# NN Modules (PyTorch)¶

## Conv Layers¶

Torch modules for graph convolutions.

### GraphConv¶

class dgl.nn.pytorch.conv.GraphConv(in_feats, out_feats, norm='both', weight=True, bias=True, activation=None, allow_zero_in_degree=False)[source]

Bases: torch.nn.modules.module.Module

Graph convolution was introduced in GCN and mathematically is defined as follows:

$h_i^{(l+1)} = \sigma(b^{(l)} + \sum_{j\in\mathcal{N}(i)}\frac{1}{c_{ji}}h_j^{(l)}W^{(l)})$

where $$\mathcal{N}(i)$$ is the set of neighbors of node $$i$$, $$c_{ji}$$ is the product of the square root of node degrees (i.e., $$c_{ji} = \sqrt{|\mathcal{N}(j)|}\sqrt{|\mathcal{N}(i)|}$$), and $$\sigma$$ is an activation function.

If a weight tensor on each edge is provided, the weighted graph convolution is defined as:

$h_i^{(l+1)} = \sigma(b^{(l)} + \sum_{j\in\mathcal{N}(i)}\frac{e_{ji}}{c_{ji}}h_j^{(l)}W^{(l)})$

where $$e_{ji}$$ is the scalar weight on the edge from node $$j$$ to node $$i$$. This is NOT equivalent to the weighted graph convolutional network formulation in the paper.

To customize the normalization term $$c_{ji}$$, one can first set norm='none' for the model, and send the pre-normalized $$e_{ji}$$ to the forward computation. We provide EdgeWeightNorm to normalize scalar edge weight following the GCN paper.

Parameters
• in_feats (int) – Input feature size; i.e, the number of dimensions of $$h_j^{(l)}$$.

• out_feats (int) – Output feature size; i.e., the number of dimensions of $$h_i^{(l+1)}$$.

• norm (str, optional) –

How to apply the normalizer. Can be one of the following values:

• right, to divide the aggregated messages by each node’s in-degrees, which is equivalent to averaging the received messages.

• none, where no normalization is applied.

• both (default), where the messages are scaled with $$1/c_{ji}$$ above, equivalent to symmetric normalization.

• left, to divide the messages sent out from each node by its out-degrees, equivalent to random walk normalization.

• weight (bool, optional) – If True, apply a linear layer. Otherwise, aggregating the messages without a weight matrix.

• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True.

• activation (callable activation function/layer or None, optional) – If not None, applies an activation function to the updated node features. Default: None.

• allow_zero_in_degree (bool, optional) – If there are 0-in-degree nodes in the graph, output for those nodes will be invalid since no message will be passed to those nodes. This is harmful for some applications causing silent performance regression. This module will raise a DGLError if it detects 0-in-degree nodes in input graph. By setting True, it will suppress the check and let the users handle it by themselves. Default: False.

weight

The learnable weight tensor.

Type

torch.Tensor

bias

The learnable bias tensor.

Type

torch.Tensor

Note

Zero in-degree nodes will lead to invalid output value. This is because no message will be passed to those nodes, the aggregation function will be appied on empty input. A common practice to avoid this is to add a self-loop for each node in the graph if it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph


Calling add_self_loop will not work for some graphs, for example, heterogeneous graph since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree to True for those cases to unblock the code and handle zero-in-degree nodes manually. A common practise to handle this is to filter out the nodes with zero-in-degree when use after conv.

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import GraphConv

>>> # Case 1: Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = GraphConv(10, 2, norm='both', weight=True, bias=True)
>>> res = conv(g, feat)
>>> print(res)
tensor([[ 1.3326, -0.2797],
[ 1.4673, -0.3080],
[ 1.3326, -0.2797],
[ 1.6871, -0.3541],
[ 1.7711, -0.3717],
>>> # allow_zero_in_degree example
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> conv = GraphConv(10, 2, norm='both', weight=True, bias=True, allow_zero_in_degree=True)
>>> res = conv(g, feat)
>>> print(res)
tensor([[-0.2473, -0.4631],
[-0.3497, -0.6549],
[-0.3497, -0.6549],
[-0.4221, -0.7905],
[-0.3497, -0.6549],

