update

index.md

@@ -18,6 +18,7 @@ We are always looking for excellent PhD students and PostDocs.  If you are inter
 
 
 ### News and Events
+***April 5, 2024*** -- New [paper](https://arxiv.org/abs/2404.03434) accepted at ICLR and available on arxiv as well.       
 ***March 11, 2024*** --  I have given an invited talk at this years Young European Probabilists meeting (YEP 2024) in Eindhoven.      
 ***February 1, 2024*** --  I have joined the editorial board of Science Advances.      
 ***January, 22, 2024*** -- I will be giving a [virtual talk](https://www.c3s-frankfurt.de/what-we-do#whats-happening) at the Center for Critical Computational Studies at Frankfurt University.       

publications.bib

@@ -917,9 +917,11 @@ @InProceedings{Scholkemper2023
   booktitle = {Advances in Neural Information Processing Systems (NeurIPS 2023)},
   title     = {{An Optimization-based Approach To Node Role Discovery in Networks: Approximating Equitable Partitions}},
   year      = {2023},
-  month     = oct,
-  note      = {accepted for publication},
+  month     = dec,
+  pages     = {71358--71374},
+  volume    = {36},
   abstract  = {Similar to community detection, partitioning the nodes of a network according to their structural roles aims to identify fundamental building blocks of a network. The found partitions can be used, e.g., to simplify descriptions of the network connectivity, to derive reduced order models for dynamical processes unfolding on processes, or as ingredients for various graph mining tasks. In this work, we offer a fresh look on the problem of role extraction and its differences to community detection and present a definition of node roles related to graph-isomorphism tests, the Weisfeiler-Leman algorithm and equitable partitions. We study two associated optimization problems (cost functions) grounded in ideas from graph isomorphism testing, and present theoretical guarantees associated to the solutions of these problems. Finally, we validate our approach via a novel "role-infused partition benchmark", a network model from which we can sample networks in which nodes are endowed with different roles in a stochastic way.},
+  eprint    = {https://proceedings.neurips.cc/paper_files/paper/2023/file/e1c73e9595126794186536cfbbed012f-Paper-Conference.pdf},
   url       = {https://arxiv.org/abs/2305.19087},
 }
 
@@ -938,7 +940,7 @@ @InProceedings{Hoppe2023
   booktitle = {Learning on Graphs 2023},
   title     = {Representing Edge Flows on Graphs via Sparse Cell Complexes},
   year      = {2023},
-  month     = sep,
+  month     = nov,
   abstract  = {Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such representations is to lift the graph structure to a simplicial complex: The eigenvectors of the associated Hodge-Laplacian, respectively the incidence matrices of the corresponding simplicial complex then induce a Hodge decomposition, which can be used to represent the observed data in terms of gradient, curl, and harmonic flows. In this paper, we generalize this approach to cellular complexes and introduce the cell inference optimization problem, i.e., the problem of augmenting the observed graph by a set of cells, such that the eigenvectors of the associated Hodge Laplacian provide a sparse, interpretable representation of the observed edge flows on the graph. We show that this problem is NP-hard and introduce an efficient approximation algorithm for its solution. Experiments on real-world and synthetic data demonstrate that our algorithm outperforms current state-of-the-art methods while being computationally efficient.},
   comment   = {Best paper Award},
   url       = {https://arxiv.org/abs/2309.01632},
@@ -961,7 +963,7 @@ @InProceedings{grande2023non
   booktitle = {Learning on Graphs 2023},
   title     = {Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PH},
   year      = {2023},
-  month     = oct,
+  month     = nov,
   abstract  = {Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend (implicitly) on a chosen metric, which is typically agnostically chosen as the standard Euclidean metric on R^n. Recent work has tried to uncover the 'true' metric on the point cloud using distance-to-measure functions, in order to obtain more meaningful persistent homology results. Here we propose an alternative look at this problem: we posit that information on the point cloud is lost when restricting persistent homology to a single (correct) distance function. Instead, we show how by varying the distance function on the underlying space and analysing the corresponding shifts in the persistence diagrams, we can extract additional topological and geometrical information. Finally, we numerically show that non-isotropic persistent homology can extract information on orientation, orientational variance, and scaling of randomly generated point clouds with good accuracy and conduct some experiments on real-world data.},
   url       = {https://arxiv.org/abs/2310.16437},
 }
@@ -979,14 +981,16 @@ @InProceedings{Grande2024
   url          = {https://arxiv.org/abs/2311.14427},
 }
 
