GATs

Graph Attention Networks (GATs) are a class of neural networks designed to operate on graph-structured data by applying attention mechanisms to the neighborhood aggregation process. They assign learned, dynamic weights to neighboring nodes when computing a node’s representation, rather than following a uniform average as in some earlier graph convolutional methods. This allows the model to focus on the most relevant neighbors for each node and to adapt to heterogeneous neighborhood sizes.

In a single attention head, the model first applies a shared linear transformation to the input features of all nodes. For each edge between a node i and its neighbor j, an attention coefficient eij is computed using a small feed-forward network on the transformed features, typically followed by a nonlinearity such as LeakyReLU. The coefficients for node i are then normalized across its neighbors with a softmax, producing αij that sum to one. The updated feature for node i is a weighted sum of the transformed neighbor features, using αij as weights. This process is repeated for multiple attention heads, and their outputs are either concatenated or averaged to form the next layer’s representation.

GATs support inductive learning on unseen nodes and can scale to graphs without requiring eigenvector computations, making them a flexible alternative to spectral methods. They have been shown to perform well on standard semi-supervised node classification tasks, such as citation networks, and have inspired numerous extensions and variants, including deeper architectures and alternative attention mechanisms.

Key considerations when using GATs include computational cost on large graphs, the choice of the number of attention heads, and how to integrate multi-head outputs. While effective in many settings, their performance depends on data quality and appropriate hyperparameter tuning.