>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.heterograph({('_U', '_E', '_V') : (u, v)})
>>> u_fea = th.rand(2, 5)
>>> v_fea = th.rand(4, 5)
>>> conv = GraphConv(5, 2, norm='both', weight=True, bias=True)
>>> res = conv(g, (u_fea, v_fea))
>>> res
tensor([[-0.2994,  0.6106],
[-0.4482,  0.5540],
[-0.5287,  0.8235],

forward(graph, feat, weight=None, edge_weight=None)[source]

Compute graph convolution.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor or pair of torch.Tensor) – If a torch.Tensor is given, it represents the input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes. If a pair of torch.Tensor is given, which is the case for bipartite graph, the pair must contain two tensors of shape $$(N_{in}, D_{in_{src}})$$ and $$(N_{out}, D_{in_{dst}})$$.

• weight (torch.Tensor, optional) – Optional external weight tensor.

• edge_weight (torch.Tensor, optional) – Optional tensor on the edge. If given, the convolution will weight with regard to the message.

Returns

The output feature

Return type

torch.Tensor

Raises

DGLError – Case 1: If there are 0-in-degree nodes in the input graph, it will raise DGLError since no message will be passed to those nodes. This will cause invalid output. The error can be ignored by setting allow_zero_in_degree parameter to True. Case 2: External weight is provided while at the same time the module has defined its own weight parameter.

Note

• Input shape: $$(N, *, \text{in_feats})$$ where * means any number of additional dimensions, $$N$$ is the number of nodes.

• Output shape: $$(N, *, \text{out_feats})$$ where all but the last dimension are the same shape as the input.

• Weight shape: $$(\text{in_feats}, \text{out_feats})$$.

reset_parameters()[source]

Reinitialize learnable parameters.

Note

The model parameters are initialized as in the original implementation where the weight $$W^{(l)}$$ is initialized using Glorot uniform initialization and the bias is initialized to be zero.

### EdgeWeightNorm¶

class dgl.nn.pytorch.conv.EdgeWeightNorm(norm='both', eps=0.0)[source]

Bases: torch.nn.modules.module.Module

This module normalizes positive scalar edge weights on a graph following the form in GCN.

Mathematically, setting norm='both' yields the following normalization term:

$c_{ji} = (\sqrt{\sum_{k\in\mathcal{N}(j)}e_{jk}}\sqrt{\sum_{k\in\mathcal{N}(i)}e_{ki}})$

And, setting norm='right' yields the following normalization term:

$c_{ji} = (\sum_{k\in\mathcal{N}(i)}e_{ki})$

where $$e_{ji}$$ is the scalar weight on the edge from node $$j$$ to node $$i$$.

The module returns the normalized weight $$e_{ji} / c_{ji}$$.

Parameters
• norm (str, optional) – The normalizer as specified above. Default is ‘both’.

• eps (float, optional) – A small offset value in the denominator. Default is 0.

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import EdgeWeightNorm, GraphConv

>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> edge_weight = th.tensor([0.5, 0.6, 0.4, 0.7, 0.9, 0.1, 1, 1, 1, 1, 1, 1])
>>> norm = EdgeWeightNorm(norm='both')
>>> norm_edge_weight = norm(g, edge_weight)
>>> conv = GraphConv(10, 2, norm='none', weight=True, bias=True)
>>> res = conv(g, feat, edge_weight=norm_edge_weight)
>>> print(res)
tensor([[-1.1849, -0.7525],
[-1.3514, -0.8582],
[-1.2384, -0.7865],
[-1.9949, -1.2669],
[-1.3658, -0.8674],

forward(graph, edge_weight)[source]

Compute normalized edge weight for the GCN model.

Parameters
• graph (DGLGraph) – The graph.

• edge_weight (torch.Tensor) – Unnormalized scalar weights on the edges. The shape is expected to be $$(|E|)$$.

Returns

The normalized edge weight.

Return type

torch.Tensor

Raises

DGLError – Case 1: The edge weight is multi-dimensional. Currently this module only supports a scalar weight on each edge. Case 2: The edge weight has non-positive values with norm='both'. This will trigger square root and division by a non-positive number.