-@Misc{Hajij2023a,
-  author       = {Mustafa Hajij and Ghada Zamzmi and Theodore Papamarkou and Aldo Guzmán-Sáenz and Tolga Birdal and Michael T. Schaub},
-  howpublished = {arxiv},
-  month        = dec,
-  title        = {Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs},
-  year         = {2023},
-  abstract     = {Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively represent the complex relations found in high-dimensional data. Such higher-order domains are typically modeled either as hypergraphs, or as simplicial, cubical or other cell complexes. In this context, cell complexes are often seen as a subclass of hypergraphs with additional algebraic structure that can be exploited, e.g., to develop a spectral theory. In this article, we promote an alternative perspective. We argue that hypergraphs and cell complexes emphasize \emph{different} types of relations, which may have different utility depending on the application context. Whereas hypergraphs are effective in modeling set-type, multi-body relations between entities, cell complexes provide an effective means to model hierarchical, interior-to-boundary type relations. We discuss the relative advantages of these two choices and elaborate on the previously introduced concept of a combinatorial complex that enables co-existing set-type and hierarchical relations. Finally, we provide a brief numerical experiment to demonstrate that this modelling flexibility can be advantageous in learning tasks.},
-  url          = {https://arxiv.org/abs/2312.09504},
+@InProceedings{Hajij2023a,
+  author    = {Mustafa Hajij and Ghada Zamzmi and Theodore Papamarkou and Aldo Guzmán-Sáenz and Tolga Birdal and Michael T. Schaub},
+  booktitle = {57th Asilomar Conference on Signals, Systems, and Computers},
+  title     = {Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs},
+  year      = {2023},
+  month     = dec,
+  pages     = {799-803},
+  abstract  = {Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively represent the complex relations found in high-dimensional data. Such higher-order domains are typically modeled either as hypergraphs, or as simplicial, cubical or other cell complexes. In this context, cell complexes are often seen as a subclass of hypergraphs with additional algebraic structure that can be exploited, e.g., to develop a spectral theory. In this article, we promote an alternative perspective. We argue that hypergraphs and cell complexes emphasize \emph{different} types of relations, which may have different utility depending on the application context. Whereas hypergraphs are effective in modeling set-type, multi-body relations between entities, cell complexes provide an effective means to model hierarchical, interior-to-boundary type relations. We discuss the relative advantages of these two choices and elaborate on the previously introduced concept of a combinatorial complex that enables co-existing set-type and hierarchical relations. Finally, we provide a brief numerical experiment to demonstrate that this modelling flexibility can be advantageous in learning tasks.},
+  doi       = {10.1109/IEEECONF59524.2023.10477018},
+  url       = {https://arxiv.org/abs/2312.09504},
 }
 
 @Misc{Stamm2024,
@@ -1017,9 +1021,39 @@ @InProceedings{Loveland2023
   title     = {On Performance Discrepancies Across Local Homophily Levels in Graph Neural Networks},
   year      = {2023},
   month     = nov,
-  note      = {accepted},
   abstract  = {Graph Neural Network (GNN) research has highlighted a relationship between high homophily (i.e., the tendency of nodes of the same class to connect) and strong predictive performance in node classification. However, recent work has found the relationship to be more nuanced, demonstrating that simple GNNs can learn in certain heterophilous settings. To resolve these conflicting findings and align closer to real-world datasets, we go beyond the assumption of a global graph homophily level and study the performance of GNNs when the local homophily level of a node deviates from the global homophily level. Through theoretical and empirical analysis, we systematically demonstrate how shifts in local homophily can introduce performance degradation, leading to performance discrepancies across local homophily levels. We ground the practical implications of this work through granular analysis on five real-world datasets with varying global homophily levels, demonstrating that (a) GNNs can fail to generalize to test nodes that deviate from the global homophily of a graph, and (b) high local homophily does not necessarily confer high performance for a node. We further show that GNNs designed for globally heterophilous graphs can alleviate performance discrepancy by improving performance across local homophily levels, offering a new perspective on how these GNNs achieve stronger global performance.},
   url       = {https://arxiv.org/abs/2306.05557v3},
 }
 
