Constructing transferable descriptors for conformation representation of molecular and biological systems finds numerous applications in drug discovery, learning-based molecular dynamics, and protein mechanism analysis. Geometric graph neural networks (Geom-GNNs) with all-atom information have transformed atomistic simulations by serving as a general learnable geometric descriptors for downstream tasks including prediction of interatomic potential and molecular properties. However, common practices involve supervising Geom-GNNs on specific downstream tasks, which suffer from the lack of high-quality data and inaccurate labels leading to poor generalization and performance degradation on out-of-distribution (OOD) scenarios. In this work, we explored the possibility of using pre-trained Geom-GNNs as transferable and highly effective geometric descriptors for improved generalization. To explore their representation power, we studied the scaling behaviors of Geom-GNNs under self-supervised pre-training, supervised and unsupervised learning setups. We find that the expressive power of different architectures can differ on the pre-training task. Interestingly, Geom-GNNs do not follow the power-law scaling on the pre-training task, and universally lack predictable scaling behavior on the supervised tasks with quantum chemical labels important for screening and design of novel molecules. More importantly, we demonstrate how all-atom graph embedding can be organically combined with other neural architectures to enhance the expressive power. Meanwhile, the low-dimensional projection of the latent space shows excellent agreement with conventional geometrical descriptors.
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