### RelGraphConv¶

class dgl.nn.pytorch.conv.RelGraphConv(in_feat, out_feat, num_rels, regularizer='basis', num_bases=None, bias=True, activation=None, self_loop=True, low_mem=False, dropout=0.0, layer_norm=False)[source]

Bases: torch.nn.modules.module.Module

Relational graph convolution layer.

Relational graph convolution is introduced in “Modeling Relational Data with Graph Convolutional Networks” and can be described in DGL as below:

$h_i^{(l+1)} = \sigma(\sum_{r\in\mathcal{R}} \sum_{j\in\mathcal{N}^r(i)}e_{j,i}W_r^{(l)}h_j^{(l)}+W_0^{(l)}h_i^{(l)})$

where $$\mathcal{N}^r(i)$$ is the neighbor set of node $$i$$ w.r.t. relation $$r$$. $$e_{j,i}$$ is the normalizer. $$\sigma$$ is an activation function. $$W_0$$ is the self-loop weight.

The basis regularization decomposes $$W_r$$ by:

$W_r^{(l)} = \sum_{b=1}^B a_{rb}^{(l)}V_b^{(l)}$

where $$B$$ is the number of bases, $$V_b^{(l)}$$ are linearly combined with coefficients $$a_{rb}^{(l)}$$.

The block-diagonal-decomposition regularization decomposes $$W_r$$ into $$B$$ number of block diagonal matrices. We refer $$B$$ as the number of bases.

The block regularization decomposes $$W_r$$ by:

$W_r^{(l)} = \oplus_{b=1}^B Q_{rb}^{(l)}$

where $$B$$ is the number of bases, $$Q_{rb}^{(l)}$$ are block bases with shape $$R^{(d^{(l+1)}/B)*(d^{l}/B)}$$.

Parameters
• in_feat (int) – Input feature size; i.e, the number of dimensions of $$h_j^{(l)}$$.

• out_feat (int) – Output feature size; i.e., the number of dimensions of $$h_i^{(l+1)}$$.

• num_rels (int) – Number of relations. .

• regularizer (str) – Which weight regularizer to use “basis” or “bdd”. “basis” is short for basis-diagonal-decomposition. “bdd” is short for block-diagonal-decomposition.

• num_bases (int, optional) – Number of bases. If is none, use number of relations. Default: None.

• bias (bool, optional) – True if bias is added. Default: True.

• activation (callable, optional) – Activation function. Default: None.

• self_loop (bool, optional) – True to include self loop message. Default: True.

• low_mem (bool, optional) – True to use low memory implementation of relation message passing function. Default: False. This option trades speed with memory consumption, and will slowdown the forward/backward. Turn it on when you encounter OOM problem during training or evaluation. Default: False.

• dropout (float, optional) – Dropout rate. Default: 0.0

• layer_norm (float, optional) – Add layer norm. Default: False

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import RelGraphConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = RelGraphConv(10, 2, 3, regularizer='basis', num_bases=2)
>>> conv.weight.shape
torch.Size([2, 10, 2])
>>> etype = th.tensor(np.array([0,1,2,0,1,2]).astype(np.int64))
>>> res = conv(g, feat, etype)
>>> res
tensor([[ 0.3996, -2.3303],
[-0.4323, -0.1440],
[ 0.3996, -2.3303],
[ 2.1046, -2.8654],
[-0.4323, -0.1440],

>>> # One-hot input
>>> one_hot_feat = th.tensor(np.array([0,1,2,3,4,5]).astype(np.int64))
>>> res = conv(g, one_hot_feat, etype)
>>> res
tensor([[ 0.5925,  0.0985],
[-0.3953,  0.8408],
[-0.9819,  0.5284],
[-1.0085, -0.1721],
[ 0.5962,  1.2002],

forward(g, feat, etypes, norm=None)[source]

Forward computation.

Parameters
• g (DGLGraph) – The graph.

