38 citations · 199 across the 44 of their papers we have counts for
24 papers · 1 filter
TopoEmbedX: A General Framework for Representation Learning on Topological Domains
Florian Frantzen, Ibrahem AlJabea, Ines Henriques-Cadby +3
Topological structures such as simplicial complexes, hypergraphs, and cell complexes extend standard graph models by modeling higher-order relationships. These structures appear in…
Topological Neural Operators
Lennart Bastian, Samuel Leventhal, Mustafa Hajij +1
We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or e…
TopoU-Net: a U-Net architecture for topological domains
Gaurav Gaurav, Ibrahem ALJabea, Yaroslav Zakomornyy +4
Many modern datasets mix points, edges, regions, groups, objects, events, hyperedges, and relations. Yet neural architectures often force such data into grids, graphs, or sequences…
Topotein: Topological Deep Learning for Protein Representation Learning
Zhiyu Wang, Arian Jamasb, Mustafa Hajij +3
Protein representation learning (PRL) is crucial for understanding structure-function relationships, yet current sequence- and graph-based methods fail to capture the hierarchical…
Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework
Mustafa Hajij, Lennart Bastian, Sarah Osentoski +9
We introduce copresheaf topological neural networks (CTNNs), a powerful unifying framework that encapsulates a wide spectrum of deep learning architectures, designed to operate on…
ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain
Guillermo Bernárdez, Lev Telyatnikov, Marco Montagna +70
This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learnin…
TopoBench: A Framework for Benchmarking Topological Deep Learning
Lev Telyatnikov, Guillermo Bernardez, Marco Montagna +34
This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL int…
Attending to Topological Spaces: The Cellular Transformer
Rubén Ballester, Pablo Hernández-García, Mathilde Papillon +6
Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks opera…
Position: Topological Deep Learning is the New Frontier for Relational Learning
Theodore Papamarkou, Tolga Birdal, Michael Bronstein +19
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 fron…
TopoX: A Suite of Python Packages for Machine Learning on Topological Domains
Mustafa Hajij, Mathilde Papillon, Florian Frantzen +40
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: h…
Topo-MLP : A Simplicial Network Without Message Passing
Karthikeyan Natesan Ramamurthy, Aldo Guzmán-Sáenz, Mustafa Hajij
Due to their ability to model meaningful higher order relations among a set of entities, higher order network models have emerged recently as a powerful alternative for graph-based…
Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs
Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou +3
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 t…
ICML 2023 Topological Deep Learning Challenge : Design and Results
Mathilde Papillon, Mustafa Hajij, Helen Jenne +53
This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competi…
Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks
Mathilde Papillon, Sophia Sanborn, Mustafa Hajij +1
The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to elec…
Topological Deep Learning: Going Beyond Graph Data
Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou +11
Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes…
Data-Centric AI Requires Rethinking Data Notion
Mustafa Hajij, Ghada Zamzmi, Karthikeyan Natesan Ramamurthy +1
The transition towards data-centric AI requires revisiting data notions from mathematical and implementational standpoints to obtain unified data-centric machine learning packages.…
Signal Processing on Cell Complexes
T. Mitchell Roddenberry, Michael T. Schaub, Mustafa Hajij
The processing of signals supported on non-Euclidean domains has attracted large interest recently. Thus far, such non-Euclidean domains have been abstracted primarily as graphs wi…
Simplicial Complex Representation Learning
Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou +2
Simplicial complexes form an important class of topological spaces that are frequently used in many application areas such as computer-aided design, computer graphics, and simulati…
Topological Deep Learning: Classification Neural Networks
Mustafa Hajij, Kyle Istvan
Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to form…
Persistent Homology and Graphs Representation Learning
Mustafa Hajij, Ghada Zamzmi, Xuanting Cai
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically,…
Algebraically-Informed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures
Mustafa Hajij, Ghada Zamzmi, Matthew Dawson +1
One of the central problems in the interface of deep learning and mathematics is that of building learning systems that can automatically uncover underlying mathematical laws from…
Cell Complex Neural Networks
Mustafa Hajij, Kyle Istvan, Ghada Zamzmi
Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domain…
A Topological Framework for Deep Learning
Mustafa Hajij, Kyle Istvan
We utilize classical facts from topology to show that the classification problem in machine learning is always solvable under very mild conditions. Furthermore, we show that a soft…
PageRank and The K-Means Clustering Algorithm
Mustafa Hajij, Eyad Said, Robert Todd
We utilize the PageRank vector to generalize the -means clustering algorithm to directed and undirected graphs. We demonstrate that PageRank and other centrality measures can be…