Dense Layers

The k3_node.layers.dense module implements dense tensor graph operations operating on dense adjacency matrices of shape (batch_size, num_nodes, num_nodes).

Dense Convolutions

DenseGCNConv

`k3_node.layers.dense.DenseGCNConv`

Bases: Layer

Applies the dense convolutional operator from the "Semi-supervised Classification with Graph Convolutional Networks" <https://arxiv.org/abs/1609.02907>_ paper.

.. math:: \mathbf{X}^{\prime} = \mathbf{\tilde{D}}^{-1/2} \mathbf{\tilde{A}} \mathbf{\tilde{D}}^{-1/2} \mathbf{X} \mathbf{\Theta}

Parameters:

Name	Type	Description	Default
`in_channels`	`int`	Size of each input sample.	required
`out_channels`	`int`	Size of each output sample.	required
`improved`	`bool`	If set to :obj:`True`, the layer computes :math:`\mathbf{\tilde{A}} = \mathbf{A} + 2 \mathbf{I}`. (default: :obj:`False`)	`False`
`bias`	`bool`	If set to :obj:`False`, the layer will not learn an additive bias. (default: :obj:`True`)	`True`

DenseGATConv

`k3_node.layers.dense.DenseGATConv`

Bases: Layer

See :class:torch_geometric.nn.conv.GATConv.

DenseGINConv

`k3_node.layers.dense.DenseGINConv`

Bases: Layer

Applies the dense Graph Isomorphism Network (GIN) convolutional operator from the "How Powerful are Graph Neural Networks?" <https://arxiv.org/abs/1810.00826>_ paper.

.. math:: \mathbf{X}^{\prime} = \mathrm{MLP} \left( \left( \mathbf{A} + (1 + \epsilon) \cdot \mathbf{I} \right) \cdot \mathbf{X} \right)

Parameters:

Name	Type	Description	Default
`nn`	`callable`	A neural network layer (e.g. MLP or Dense) mapping feature representations to output representations.	required
`eps`	`float`	(Initial) :math:`\epsilon`-value. (default: :obj:`0.0`)	`0.0`
`train_eps`	`bool`	If set to :obj:`True`, :math:`\epsilon` will be a trainable parameter. (default: :obj:`False`)	`False`

DenseGraphConv

`k3_node.layers.dense.DenseGraphConv`

Bases: Layer

See :class:torch_geometric.nn.conv.GraphConv.

DenseSAGEConv

`k3_node.layers.dense.DenseSAGEConv`

Bases: Layer

See :class:torch_geometric.nn.conv.SAGEConv.

Dense Pooling

DMoNPooling

`k3_node.layers.dense.DMoNPooling`

Bases: Layer

The spectral modularity pooling operator from the "Graph Clustering with Graph Neural Networks" <https://arxiv.org/abs/2006.16904>_ paper.

.. math:: \mathbf{X}^{\prime} &= {\mathrm{softmax}(\mathbf{S})}^{\top} \cdot \mathbf{X}

\mathbf{A}^{\prime} &= {\mathrm{softmax}(\mathbf{S})}^{\top} \cdot
\mathbf{A} \cdot \mathrm{softmax}(\mathbf{S})

Parameters:

Name	Type	Description	Default
`channels`	`int or List[int]`	Size of each input sample. If given as a list, will construct an MLP based on the given feature sizes.	required
`k`	`int`	The number of clusters.	required
`dropout`	`float`	Dropout probability. (default: :obj:`0.0`)	`0.0`

`call(x, adj, mask=None, training=False)`

Forward pass.

Parameters:

Name	Type	Description	Default
`x`		Node feature tensor [B, N, F] or [N, F].	required
`adj`		Adjacency tensor [B, N, N] or [N, N].	required
`mask`	`Optional[any]`	Mask tensor [B, N] indicating valid nodes. (default: None)	`None`
`training`	`bool`	Whether layer is in training mode.	`False`

`reset_parameters()`

Resets all learnable parameters of the module.

dense_diff_pool

`k3_node.layers.dense.dense_diff_pool(x, adj, s, mask=None, normalize=True)`

The differentiable pooling operator from the "Hierarchical Graph Representation Learning with Differentiable Pooling" <https://arxiv.org/abs/1806.08804>_ paper.

