Related papers: Topological structure of complex predictions

With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural…

For safety and robustness of AI systems, we introduce topological parallax as a theoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure.…

How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…

Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…

Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…

Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…

Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…

Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…

Graphs have a superior ability to represent relational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison,…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

In recent years, the rise of deep learning and automation requirements in the software industry has elevated Intelligent Software Engineering to new heights. The number of approaches and applications in code understanding is growing, with…

The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…

In this paper we presented a novel constructive approach for training deep neural networks using geometric approaches. We show that a topological covering can be used to define a class of distributed linear matrix inequalities, which in…

Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological…

Topological data analysis is an emerging field that applies the study of topological invariants to data. Perhaps the simplest of these invariants is the number of connected components or clusters. In this work, we explore a topological…

Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks.…

Complex nonlinear models such as deep neural network (DNNs) have become an important tool for image classification, speech recognition, natural language processing, and many other fields of application. These models however lack…

Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…