  Although recent advances in higher-order Graph Neural Networks (GNNs) improve
the theoretical expressiveness and molecular property predictive performance,
they often fall short of the empirical performance of models that explicitly
use fragment information as inductive bias. However, for these approaches,
there exists no theoretic expressivity study. In this work, we propose the
Fragment-WL test, an extension to the well-known Weisfeiler & Leman (WL) test,
which enables the theoretic analysis of these fragment-biased GNNs. Building on
the insights gained from the Fragment-WL test, we develop a new GNN
architecture and a fragmentation with infinite vocabulary that significantly
boosts expressiveness. We show the effectiveness of our model on synthetic and
real-world data where we outperform all GNNs on Peptides and have 12% lower
error than all GNNs on ZINC and 34% lower error than other fragment-biased
models. Furthermore, we show that our model exhibits superior generalization
capabilities compared to the latest transformer-based architectures,
positioning it as a robust solution for a range of molecular modeling tasks.
