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Transformer models have consistently achieved remarkable results in various domains such as natural language processing and computer vision. However, despite ongoing research efforts to better understand these models, the field still lacks…

A recent advance in networking is the deployment of path-aware multipath network architectures, where network endpoints are given multiple network paths to send their data on. In this work, we tackle the challenge of selecting paths for…

Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation…

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…

Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…

Understanding network health is essential to improve Internet reliability. For instance, detecting disruptions in peer and provider networks facilitates the identification of connectivity problems. Currently this task is time consuming for…

Modern social networks frequently encompass multiple distinct types of connectivity information; for instance, explicitly acknowledged friend relationships might complement behavioral measures that link users according to their actions or…

In recent years extensions of manifold Ricci curvature to discrete combinatorial objects such as graphs and hypergraphs (popularly called as "network shapes"), have found a plethora of applications in a wide spectrum of research areas…

Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…

We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…

Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…

Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromov's "thin triangle condition", which is tightly related to core congestion and route reliability. In this work we analyze the…

Computation of persistent homology of simplicial representations such as the Rips and the C\v{e}ch complexes do not efficiently scale to large point clouds. It is, therefore, meaningful to devise approximate representations and evaluate the…

Motivated by the methods and results of manifold sampling based on Ricci curvature, we propose a similar approach for networks. To this end we make appeal to three types of discrete curvature, namely the graph Forman-, full Forman- and…

Anomaly detection is critical for finding suspicious behavior in innumerable systems. We need to detect anomalies in real-time, i.e. determine if an incoming entity is anomalous or not, as soon as we receive it, to minimize the effects of…

Many data analysis problems rely on dynamic networks, such as social or communication network analyses. Providing a scalable overview of long sequences of such dynamic networks remains challenging due to the underlying large-scale data…

In temporal ( event-based ) networks, time is a continuous axis, with real-valued time coordinates for each node and edge. Computing a layout for such graphs means embedding the node trajectories and edge surfaces over time in a 2D+t space,…

Many complex networks in the real world have community structures -- groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.…

We present a method for generating high-quality watertight manifold meshes from multi-view input images. Existing volumetric rendering methods are robust in optimization but tend to generate noisy meshes with poor topology. Differentiable…