Have Graph -- Will Lift? The Case for Higher-Order Benchmarks

TL;DR

This paper advocates for developing new higher-order benchmark datasets to advance geometric deep learning, which currently relies heavily on lifted graph datasets due to a lack of suitable benchmarks.

Contribution

It highlights the need for original datasets in higher-order geometric deep learning to strengthen research foundations.

Findings

Current benchmarks are limited, leading to reliance on lifted graph datasets.

Diverse models exist, but benchmark scarcity hampers progress.

Encourages community to source and develop new datasets.

Abstract

After a somewhat rocky start, geometry and topology have established a foothold in machine learning. Message passing, either on graphs or higher-order complexes, is one of the main drivers of geometric deep learning, and paradigms that were once considered to be firmly in the realm of the abstract-like sheaves-have been "tamed" to serve as novel inductive biases for model architectures in topological deep learning. The veritable diversity of models, however, is in stark contrast to the scarcity of suitable benchmark datasets. As a result, researchers often resort to lifting existing graph datasets to include higher-order information. In this opinion paper, I want to encourage the community to also source new datasets, which may be used to prop up the foundations of our research field.