Pooling Layers

GlobalAttentionPool(fgate, ffeat=identity)

Global soft attention layer from the Gated Graph Sequence Neural Networks paper

\[\mathbf{u}_V = \sum_{i\in V} \alpha_i\, f_{feat}(\mathbf{x}_i)\]

where the coefficients $\alpha_i$ are given by a softmax_nodes operation:

\[\alpha_i = \frac{e^{f_{gate}(\mathbf{x}_i)}} {\sum_{i'\in V} e^{f_{gate}(\mathbf{x}_{i'})}}.\]

Arguments

• fgate: The function $f_{gate}: \mathbb{R}^{D_{in}} \to \mathbb{R}$. It is tipically expressed by a neural network.

• ffeat: The function $f_{feat}: \mathbb{R}^{D_{in}} \to \mathbb{R}^{D_{out}}$. It is tipically expressed by a neural network.

Examples

chin = 6
chout = 5    

fgate = Dense(chin, 1)
ffeat = Dense(chin, chout)
pool = GlobalAttentionPool(fgate, ffeat)

g = Flux.batch([GNNGraph(random_regular_graph(10, 4), 
                         ndata=rand(Float32, chin, 10)) 
                for i=1:3])

u = pool(g, g.ndata.x)

@assert size(u) == (chout, g.num_graphs)

GlobalPool(aggr)

Global pooling layer for graph neural networks. Takes a graph and feature nodes as inputs and performs the operation

\[\mathbf{u}_V = \square_{i \in V} \mathbf{x}_i\]

where $V$ is the set of nodes of the input graph and the type of aggregation represented by $\square$ is selected by the aggr argument. Commonly used aggregations are mean, max, and +.

See also reduce_nodes.

Examples

using Flux, GraphNeuralNetworks, Graphs

pool = GlobalPool(mean)

g = GNNGraph(erdos_renyi(10, 4))
X = rand(32, 10)
pool(g, X) # => 32x1 matrix


g = Flux.batch([GNNGraph(erdos_renyi(10, 4)) for _ in 1:5])
X = rand(32, 50)
pool(g, X) # => 32x5 matrix

Set2Set(n_in, n_iters, n_layers = 1)

Set2Set layer from the paper Order Matters: Sequence to sequence for sets.

For each graph in the batch, the layer computes an output vector of size 2*n_in by iterating the following steps n_iters times:

\[\mathbf{q} = \mathrm{LSTM}(\mathbf{q}_{t-1}^*) \alpha_{i} = \frac{\exp(\mathbf{q}^T \mathbf{x}_i)}{\sum_{j=1}^N \exp(\mathbf{q}^T \mathbf{x}_j)} \mathbf{r} = \sum_{i=1}^N \alpha_{i} \mathbf{x}_i \mathbf{q}^*_t = [\mathbf{q}; \mathbf{r}]\]

where N is the number of nodes in the graph, LSTM is a Long-Short-Term-Memory network with n_layers layers, input size 2*n_in and output size n_in.

Given a batch of graphs g and node features x, the layer returns a matrix of size (2*n_in, n_graphs). ```

TopKPool(adj, k, in_channel)

Top-k pooling layer.

Arguments

• adj: Adjacency matrix of a graph.
• k: Top-k nodes are selected to pool together.
• in_channel: The dimension of input channel.