Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learning

TL;DR

This paper critically examines and clarifies common beliefs in graph machine learning, especially regarding oversmoothing, oversquashing, heterophily, and long-range tasks, to improve research focus and understanding.

Contribution

It explicitly states and refutes universal assumptions in the field, promoting clearer conceptual distinctions and more targeted research questions.

Findings

Identifies ambiguities caused by unverified beliefs

Provides counterexamples to common assumptions

Clarifies conceptual differences in graph ML topics

Abstract

After a renaissance phase in which researchers revisited the message-passing paradigm through the lens of deep learning, the graph machine learning community shifted its attention towards a deeper and practical understanding of message-passing's benefits and limitations. In this paper, we notice how the fast pace of progress around the topics of oversmoothing and oversquashing, the homophily-heterophily dichotomy, and long-range tasks, came with the consolidation of commonly accepted beliefs and assumptions -- under the form of universal statements -- that are not always true nor easy to distinguish from each other. We argue that this has led to ambiguities around the investigated problems, preventing researchers from focusing on and addressing precise research questions while causing a good amount of misunderstandings. Our contribution is to make such common beliefs explicit and encourage critical thinking around these topics, refuting universal statements via simple yet formally sufficient counterexamples. The end goal is to clarify conceptual differences, helping researchers address more clearly defined and targeted problems.