Related papers: Topological, or Non-topological? A Deep Learning B…
In artificial-intelligence-aided signal processing, existing deep learning models often exhibit a black-box structure, and their validity and comprehensibility remain elusive. The integration of topological methods, despite its relatively…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
Network tomography is a crucial problem in network monitoring, where the observable path performance metric values are used to infer the unobserved ones, making it essential for tasks such as route selection, fault diagnosis, and traffic…
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…
In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…
Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale…
Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…
The theory of symmetry indicators has enabled database searches for topological materials in normal conducting phases, which has led to several encyclopedic topological material databases. To date, such a database for topological…
One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
The continuous effort towards topological quantum devices calls for an efficient and non-invasive method to assess the conformity of components in different topological phases. Here, we show that machine learning paves the way towards…
Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of…
The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn…
Various topological techniques and tools have been applied to neural networks in terms of network complexity, explainability, and performance. One fundamental assumption of this line of research is the existence of a global (Euclidean)…
The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However,…
This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…
This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small…