.. math:: \mathbf{X}^{\prime} &= {\mathrm{softmax}(\mathbf{S})}^{\top} \cdot \mathbf{X}

\mathbf{A}^{\prime} &= {\mathrm{softmax}(\mathbf{S})}^{\top} \cdot
\mathbf{A} \cdot \mathrm{softmax}(\mathbf{S})

Parameters:

Name	Type	Description	Default
`x`		Node feature tensor [B, N, F] or [N, F].	required
`adj`		Adjacency tensor [B, N, N] or [N, N].	required
`s`		Assignment tensor [B, N, C] or [N, C].	required
`mask`	`Optional[any]`	Mask tensor [B, N] indicating valid nodes. (default: None)	`None`
`normalize`	`bool`	If set to False, link prediction loss is not divided by total elements.	`True`

dense_mincut_pool

`k3_node.layers.dense.dense_mincut_pool(x, adj, s, mask=None, temp=1.0)`

The MinCut pooling operator from the "Spectral Clustering in Graph Neural Networks for Graph Pooling" <https://arxiv.org/abs/1907.00481>_ paper.

.. math:: \mathbf{X}^{\prime} &= {\mathrm{softmax}(\mathbf{S})}^{\top} \cdot \mathbf{X}

\mathbf{A}^{\prime} &= {\mathrm{softmax}(\mathbf{S})}^{\top} \cdot
\mathbf{A} \cdot \mathrm{softmax}(\mathbf{S})

Parameters:

Name	Type	Description	Default
`x`		Node feature tensor [B, N, F] or [N, F].	required
`adj`		Adjacency tensor [B, N, N] or [N, N].	required
`s`		Assignment tensor [B, N, C] or [N, C].	required
`mask`	`Optional[any]`	Mask tensor [B, N] indicating valid nodes. (default: None)	`None`
`temp`	`float`	Temperature parameter for softmax function. (default: 1.0)	`1.0`

Dense Linear Layers

Linear

`k3_node.layers.dense.Linear`

Bases: Layer

Applies a linear transformation to the incoming data:

.. math:: \mathbf{x}^{\prime} = \mathbf{x} \mathbf{W} + \mathbf{b}

Parameters:

Name	Type	Description	Default
`in_channels`	`int`	Size of each input sample.	required
`out_channels`	`int`	Size of each output sample.	required
`bias`	`bool`	If set to :obj:`False`, the layer will not learn an additive bias. (default: :obj:`True`)	`True`
`weight_initializer`	`str`	The initializer for the weight matrix (:obj:`"glorot"`, :obj:`"uniform"`, :obj:`"kaiming_uniform"` or :obj:`None`). (default: :obj:`None`)	`None`
`bias_initializer`	`str`	The initializer for the bias vector (:obj:`"zeros"` or :obj:`None`). (default: :obj:`None`)	`None`

HeteroLinear

`k3_node.layers.dense.HeteroLinear`

Bases: Layer

Applies separate linear transformations to the incoming data according to types.

.. math:: \mathbf{x}^{\prime}i = \mathbf{x}_i \mathbf{\Theta} + \mathbf{b}_{\kappa_i}

Parameters:

Name	Type	Description	Default
`in_channels`	`int`	Size of each input sample.	required
`out_channels`	`int`	Size of each output sample.	required
`num_types`	`int`	The number of types.	required
`is_sorted`	`bool`	If set to :obj:`True`, assumes that :obj:`type_vec` is sorted. (default: :obj:`False`)	`False`
`bias`	`bool`	If set to :obj:`False`, the layer will not learn an additive bias. (default: :obj:`True`)	`True`
`weight_initializer`	`str`	The initializer for the weight matrix (:obj:`"glorot"`, :obj:`"uniform"`, :obj:`"kaiming_uniform"` or :obj:`None`). (default: :obj:`None`)	`None`
`bias_initializer`	`str`	The initializer for the bias vector (:obj:`"zeros"` or :obj:`None`). (default: :obj:`None`)	`None`