Geometric graph is a special kind of graph with geometric features, which is vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections, making them ineffectively processed by current Graph Neural Networks (GNNs). To tackle this issue, researchers proposed a variety of Geometric Graph Neural Networks equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs. Given the current progress in this field, it is imperative to conduct a comprehensive survey of data structures, models, and applications related to geometric GNNs. In this paper, based on the necessary but concise mathematical preliminaries, we provide a unified view of existing models from the geometric message passing perspective. Additionally, we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation. We also discuss the challenges and future potential directions of Geometric GNNs at the end of this survey.
Pretraining on a large number of unlabeled 3D molecules has showcased superiority in various scientific applications. However, prior efforts typically focus on pretraining models on a specific domain, either proteins or small molecules, missing the opportunity to leverage the cross-domain knowledge. To mitigate this gap, we introduce Equivariant Pretrained Transformer (EPT), a novel pretraining framework designed to harmonize the geometric learning of small molecules and proteins. To be specific, EPT unifies the geometric modeling of multi-domain molecules via the block-enhanced representation that can attend a broader context of each atom. Upon transformer framework, EPT is further enhanced with E(3) equivariance to facilitate the accurate representation of 3D structures. Another key innovation of EPT is its block-level pretraining task, which allows for joint pretraining on datasets comprising both small molecules and proteins. Experimental evaluations on a diverse group of benchmarks, including ligand binding affinity prediction, molecular property prediction, and protein property prediction, show that EPT significantly outperforms previous SOTA methods for affinity prediction, and achieves the best or comparable performance with existing domain-specific pretraining models for other tasks.
Crystals are the foundation of numerous scientific and industrial applications. While various learning-based approaches have been proposed for crystal generation, existing methods seldom consider the space group constraint which is crucial in describing the geometry of crystals and closely relevant to many desirable properties. However, considering space group constraint is challenging owing to its diverse and nontrivial forms. In this paper, we reduce the space group constraint into an equivalent formulation that is more tractable to be handcrafted into the generation process. In particular, we translate the space group constraint into two parts: the basis constraint of the invariant logarithmic space of the lattice matrix and the Wyckoff position constraint of the fractional coordinates. Upon the derived constraints, we then propose DiffCSP++, a novel diffusion model that has enhanced a previous work DiffCSP by further taking space group constraint into account. Experiments on several popular datasets verify the benefit of the involvement of the space group constraint, and show that our DiffCSP++ achieves promising performance on crystal structure prediction, ab initio crystal generation and controllable generation with customized space groups.
Predicting Click-Through Rate (CTR) in billion-scale recommender systems poses a long-standing challenge for Graph Neural Networks (GNNs) due to the overwhelming computational complexity involved in aggregating billions of neighbors. To tackle this, GNN-based CTR models usually sample hundreds of neighbors out of the billions to facilitate efficient online recommendations. However, sampling only a small portion of neighbors results in a severe sampling bias and the failure to encompass the full spectrum of user or item behavioral patterns. To address this challenge, we name the conventional user-item recommendation graph as "micro recommendation graph" and introduce a more suitable MAcro Recommendation Graph (MAG) for billion-scale recommendations. MAG resolves the computational complexity problems in the infrastructure by reducing the node count from billions to hundreds. Specifically, MAG groups micro nodes (users and items) with similar behavior patterns to form macro nodes. Subsequently, we introduce tailored Macro Graph Neural Networks (MacGNN) to aggregate information on a macro level and revise the embeddings of macro nodes. MacGNN has already served Taobao's homepage feed for two months, providing recommendations for over one billion users. Extensive offline experiments on three public benchmark datasets and an industrial dataset present that MacGNN significantly outperforms twelve CTR baselines while remaining computationally efficient. Besides, online A/B tests confirm MacGNN's superiority in billion-scale recommender systems.
The study of rigid protein-protein docking plays an essential role in a variety of tasks such as drug design and protein engineering. Recently, several learning-based methods have been proposed for the task, exhibiting much faster docking speed than those computational methods. In this paper, we propose a novel learning-based method called ElliDock, which predicts an elliptic paraboloid to represent the protein-protein docking interface. To be specific, our model estimates elliptic paraboloid interfaces for the two input proteins respectively, and obtains the roto-translation transformation for docking by making two interfaces coincide. By its design, ElliDock is independently equivariant with respect to arbitrary rotations/translations of the proteins, which is an indispensable property to ensure the generalization of the docking process. Experimental evaluations show that ElliDock achieves the fastest inference time among all compared methods and is strongly competitive with current state-of-the-art learning-based models such as DiffDock-PP and Multimer particularly for antibody-antigen docking.
