residual-matching pipelines rely on static real patches, creating a fit-complexity gap and…

Pre-trained Language Models (LMs) exhibit strong zero-shot and in-context learning capabilities; however, their behaviors are often difficult to control. By utilizing Reinforcement Learning from Human Feedback (RLHF), it is possible to…

Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the…

In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may…