Pooling Layers
Index
GraphNeuralNetworks.GlobalAttentionPool
GraphNeuralNetworks.GlobalPool
GraphNeuralNetworks.Set2Set
GraphNeuralNetworks.TopKPool
Docs
GraphNeuralNetworks.GlobalAttentionPool
— TypeGlobalAttentionPool(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)
GraphNeuralNetworks.GlobalPool
— TypeGlobalPool(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
GraphNeuralNetworks.Set2Set
— TypeSet2Set(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)
. ```
GraphNeuralNetworks.TopKPool
— TypeTopKPool(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.