• feat (torch.Tensor) –

Input node features. Could be either

• $$(|V|, D)$$ dense tensor

• $$(|V|,)$$ int64 vector, representing the categorical values of each node. It then treat the input feature as an one-hot encoding feature.

• etypes (torch.Tensor or list[int]) –

Edge type data. Could be either

• An $$(|E|,)$$ dense tensor. Each element corresponds to the edge’s type ID. Preferred format if lowmem == False.

• An integer list. The i^th element is the number of edges of the i^th type. This requires the input graph to store edges sorted by their type IDs. Preferred format if lowmem == True.

• norm (torch.Tensor, optional) –

Edge normalizer. Could be either

• An $$(|E|, 1)$$ tensor storing the normalizer on each edge.

Returns

New node features.

Return type

torch.Tensor

Notes

Under the low_mem mode, DGL will sort the graph based on the edge types and compute message passing one type at a time. DGL recommends sorts the graph beforehand (and cache it if possible) and provides the integer list format to the etypes argument. Use DGL’s to_homogeneous() API to get a sorted homogeneous graph from a heterogeneous graph. Pass return_count=True to it to get the etypes in integer list.

### TAGConv¶

class dgl.nn.pytorch.conv.TAGConv(in_feats, out_feats, k=2, bias=True, activation=None)[source]

Bases: torch.nn.modules.module.Module

Topology Adaptive Graph Convolutional layer from paper Topology Adaptive Graph Convolutional Networks.

$H^{K} = {\sum}_{k=0}^K (D^{-1/2} A D^{-1/2})^{k} X {\Theta}_{k},$

where $$A$$ denotes the adjacency matrix, $$D_{ii} = \sum_{j=0} A_{ij}$$ its diagonal degree matrix, $${\Theta}_{k}$$ denotes the linear weights to sum the results of different hops together.

Parameters
• in_feats (int) – Input feature size. i.e, the number of dimensions of $$X$$.

• out_feats (int) – Output feature size. i.e, the number of dimensions of $$H^{K}$$.

• k (int, optional) – Number of hops $$K$$. Default: 2.

• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True.

• activation (callable activation function/layer or None, optional) – If not None, applies an activation function to the updated node features. Default: None.

lin

The learnable linear module.

Type

torch.Module

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import TAGConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = TAGConv(10, 2, k=2)
>>> res = conv(g, feat)
>>> res
tensor([[ 0.5490, -1.6373],
[ 0.5490, -1.6373],
[ 0.5490, -1.6373],
[ 0.5513, -1.8208],
[ 0.5215, -1.6044],

forward(graph, feat)[source]

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor) – The input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes.

Returns

The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is size of output feature.

Return type

torch.Tensor

### GATConv¶

class dgl.nn.pytorch.conv.GATConv(in_feats, out_feats, num_heads, feat_drop=0.0, attn_drop=0.0, negative_slope=0.2, residual=False, activation=None, allow_zero_in_degree=False, bias=True)[source]

Bases: torch.nn.modules.module.Module

Apply Graph Attention Network over an input signal.

$h_i^{(l+1)} = \sum_{j\in \mathcal{N}(i)} \alpha_{i,j} W^{(l)} h_j^{(l)}$

where $$\alpha_{ij}$$ is the attention score bewteen node $$i$$ and node $$j$$:

\begin{align}\begin{aligned}\alpha_{ij}^{l} &= \mathrm{softmax_i} (e_{ij}^{l})\\e_{ij}^{l} &= \mathrm{LeakyReLU}\left(\vec{a}^T [W h_{i} \| W h_{j}]\right)\end{aligned}\end{align}
Parameters
• in_feats (int, or pair of ints) – Input feature size; i.e, the number of dimensions of $$h_i^{(l)}$$. GATConv can be applied on homogeneous graph and unidirectional bipartite graph. If the layer is to be applied to a unidirectional bipartite graph, in_feats specifies the input feature size on both the source and destination nodes. If a scalar is given, the source and destination node feature size would take the same value.

• out_feats (int) – Output feature size; i.e, the number of dimensions of $$h_i^{(l+1)}$$.

• feat_drop (float, optional) – Dropout rate on feature. Defaults: 0.

