Related papers: Topology Distance: A Topology-Based Approach For E…

Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…

Generative Adversarial Networks (GANs) have made great progress in synthesizing realistic images in recent years. However, they are often trained on image datasets with either too few samples or too many classes belonging to different data…

We propose a method for learning topology-preserving data representations (dimensionality reduction). The method aims to provide topological similarity between the data manifold and its latent representation via enforcing the similarity in…

We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…

In this article, we introduce a new mode for training Generative Adversarial Networks (GANs). Rather than minimizing the distance of evidence distribution $\tilde{p}(x)$ and the generative distribution $q(x)$, we minimize the distance of…

Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…

We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…

Generative adversarial networks (GANs) form a generative modeling approach known for producing appealing samples, but they are notably difficult to train. One common way to tackle this issue has been to propose new formulations of the GAN…

Evaluating the performance of generative models in image synthesis is a challenging task. Although the Fr\'echet Inception Distance is a widely accepted evaluation metric, it integrates different aspects (e.g., fidelity and diversity) of…

This paper is first-line research expanding GANs into graph topology analysis. By leveraging the hierarchical connectivity structure of a graph, we have demonstrated that generative adversarial networks (GANs) can successfully capture…

Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or matrix distances may fail to capture underlying subtle…

Generative adversarial networks (GANs) are a novel approach to generative modelling, a task whose goal it is to learn a distribution of real data points. They have often proved difficult to train: GANs are unlike many techniques in machine…

We present a novel set of rigorous and computationally efficient topology-based complexity notions that exhibit a strong correlation with the generalization gap in modern deep neural networks (DNNs). DNNs show remarkable generalization…

Geometrical and appearance quality requirements set the limits of the current industrial performance in injection molding. To guarantee the product's quality, it is necessary to adjust the process settings in a closed loop. Those…

Generative networks are fundamentally different in their aim and methods compared to CNNs for classification, segmentation, or object detection. They have initially not been meant to be an image analysis tool, but to produce naturally…

Despite the recency of their conception, Generative Adversarial Networks (GANs) constitute an extensively researched machine learning sub-field for the creation of synthetic data through deep generative modeling. GANs have consequently been…

Generative adversarial networks, which can generate metasurfaces based on a training set of high performance device layouts, have the potential to significantly reduce the computational cost of the metasurface design process. However, basic…

Recent advances in generative modeling have led to an increased interest in the study of statistical divergences as means of model comparison. Commonly used evaluation methods, such as the Frechet Inception Distance (FID), correlate well…