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Furthermore, an interesting discussion concerns the trade-off between representational power (usually gained through learnable functions implemented as neural networks) and the formal property of permutation invariance ( Buterez et al.

Applies Batch Normalization over a N-Dimensional input (a mini-batch of [N-2]D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift . The graph neural network operator from the "Convolutional Networks on Graphs for Learning Molecular Fingerprints" paper. A generic wrapper for computing graph convolution on directed graphs as described in the "Edge Directionality Improves Learning on Heterophilic Graphs" paper. BatchNorm2d module with lazy initialization of the num_features argument of the BatchNorm2d that is inferred from the input. The k-NN interpolation from the "PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space" paper.The Graph U-Net model from the "Graph U-Nets" paper which implements a U-Net like architecture with graph pooling and unpooling operations. Creates a criterion that measures the triplet loss given input tensors a a a, p p p, and n n n (representing anchor, positive, and negative examples, respectively), and a nonnegative, real-valued function ("distance function") used to compute the relationship between the anchor and positive example ("positive distance") and the anchor and negative example ("negative distance"). InstanceNorm1d module with lazy initialization of the num_features argument of the InstanceNorm1d that is inferred from the input. The softmax aggregation operator based on a temperature term, as described in the "DeeperGCN: All You Need to Train Deeper GCNs" paper.

Performs Deep Sets aggregation in which the elements to aggregate are first transformed by a Multi-Layer Perceptron (MLP) \(\phi_{\mathbf{\Theta}}\), summed, and then transformed by another MLP \(\rho_{\mathbf{\Theta}}\), as suggested in the "Graph Neural Networks with Adaptive Readouts" paper. The Node2Vec model from the "node2vec: Scalable Feature Learning for Networks" paper where random walks of length walk_length are sampled in a given graph, and node embeddings are learned via negative sampling optimization. The graph convolutional operator with initial residual connections and identity mapping (GCNII) from the "Simple and Deep Graph Convolutional Networks" paper. The DimeNet++ from the "Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules" paper.A meta layer for building any kind of graph network, inspired by the "Relational Inductive Biases, Deep Learning, and Graph Networks" paper. The RotatE model from the "RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space" paper. The graph convolutional operator from the "Semi-supervised Classification with Graph Convolutional Networks" paper. The ClusterGCN graph convolutional operator from the "Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks" paper. g., Dynamic Edge-Conditioned Filters in Convolutional Networks on Graphs paper, which overlays a regular grid of user-defined size over a point cloud and clusters all points within the same voxel.

mathrm{top}_k\) pooling operator from the "Graph U-Nets", "Towards Sparse Hierarchical Graph Classifiers" and "Understanding Attention and Generalization in Graph Neural Networks" papers. Aggregation functions play an important role in the message passing framework and the readout functions of Graph Neural Networks. The path integral based pooling operator from the "Path Integral Based Convolution and Pooling for Graph Neural Networks" paper. Applies Batch Normalization over a 2D or 3D input as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift . For example, mean aggregation captures the distribution (or proportions) of elements, max aggregation proves to be advantageous to identify representative elements, and sum aggregation enables the learning of structural graph properties ( Xu et al.The continuous-filter convolutional neural network SchNet from the "SchNet: A Continuous-filter Convolutional Neural Network for Modeling Quantum Interactions" paper that uses the interactions blocks of the form.