• attn_drop (float, optional) – Dropout rate on attention weight. Defaults: 0.

• negative_slope (float, optional) – LeakyReLU angle of negative slope. Defaults: 0.2.

• residual (bool, optional) – If True, use residual connection. Defaults: False.

• activation (callable activation function/layer or None, optional.) – If not None, applies an activation function to the updated node features. Default: None.

• allow_zero_in_degree (bool, optional) – If there are 0-in-degree nodes in the graph, output for those nodes will be invalid since no message will be passed to those nodes. This is harmful for some applications causing silent performance regression. This module will raise a DGLError if it detects 0-in-degree nodes in input graph. By setting True, it will suppress the check and let the users handle it by themselves. Defaults: False.

• bias (bool, optional) – If True, learns a bias term. Defaults: True.

Note

Zero in-degree nodes will lead to invalid output value. This is because no message will be passed to those nodes, the aggregation function will be appied on empty input. A common practice to avoid this is to add a self-loop for each node in the graph if it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph


Calling add_self_loop will not work for some graphs, for example, heterogeneous graph since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree to True for those cases to unblock the code and handle zero-in-degree nodes manually. A common practise to handle this is to filter out the nodes with zero-in-degree when use after conv.

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import GATConv

>>> # Case 1: Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> gatconv = GATConv(10, 2, num_heads=3)
>>> res = gatconv(g, feat)
>>> res
tensor([[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],

>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.heterograph({('A', 'r', 'B'): (u, v)})
>>> u_feat = th.tensor(np.random.rand(2, 5).astype(np.float32))
>>> v_feat = th.tensor(np.random.rand(4, 10).astype(np.float32))
>>> gatconv = GATConv((5,10), 2, 3)
>>> res = gatconv(g, (u_feat, v_feat))
>>> res
tensor([[[-0.6066,  1.0268],
[-0.5945, -0.4801],
[ 0.1594,  0.3825]],
[[ 0.0268,  1.0783],
[ 0.5041, -1.3025],
[ 0.6568,  0.7048]],
[[-0.2688,  1.0543],
[-0.0315, -0.9016],
[ 0.3943,  0.5347]],
[[-0.6066,  1.0268],
[-0.5945, -0.4801],

forward(graph, feat, get_attention=False)[source]

Compute graph attention network layer.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor or pair of torch.Tensor) – If a torch.Tensor is given, the input feature of shape $$(N, *, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes. If a pair of torch.Tensor is given, the pair must contain two tensors of shape $$(N_{in}, *, D_{in_{src}})$$ and $$(N_{out}, *, D_{in_{dst}})$$.

• get_attention (bool, optional) – Whether to return the attention values. Default to False.

Returns

• torch.Tensor – The output feature of shape $$(N, *, H, D_{out})$$ where $$H$$ is the number of heads, and $$D_{out}$$ is size of output feature.

• torch.Tensor, optional – The attention values of shape $$(E, *, H, 1)$$, where $$E$$ is the number of edges. This is returned only when get_attention is True.

Raises

DGLError – If there are 0-in-degree nodes in the input graph, it will raise DGLError since no message will be passed to those nodes. This will cause invalid output. The error can be ignored by setting allow_zero_in_degree parameter to True.

### EdgeConv¶

class dgl.nn.pytorch.conv.EdgeConv(in_feat, out_feat, batch_norm=False, allow_zero_in_degree=False)[source]

Bases: torch.nn.modules.module.Module

EdgeConv layer.

Introduced in “Dynamic Graph CNN for Learning on Point Clouds”. Can be described as follows:

$h_i^{(l+1)} = \max_{j \in \mathcal{N}(i)} ( \Theta \cdot (h_j^{(l)} - h_i^{(l)}) + \Phi \cdot h_i^{(l)})$

where $$\mathcal{N}(i)$$ is the neighbor of $$i$$. $$\Theta$$ and $$\Phi$$ are linear layers.

Note

The original formulation includes a ReLU inside the maximum operator. This is equivalent to first applying a maximum operator then applying the ReLU.

Parameters
• in_feat (int) – Input feature size; i.e, the number of dimensions of $$h_j^{(l)}$$.

