Seminal works on graph neural networks have primarily targeted semi-supervised node classification problems with few observed labels and high-dimensional signals. With the development of graph networks, this setup has become a de facto benchmark for a significant body of research. Interestingly, several works have recently shown that graph neural networks do not perform much better than predefined lowpass filters followed by a linear classifier in these particular settings. However, when learning with little data in a highdimensional space, it is not surprising that simple and heavily regularized learning methods are near-optimal. In this paper, we show empirically that in settings with fewer features and more training data, more complex graph networks significantly outperform simpler architectures, and propose a few insights towards to the proper choice of graph neural networks architectures. We finally outline the importance of using sufficiently diverse benchmarks (including lower dimensional signals as well) when designing and studying new types of graph neural networks.

This work introduces a diffusion model for molecule generation in 3D that is equivariant to Euclidean transformations. Our E(3) Equivariant Diffusion Model (EDM) learns to denoise a diffusion process with an equivariant network that jointly operates on both continuous (atom coordinates) and categorical features (atom types). In addition, we provide a probabilistic analysis which admits likelihood computation of molecules using our model. Experimentally, the proposed method significantly outperforms previous 3D molecular generative methods regarding the quality of generated samples and efficiency at training time.

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Message-passing has proved to be an effective way to design graph neural networks, as it is able to leverage both permutation equivariance and an inductive bias towards learning local structures to achieve good generalization. However, current message-passing architectures have a limited representation power and fail to learn basic topological properties of graphs. We address this problem and propose a new message-passing framework that is powerful while preserving permutation equivariance. Specifically, we propagate unique node identifiers in the form of a one-hot encoding in order to learn a local context around each node. We show that our model is computationally universal in the limit, while also being equivariant. Experimentally, we find our model to be superior at predicting various graph topological properties, opening the way to novel powerful architectures that are both equivariant and computationally efficient.Preprint. Under review.

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