Zobrazeno 1 - 10
of 1 729
pro vyhledávání: '"Schaub Michael"'
We consider the problem of classifying trajectories on a discrete or discretised 2-dimensional manifold modelled by a simplicial complex. Previous works have proposed to project the trajectories into the harmonic eigenspace of the Hodge Laplacian, an
Externí odkaz:
http://arxiv.org/abs/2412.03145
Autor:
Telyatnikov, Lev, Bernardez, Guillermo, Montagna, Marco, Vasylenko, Pavlo, Zamzmi, Ghada, Hajij, Mustafa, Schaub, Michael T, Miolane, Nina, Scardapane, Simone, Papamarkou, Theodore
This work introduces TopoBenchmarkX, a modular open-source library designed to standardize benchmarking and accelerate research in Topological Deep Learning (TDL). TopoBenchmarkX maps the TDL pipeline into a sequence of independent and modular compon
Externí odkaz:
http://arxiv.org/abs/2406.06642
Residual connections and normalization layers have become standard design choices for graph neural networks (GNNs), and were proposed as solutions to the mitigate the oversmoothing problem in GNNs. However, how exactly these methods help alleviate th
Externí odkaz:
http://arxiv.org/abs/2406.02997
Autor:
Grande, Vincent P., Schaub, Michael T.
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description of the gl
Externí odkaz:
http://arxiv.org/abs/2406.02300
Graph neural networks (GNNs) have emerged as powerful tools for processing relational data in applications. However, GNNs suffer from the problem of oversmoothing, the property that the features of all nodes exponentially converge to the same vector
Externí odkaz:
http://arxiv.org/abs/2406.02269
Autor:
Hoppe, Josef, Schaub, Michael T.
We define a model for random (abstract) cell complexes (CCs), similiar to the well-known Erd\H{o}s-R\'enyi model for graphs and its extensions for simplicial complexes. To build a random cell complex, we first draw from an Erd\H{o}s-R\'enyi graph, an
Externí odkaz:
http://arxiv.org/abs/2406.01999
Autor:
Frantzen, Florian, Schaub, Michael T.
Triggered by limitations of graph-based deep learning methods in terms of computational expressivity and model flexibility, recent years have seen a surge of interest in computational models that operate on higher-order topological domains such as hy
Externí odkaz:
http://arxiv.org/abs/2404.03434
Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis tools are b
Externí odkaz:
http://arxiv.org/abs/2403.15023
Autor:
Papamarkou, Theodore, Birdal, Tolga, Bronstein, Michael, Carlsson, Gunnar, Curry, Justin, Gao, Yue, Hajij, Mustafa, Kwitt, Roland, Liò, Pietro, Di Lorenzo, Paolo, Maroulas, Vasileios, Miolane, Nina, Nasrin, Farzana, Ramamurthy, Karthikeyan Natesan, Rieck, Bastian, Scardapane, Simone, Schaub, Michael T., Veličković, Petar, Wang, Bei, Wang, Yusu, Wei, Guo-Wei, Zamzmi, Ghada
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation
Externí odkaz:
http://arxiv.org/abs/2402.08871
Autor:
Hajij, Mustafa, Papillon, Mathilde, Frantzen, Florian, Agerberg, Jens, AlJabea, Ibrahem, Ballester, Rubén, Battiloro, Claudio, Bernárdez, Guillermo, Birdal, Tolga, Brent, Aiden, Chin, Peter, Escalera, Sergio, Fiorellino, Simone, Gardaa, Odin Hoff, Gopalakrishnan, Gurusankar, Govil, Devendra, Hoppe, Josef, Karri, Maneel Reddy, Khouja, Jude, Lecha, Manuel, Livesay, Neal, Meißner, Jan, Mukherjee, Soham, Nikitin, Alexander, Papamarkou, Theodore, Prílepok, Jaro, Ramamurthy, Karthikeyan Natesan, Rosen, Paul, Guzmán-Sáenz, Aldo, Salatiello, Alessandro, Samaga, Shreyas N., Scardapane, Simone, Schaub, Michael T., Scofano, Luca, Spinelli, Indro, Telyatnikov, Lev, Truong, Quang, Walters, Robin, Yang, Maosheng, Zaghen, Olga, Zamzmi, Ghada, Zia, Ali, Miolane, Nina
We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. To
Externí odkaz:
http://arxiv.org/abs/2402.02441