Topological Deep Learning (TDL) has advanced beyond traditional Graph Neural Networks (GNNs) by modeling complex multi-way relationships, which is imperative for understanding complex systems like social networks and protein interactions. A key subset of TDL, known as Topological Neural Networks (TNNs), are proficient at handling higher-order relational data and have demonstrated superior performance in various machine-learning tasks. However, challenges such as reproducibility, standardization, and benchmarking in TDL still persist.
To address these challenges, researchers from institutions like Sapienza University and UC Santa Barbara have developed an open-source benchmarking library called TopoBenchmarkX. This framework organizes TDL workflows into modular components for data processing, model training, and evaluation, facilitating user-friendly adaptability. The framework can transform graph data into higher-order topological formations, causing an enhancement in data representation and analysis.
Several software tools assist with graph-based learning. For example, NetworkX is used for graph computations. KarateClub provides unsupervised learning algorithms for graph data. Both PyG and DGL cater to Geometric Deep Learning (GDL) and general graph learning. For higher-order domains, HyperNetX and XGI handle hypergraphs and simplicial complexes, while DHG provides deep learning for graphs and hypergraphs.
The TopoX suite, consisting of TopoNetX, TopoEmbedX, and TopoModelX, supports computations, embeddings, and learning with TNNs across varied topological structures. However, TopoBenchmarkX is unique as it is specially designed to benchmark TNNs and generate higher-order datasets for TDL.
TopoBenchmarkX can convert graphs into “featured topological domains” extending to structures like cell complexes. It uses a “lifting” method to transform a graph into a higher-order domain, a process that can be fixed using predefined rules or may be learnable and optimized.
TopoBenchmarkX was tested on twelve neural network models across graphs, hypergraphs, and topological domains using 22 datasets for four tasks. The results demonstrated that higher-order neural networks outperformed GNNs on 16 out of 22 datasets.
One shortcoming of TopoBenchmarkX is the lack of features like learnable liftings and built-in higher-order datasets, which are issues the researchers plan to address in future work.
Overall, TopoBenchmarkX represents a significant milestone in making the application of TDL more robust and user-friendly, thus accelerating research in this area. However, there is still much work to be done, and the researchers are encouraging others to contribute to this open-source project.
