TopoBench: A Framework for Benchmarking Topological Deep Learning (2406.06642v2)

Abstract: This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL into a sequence of independent modules for data generation, loading, transforming and processing, as well as model training, optimization and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBench is its support for transformations and lifting across topological domains. Mapping the topology and features of a graph to higher-order topological domains, such as simplicial and cell complexes, enables richer data representations and more fine-grained analyses. The applicability of TopoBench is demonstrated by benchmarking several TDL architectures across diverse tasks and datasets.

• The paper introduces an open-source, modular framework that benchmarks topological deep learning by transforming graph data into richer, higher-order representations.
• It deconstructs the TDL pipeline into customizable components for data loading, model training, optimization, and evaluation across various neural network architectures.
• Numerical experiments on twenty-two datasets reveal that higher-order networks often outperform traditional GNNs, emphasizing the impact of topological complexity on analysis.

TopoBenchmarkX: A Framework for Benchmarking Topological Deep Learning

The paper presents TopoBenchmarkX, an open-source, modular framework designed to address the benchmarking needs of the emerging field of Topological Deep Learning (TDL). TDL extends beyond traditional Graph Neural Networks (GNNs) by enabling the modeling of complex, multi-way interactions using topological structures such as simplicial and cell complexes. The flexibility and applicability of TopoBenchmarkX lie in its capability to shift between these topological domains, a feature critical for capturing and analyzing rich data representations.

Key Features and Methodology

TopoBenchmarkX deconstructs the TDL pipeline into distinct, modular components, facilitating customizable configurations for data loading, processing, model training, optimization, and evaluation. It emphasizes the transformation and lifting of data across topological domains to enhance data expressivity and analytical granularity. For instance, by transforming graph data into higher-order topological representations, researchers can perform more detailed analyses and obtain richer feature mappings.

The framework addresses several challenges in TDL, such as the scarcity of topological datasets, non-trivial standardization across domains, and diversity within Topological Neural Network (TNN) architectures. TopoBenchmarkX implements fixed lifting algorithms to simulate higher-order datasets from graphs, helping overcome data scarcity. It also provides a standardized input-output interface compatible across multiple TNN architectures.

Numerical Experiments

The framework's effectiveness is demonstrated through comprehensive benchmarking experiments involving twelve neural network models. These models span four topological domains and tackle four learning tasks using twenty-two datasets. Higher-order networks frequently outperform traditional GNNs, underscoring the importance of capturing multi-relational data for complex systems analysis.

Performance metrics indicate that while GNNs show strengths in regression tasks, TNNs generally excel in classification scenarios. This highlights the nuanced advantages of higher-order networks and suggests that leveraging topological complexity can yield improved results, especially in domains characterized by intricate data structures.

Implications and Future Directions

The paper identifies several open areas for future work, including integrating learnable liftings to optimize data transformations and expanding the framework to include real higher-order datasets. Moreover, the development of evaluation metrics tailored to TDL could offer deeper insights into the comparative strengths of different models, further advancing theoretical understanding and practical application of topological methods.

TopoBenchmarkX lays the groundwork for standardized, reproducible research in TDL, offering researchers a robust platform to explore, develop, and optimize models across diverse topological domains. As the field progresses, this framework is poised to play a pivotal role in accelerating developments and ensuring the scalability and applicability of TDL across various complex systems.