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TopoX: A Suite of Python Packages for Machine Learning on Topological Domains (2402.02441v5)

Published 4 Feb 2024 in cs.LG, cs.AI, stat.CO, and cs.MS

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 https://pyt-team.github.io/}{https://pyt-team.github.io/.

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Citations (8)
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Summary

  • The paper introduces TopoX, a unified suite of Python packages that advances Topological Deep Learning through integrated domain construction, embedding, and neural modeling.
  • It details how TopoNetX manipulates higher-order topological cells and how TopoEmbedX extends node2vec embeddings to complex domains with over 95% code coverage.
  • The implementation of TopoModelX in PyTorch enables efficient higher-order message passing, positioning TopoX as a valuable tool for both research and education.

Overview of TopoX Software Suite

In the field of machine learning, the burgeoning field of Topological Deep Learning (TDL) has expanded the boundaries beyond traditional Euclidean spaces, encompassing topological domains such as simplicial and cellular complexes. This paper introduces TopoX, a suite of Python packages, which stands as a significant stride in TDL, offering an all-encompassing toolkit for machine learning applications within these complex domains. The suite consists of TopoNetX for domain construction and computation, TopoEmbedX for embedding such domains into vector spaces, and TopoModelX, a PyTorch-based framework for implementing neural networks in these domains.

TopoX Functionalities and Design

The design of TopoX is noted for its adaptation and abstraction from current graph-based tools. TopoNetX is instrumental in the manipulation of higher-order cells and complex structures, whereas TopoEmbedX extrapolates node2vec-like embeddings to topological spaces, serving to advance representation learning. TopoModelX is particularly innovative, introducing TDL models that leverage higher-order message passing functions. This comprehensive suite not only bridges a gap in practical implementation of TDL theories but also boasts robust documentation, exhaustive unit testing, and an open-source MIT license repository.

Comparative Advantages

TopoX is meticulously compared with other prominent Python libraries, marking its superiority in terms of functionalities and the range of topological domains catered. Boasting a code coverage of >=95% across its packages, TopoX demonstrates reliability and robustness parallel to, or exceeding, renowned libraries like PyG, DGL, and NetworkX. Its unified API design simplifies the transition across various topological structures and enhances collaborative and parallel computing efforts within the scientific community.

Practical Applicability and Educational Value

The educational potential of TopoX is showcased through example snippets demonstrating its intuitive interface for constructing complexes and applying TDL models. These rich examples, along with bundled Jupyter notebook tutorials, make it an invaluable learning tool for users new to the world of TDL. Whether for embedding using the Stanford bunny dataset or forwarding passes with simplicial neural networks, TopoX simplifies the intricate dance of topology and deep learning into user-friendly, actionable code blocks, anchoring its place as a bridge between theory and hands-on application.

In conclusion, TopoX equips researchers and enthusiasts with powerful tools to exploit the versatile landscape of topological domains, promising a leap forward for the interdisciplinary area where machine learning meets complex topology.

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GitHub

  1. 🌐 TopoX 🍩 — TopoX documentation