demonstrate that the choice of aggregation functions contributes significantly to the representational power and performance of the model. A greedy clustering algorithm from the "Weighted Graph Cuts without Eigenvectors: A Multilevel Approach" paper of picking an unmarked vertex and matching it with one of its unmarked neighbors (that maximizes its edge weight). The LINKX model from the "Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods" paper.

Creates a criterion that optimizes a multi-class multi-classification hinge loss (margin-based loss) between input x x x (a 2D mini-batch Tensor) and output y y y (which is a 2D Tensor of target class indices). The Adversarially Regularized Variational Graph Auto-Encoder model from the "Adversarially Regularized Graph Autoencoder for Graph Embedding" paper. The Jumping Knowledge layer aggregation module from the "Representation Learning on Graphs with Jumping Knowledge Networks" paper. The Frequency Adaptive Graph Convolution operator from the "Beyond Low-Frequency Information in Graph Convolutional Networks" paper. The differentiable group normalization layer from the "Towards Deeper Graph Neural Networks with Differentiable Group Normalization" paper, which normalizes node features group-wise via a learnable soft cluster assignment.

Applies Batch Normalization over a 4D input (a mini-batch of 2D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift . The Neural Fingerprint model from the "Convolutional Networks on Graphs for Learning Molecular Fingerprints" paper to generate fingerprints of molecules. Applies layer normalization over each individual example in a batch of features as described in the "Layer Normalization" paper. The Learnable Commutative Monoid aggregation from the "Learnable Commutative Monoids for Graph Neural Networks" paper, in which the elements are aggregated using a binary tree reduction with \(\mathcal{O}(\log |\mathcal{V}|)\) depth.

Rearranges elements in a tensor of shape ( ∗ , C × r 2 , H , W ) (*, C \times r The PointNet set layer from the "PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation" and "PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space" papers. Applies a multi-layer Elman RNN with tanh ⁡ \tanh tanh or ReLU \text{ReLU} ReLU non-linearity to an input sequence.The Adaptive Structure Aware Pooling operator from the "ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations" paper. During training, randomly zeroes some of the elements of the input tensor with probability p using samples from a Bernoulli distribution. 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 anti-symmetric graph convolutional operator from the "Anti-Symmetric DGN: a stable architecture for Deep Graph Networks" paper. Creates a criterion that measures the triplet loss given an input tensors x 1 x1 x 1, x 2 x2 x 2, x 3 x3 x 3 and a margin with a value greater than 0 0 0.

The differentiable pooling operator from the "Hierarchical Graph Representation Learning with Differentiable Pooling" paper. Performs "Set Transformer" aggregation in which the elements to aggregate are processed by multi-head attention blocks, as described in the "Graph Neural Networks with Adaptive Readouts" paper. Notably, all aggregations share the same set of forward arguments, as described in detail in the torch_geometric. Applies Graph Size Normalization over each individual graph in a batch of node features as described in the "Benchmarking Graph Neural Networks" paper. The Graph Neural Network from "Graph Attention Networks" or "How Attentive are Graph Attention Networks?Applies Instance Normalization over a 5D input (a mini-batch of 3D inputs with additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization. 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 . ConvTranspose1d module with lazy initialization of the in_channels argument of the ConvTranspose1d that is inferred from the input. 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. Applies the Softmax function to an n-dimensional input Tensor rescaling them so that the elements of the n-dimensional output Tensor lie in the range [0,1] and sum to 1.