• out_feat (int) – Output feature size; i.e., the number of dimensions of $$h_i^{(l+1)}$$.

• batch_norm (bool) – Whether to include batch normalization on messages. Default: False.

• allow_zero_in_degree (bool, optional) – If there are 0-in-degree nodes in the graph, output for those nodes will be invalid since no message will be passed to those nodes. This is harmful for some applications causing silent performance regression. This module will raise a DGLError if it detects 0-in-degree nodes in input graph. By setting True, it will suppress the check and let the users handle it by themselves. Default: False.

Note

Zero in-degree nodes will lead to invalid output value. This is because no message will be passed to those nodes, the aggregation function will be appied on empty input. A common practice to avoid this is to add a self-loop for each node in the graph if it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph


Calling add_self_loop will not work for some graphs, for example, heterogeneous graph since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree to True for those cases to unblock the code and handle zero-in-degree nodes manually. A common practise to handle this is to filter out the nodes with zero-in-degree when use after conv.

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import EdgeConv

>>> # Case 1: Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = EdgeConv(10, 2)
>>> res = conv(g, feat)
>>> res
tensor([[-0.2347,  0.5849],
[-0.2347,  0.5849],
[-0.2347,  0.5849],
[-0.2347,  0.5849],
[-0.2347,  0.5849],

>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.bipartite((u, v))
>>> u_fea = th.rand(2, 5)
>>> v_fea = th.rand(4, 5)
>>> conv = EdgeConv(5, 2, 3)
>>> res = conv(g, (u_fea, v_fea))
>>> res
tensor([[ 1.6375,  0.2085],
[-1.1925, -1.2852],
[ 0.2101,  1.3466],

forward(g, feat)[source]

Forward computation

Parameters
• g (DGLGraph) – The graph.

• feat (Tensor or pair of tensors) –

$$(N, D)$$ where $$N$$ is the number of nodes and $$D$$ is the number of feature dimensions.

If a pair of tensors is given, the graph must be a uni-bipartite graph with only one edge type, and the two tensors must have the same dimensionality on all except the first axis.

Returns

New node features.

Return type

torch.Tensor

Raises

DGLError – If there are 0-in-degree nodes in the input graph, it will raise DGLError since no message will be passed to those nodes. This will cause invalid output. The error can be ignored by setting allow_zero_in_degree parameter to True.

### SAGEConv¶

class dgl.nn.pytorch.conv.SAGEConv(in_feats, out_feats, aggregator_type, feat_drop=0.0, bias=True, norm=None, activation=None)[source]

Bases: torch.nn.modules.module.Module

GraphSAGE layer from paper Inductive Representation Learning on Large Graphs.

\begin{align}\begin{aligned}h_{\mathcal{N}(i)}^{(l+1)} &= \mathrm{aggregate} \left(\{h_{j}^{l}, \forall j \in \mathcal{N}(i) \}\right)\\h_{i}^{(l+1)} &= \sigma \left(W \cdot \mathrm{concat} (h_{i}^{l}, h_{\mathcal{N}(i)}^{l+1}) \right)\\h_{i}^{(l+1)} &= \mathrm{norm}(h_{i}^{l})\end{aligned}\end{align}

If a weight tensor on each edge is provided, the aggregation becomes:

$h_{\mathcal{N}(i)}^{(l+1)} = \mathrm{aggregate} \left(\{e_{ji} h_{j}^{l}, \forall j \in \mathcal{N}(i) \}\right)$

where $$e_{ji}$$ is the scalar weight on the edge from node $$j$$ to node $$i$$. Please make sure that $$e_{ji}$$ is broadcastable with $$h_j^{l}$$.

Parameters
• in_feats (int, or pair of ints) –

Input feature size; i.e, the number of dimensions of $$h_i^{(l)}$$.

SAGEConv can be applied on homogeneous graph and unidirectional bipartite graph. If the layer applies on a unidirectional bipartite graph, in_feats specifies the input feature size on both the source and destination nodes. If a scalar is given, the source and destination node feature size would take the same value.

If aggregator type is gcn, the feature size of source and destination nodes are required to be the same.

