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://github.com/pyt-team.
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 competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.
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 electrostatic interactions between atoms in a protein. Topological Deep Learning (TDL) provides a comprehensive framework to process and extract knowledge from data associated with these systems, such as predicting the social community to which an individual belongs or predicting whether a protein can be a reasonable target for drug development. TDL has demonstrated theoretical and practical advantages that hold the promise of breaking ground in the applied sciences and beyond. However, the rapid growth of the TDL literature has also led to a lack of unification in notation and language across Topological Neural Network (TNN) architectures. This presents a real obstacle for building upon existing works and for deploying TNNs to new real-world problems. To address this issue, we provide an accessible introduction to TDL, and compare the recently published TNNs using a unified mathematical and graphical notation. Through an intuitive and critical review of the emerging field of TDL, we extract valuable insights into current challenges and exciting opportunities for future development.
We summarize the model and results of PirouNet, a semi-supervised recurrent variational autoencoder. Given a small amount of dance sequences labeled with qualitative choreographic annotations, PirouNet conditionally generates dance sequences in the style of the choreographer.
Using Artificial Intelligence (AI) to create dance choreography with intention is still at an early stage. Methods that conditionally generate dance sequences remain limited in their ability to follow choreographer-specific creative intentions, often relying on external prompts or supervised learning. In the same vein, fully annotated dance datasets are rare and labor intensive. To fill this gap and help leverage deep learning as a meaningful tool for choreographers, we propose "PirouNet", a semi-supervised conditional recurrent variational autoencoder together with a dance labeling web application. PirouNet allows dance professionals to annotate data with their own subjective creative labels and subsequently generate new bouts of choreography based on their aesthetic criteria. Thanks to the proposed semi-supervised approach, PirouNet only requires a small portion of the dataset to be labeled, typically on the order of 1%. We demonstrate PirouNet's capabilities as it generates original choreography based on the "Laban Time Effort", an established dance notion describing intention for a movement's time dynamics. We extensively evaluate PirouNet's dance creations through a series of qualitative and quantitative metrics, validating its applicability as a tool for choreographers.