It has been discovered that Graph Convolutional Networks (GCNs) encounter a remarkable drop in performance when multiple layers are piled up. The main factor that accounts for why deep GCNs fail lies in over-smoothing, which isolates the network output from the input with the increase of network depth, weakening expressivity and trainability. In this paper, we start by investigating refined measures upon DropEdge -- an existing simple yet effective technique to relieve over-smoothing. We term our method as DropEdge++ for its two structure-aware samplers in contrast to DropEdge: layer-dependent sampler and feature-dependent sampler. Regarding the layer-dependent sampler, we interestingly find that increasingly sampling edges from the bottom layer yields superior performance than the decreasing counterpart as well as DropEdge. We theoretically reveal this phenomenon with Mean-Edge-Number (MEN), a metric closely related to over-smoothing. For the feature-dependent sampler, we associate the edge sampling probability with the feature similarity of node pairs, and prove that it further correlates the convergence subspace of the output layer with the input features. Extensive experiments on several node classification benchmarks, including both full- and semi- supervised tasks, illustrate the efficacy of DropEdge++ and its compatibility with a variety of backbones by achieving generally better performance over DropEdge and the no-drop version.
Many processes in biology and drug discovery involve various 3D interactions between different molecules, such as protein and protein, protein and small molecule, etc. Designing a generalist model to learn universal molecular interactions is valuable yet challenging, given that different molecules are usually represented in different granularity. In this paper, we first propose to universally represent a 3D molecule as a geometric graph of sets, in contrast to conventional single-level representations. Upon the proposed unified representation, we then propose a Generalist Equivariant Transformer (GET) to effectively capture both sparse block-level and dense atom-level interactions. To be specific, GET consists of a bilevel attention module, a feed-forward module and a layer normalization module, where, notably, each module is E(3) equivariant to meet the symmetry of 3D world. Extensive experiments on the prediction of protein-protein affinity, ligand binding affinity, and ligand efficacy prediction verify the effectiveness of our proposed method against existing methods, and reveal its potential to learn transferable knowledge across different domains and different tasks.
Learning a shared policy that guides the locomotion of different agents is of core interest in Reinforcement Learning (RL), which leads to the study of morphology-agnostic RL. However, existing benchmarks are highly restrictive in the choice of starting point and target point, constraining the movement of the agents within 2D space. In this work, we propose a novel setup for morphology-agnostic RL, dubbed Subequivariant Graph RL in 3D environments (3D-SGRL). Specifically, we first introduce a new set of more practical yet challenging benchmarks in 3D space that allows the agent to have full Degree-of-Freedoms to explore in arbitrary directions starting from arbitrary configurations. Moreover, to optimize the policy over the enlarged state-action space, we propose to inject geometric symmetry, i.e., subequivariance, into the modeling of the policy and Q-function such that the policy can generalize to all directions, improving exploration efficiency. This goal is achieved by a novel SubEquivariant Transformer (SET) that permits expressive message exchange. Finally, we evaluate the proposed method on the proposed benchmarks, where our method consistently and significantly outperforms existing approaches on single-task, multi-task, and zero-shot generalization scenarios. Extensive ablations are also conducted to verify our design. Code and videos are available on our project page: https://alpc91.github.io/SGRL/.
Binary Neural Network (BNN) represents convolution weights with 1-bit values, which enhances the efficiency of storage and computation. This paper is motivated by a previously revealed phenomenon that the binary kernels in successful BNNs are nearly power-law distributed: their values are mostly clustered into a small number of codewords. This phenomenon encourages us to compact typical BNNs and obtain further close performance through learning non-repetitive kernels within a binary kernel subspace. Specifically, we regard the binarization process as kernel grouping in terms of a binary codebook, and our task lies in learning to select a smaller subset of codewords from the full codebook. We then leverage the Gumbel-Sinkhorn technique to approximate the codeword selection process, and develop the Permutation Straight-Through Estimator (PSTE) that is able to not only optimize the selection process end-to-end but also maintain the non-repetitive occupancy of selected codewords. Experiments verify that our method reduces both the model size and bit-wise computational costs, and achieves accuracy improvements compared with state-of-the-art BNNs under comparable budgets.
Predicting the binding sites of the target proteins plays a fundamental role in drug discovery. Most existing deep-learning methods consider a protein as a 3D image by spatially clustering its atoms into voxels and then feed the voxelized protein into a 3D CNN for prediction. However, the CNN-based methods encounter several critical issues: 1) defective in representing irregular protein structures; 2) sensitive to rotations; 3) insufficient to characterize the protein surface; 4) unaware of data distribution shift. To address the above issues, this work proposes EquiPocket, an E(3)-equivariant Graph Neural Network (GNN) for binding site prediction. In particular, EquiPocket consists of three modules: the first one to extract local geometric information for each surface atom, the second one to model both the chemical and spatial structure of the protein, and the last one to capture the geometry of the surface via equivariant message passing over the surface atoms. We further propose a dense attention output layer to better alleviate the data distribution shift effect incurred by the variable protein size. Extensive experiments on several representative benchmarks demonstrate the superiority of our framework to the state-of-the-art methods.