Weaknesses: Methodological: The work here places importance on topology/structure. For example, the message scaling is dependent on node degree. Thus this method is apt for applications where the structure is paramount, e.g. one such application mentioned is reasoning about social networks where the degree of the nodes/users provides a lot of information about that node/user. Though useful in many domains, there are domains where GNNs are useful but topology is not important. This is reflected empirically for regular grid graph of the computer vision datasets where PNA does not significantly improve over other methods.

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features---which occur regularly in real-world input domains and within the hidden layers of GNNs---and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model.

If you're a deep learning enthusiast you're probably already familiar with some of the basic mathematical primitives that have been driving the impressive capabilities of what we call deep neural networks. Although we like to think of a basic artificial neural network as some nodes with some weighted connections, it's more efficient computationally to think of neural networks as matrix multiplication all the way down. We might draw a cartoon of an artificial neural network like the figure below, with information traveling in from left to right from inputs to outputs (ignoring recurrent networks for now). This type of neural network is a feed-forward multilayer perceptron (MLP). If we want a computer to compute the forward pass for this model, it's going to use a string of matrix multiplies and some sort of non-linearity (here represented by the Greek letter sigma) in the hidden layer: MLPs are well-suited for data that can be naturally shaped as 1D vectors.

Molecular mechanics (MM) potentials have long been a workhorse of computational chemistry. Leveraging accuracy and speed, these functional forms find use in a wide variety of applications from rapid virtual screening to detailed free energy calculations. Traditionally, MM potentials have relied on human-curated, inflexible, and poorly extensible discrete chemical perception rules (atom types) for applying parameters to molecules or biopolymers, making them difficult to optimize to fit quantum chemical or physical property data. Here, we propose an alternative approach that uses graph nets to perceive chemical environments, producing continuous atom embeddings from which valence and nonbonded parameters can be predicted using a feed-forward neural network. Since all stages are built using smooth functions, the entire process of chemical perception and parameter assignment is differentiable end-to-end with respect to model parameters, allowing new force fields to be easily constructed, extended, and applied to arbitrary molecules. We show that this approach has the capacity to reproduce legacy atom types and can be fit to MM and QM energies and forces, among other targets.