A Graph Convolutional Network, or GCN, is an approach for semi-supervised learning on graph-structured data. It is based on an efficient variant of convolutional neural networks which operate directly on graphs. The choice of convolutional architecture is motivated via a localized first-order approximation of spectral graph convolutions. The model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes.
A Graph Attention Network (GAT) is a neural network architecture that operates on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over their neighborhoods’ features, a GAT enables (implicitly) specifying different weights to different nodes in a neighborhood, without requiring any kind of costly matrix operation (such as inversion) or depending on knowing the graph structure upfront. See here for an explanation by DGL.
DeepWalk learns embeddings (social representations) of a graph's vertices, by modeling a stream of short random walks. Social representations are latent features of the vertices that capture neighborhood similarity and community membership. These latent representations encode social relations in a continuous vector space with a relatively small number of dimensions. It generalizes neural language models to process a special language composed of a set of randomly-generated walks. The goal is to learn a latent representation, not only a probability distribution of node co-occurrences, and so as to introduce a mapping function $\Phi \colon v \in V \mapsto \mathbb{R}^{|V|\times d}$. This mapping $\Phi$ represents the latent social representation associated with each vertex $v$ in the graph. In practice, $\Phi$ is represented by a $|V| \times d$ matrix of free parameters.
Sparse Sinkhorn Attention is an attention mechanism that reduces the memory complexity of the dot-product attention mechanism and is capable of learning sparse attention outputs. It is based on the idea of differentiable sorting of internal representations within the self-attention module. SSA incorporates a meta sorting network that learns to rearrange and sort input sequences. Sinkhorn normalization is used to normalize the rows and columns of the sorting matrix. The actual SSA attention mechanism then acts on the block sorted sequences.
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The Sinkhorn Transformer is a type of transformer that uses Sparse Sinkhorn Attention as a building block. This component is a plug-in replacement for dense fully-connected attention (as well as local attention, and sparse attention alternatives), and allows for reduced memory complexity as well as sparse attention.
SortCut Sinkhorn Attention is a variant of Sparse Sinkhorn Attention where a post-sorting truncation of the input sequence is performed, essentially performing a hard top-k operation on the input sequence blocks within the computational graph. While most attention models mainly re-weight or assign near-zero weights during training, this allows for explicitly and dynamically truncate the input sequence. Specifically: $$ Y = \text{Softmax}\left(Q{\psi\_{S}}\left(K\right)^{T}\_{\left[:n\right]}\right)\psi\_{S}\left(V\right)\_{\left[:n\right]} $$ where $n$ is the Sortfut budget hyperparameter.