+@InProceedings{Frantzen2024,
+  author       = {Florian Frantzen and Michael T. Schaub},
+  booktitle    = {Interational Conference on Learning Representations},
+  title        = {Learning From Simplicial Data Based on Random Walks and 1D Convolutions},
+  year         = {2024},
+  month        = apr,
+  abstract     = {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 hypergraphs and simplicial complexes. While the increased expressivity of these models can indeed lead to a better classification performance and a more faithful representation of the underlying system, the computational cost of these higher-order models can increase dramatically. To this end, we here explore a simplicial complex neural network learning architecture based on random walks and fast 1D convolutions (SCRaWl), in which we can adjust the increase in computational cost by varying the length and number of random walks considered while accounting for higher-order relationships. Importantly, due to the random walk-based design, the expressivity of the proposed architecture is provably incomparable to that of existing message-passing simplicial neural networks. We empirically evaluate SCRaWl on real-world datasets and show that it outperforms other simplicial neural networks.},
+  creationdate = {2024-04-12T17:31:05},
+  url          = {https://arxiv.org/abs/2404.03434},
+}
+
+@Misc{Hajij2024,
+  author       = {Mustafa Hajij and Mathilde Papillon and Florian Frantzen and Jens Agerberg and Ibrahem AlJabea and Ruben Ballester and Claudio Battiloro and Guillermo Bernárdez and Tolga Birdal and Aiden Brent and Peter Chin and Sergio Escalera and Simone Fiorellino and Odin Hoff Gardaa and Gurusankar Gopalakrishnan and Devendra Govil and Josef Hoppe and Maneel Reddy Karri and Jude Khouja and Manuel Lecha and Neal Livesay and Jan Meißner and Soham Mukherjee and Alexander Nikitin and Theodore Papamarkou and Jaro Prílepok and Karthikeyan Natesan Ramamurthy and Paul Rosen and Aldo Guzmán-Sáenz and Alessandro Salatiello and Shreyas N. Samaga and Simone Scardapane and Michael T. Schaub and Luca Scofano and Indro Spinelli and Lev Telyatnikov and Quang Truong and Robin Walters and Maosheng Yang and Olga Zaghen and Ghada Zamzmi and Ali Zia and Nina Miolane},
+  howpublished = {arxiv},
+  month        = feb,
+  title        = {TopoX: A Suite of Python Packages for Machine Learning on Topological Domains},
+  year         = {2024},
+  abstract     = {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. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelx is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at this https URL.},
+  url          = {https://arxiv.org/abs/2402.02441},
+}
+
+@Misc{Papamarkou2024,
+  author       = {Theodore Papamarkou and Tolga Birdal and Michael Bronstein and Gunnar Carlsson and Justin Curry and Yue Gao and Mustafa Hajij and Roland Kwitt and Pietro Liò and Paolo Di Lorenzo and Vasileios Maroulas and Nina Miolane and Farzana Nasrin and Karthikeyan Natesan Ramamurthy and Bastian Rieck and Simone Scardapane and Michael T. Schaub and Petar Veličković and Bei Wang and Yusu Wang and Guo-Wei Wei and Ghada Zamzmi},
+  howpublished = {arxiv},
+  month        = feb,
+  title        = {Position Paper: Challenges and Opportunities in Topological Deep Learning},
+  year         = {2024},
+  abstract     = {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 may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.},
+  url          = {https://arxiv.org/abs/2402.08871},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}