• out_feats (int) – Output feature size; i.e, the number of dimensions of $$h_i^{(l+1)}$$.

• feat_drop (float) – Dropout rate on features, default: 0.

• aggregator_type (str) – Aggregator type to use (mean, gcn, pool, lstm).

• bias (bool) – If True, adds a learnable bias to the output. Default: True.

• norm (callable activation function/layer or None, optional) – If not None, applies normalization to the updated node features.

• activation (callable activation function/layer or None, optional) – If not None, applies an activation function to the updated node features. Default: None.

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import SAGEConv

>>> # Case 1: Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = SAGEConv(10, 2, 'pool')
>>> res = conv(g, feat)
>>> res
tensor([[-1.0888, -2.1099],
[-1.0888, -2.1099],
[-1.0888, -2.1099],
[-1.0888, -2.1099],
[-1.0888, -2.1099],

>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.bipartite((u, v))
>>> u_fea = th.rand(2, 5)
>>> v_fea = th.rand(4, 10)
>>> conv = SAGEConv((5, 10), 2, 'mean')
>>> res = conv(g, (u_fea, v_fea))
>>> res
tensor([[ 0.3163,  3.1166],
[ 0.3866,  2.5398],
[ 0.5873,  1.6597],

forward(graph, feat, edge_weight=None)[source]

Compute GraphSAGE layer.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor or pair of torch.Tensor) – If a torch.Tensor is given, it represents the input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes. If a pair of torch.Tensor is given, the pair must contain two tensors of shape $$(N_{in}, D_{in_{src}})$$ and $$(N_{out}, D_{in_{dst}})$$.

• edge_weight (torch.Tensor, optional) – Optional tensor on the edge. If given, the convolution will weight with regard to the message.

Returns

The output feature of shape $$(N_{dst}, D_{out})$$ where $$N_{dst}$$ is the number of destination nodes in the input graph, math:D_{out} is size of output feature.

Return type

torch.Tensor

### SGConv¶

class dgl.nn.pytorch.conv.SGConv(in_feats, out_feats, k=1, cached=False, bias=True, norm=None, allow_zero_in_degree=False)[source]

Bases: torch.nn.modules.module.Module

Simplifying Graph Convolution layer from paper Simplifying Graph Convolutional Networks.

$H^{K} = (\tilde{D}^{-1/2} \tilde{A} \tilde{D}^{-1/2})^K X \Theta$

where $$\tilde{A}$$ is $$A$$ + $$I$$. Thus the graph input is expected to have self-loop edges added.

Parameters
• in_feats (int) – Number of input features; i.e, the number of dimensions of $$X$$.

• out_feats (int) – Number of output features; i.e, the number of dimensions of $$H^{K}$$.

• k (int) – Number of hops $$K$$. Defaults:1.

• cached (bool) –

If True, the module would cache

$(\tilde{D}^{-\frac{1}{2}}\tilde{A}\tilde{D}^{-\frac{1}{2}})^K X\Theta$

at the first forward call. This parameter should only be set to True in Transductive Learning setting.

• bias (bool) – If True, adds a learnable bias to the output. Default: True.

• norm (callable activation function/layer or None, optional) – If not None, applies normalization to the updated node features. Default: False.

• allow_zero_in_degree (bool, optional) – If there are 0-in-degree nodes in the graph, output for those nodes will be invalid since no message will be passed to those nodes. This is harmful for some applications causing silent performance regression. This module will raise a DGLError if it detects 0-in-degree nodes in input graph. By setting True, it will suppress the check and let the users handle it by themselves. Default: False.

Note

Zero in-degree nodes will lead to invalid output value. This is because no message will be passed to those nodes, the aggregation function will be appied on empty input. A common practice to avoid this is to add a self-loop for each node in the graph if it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph


Calling add_self_loop will not work for some graphs, for example, heterogeneous graph since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree to True for those cases to unblock the code and handle zero-in-degree nodes manually. A common practise to handle this is to filter out the nodes with zero-in-degree when use after conv.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import SGConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = SGConv(10, 2, k=2, cached=True)
>>> res = conv(g, feat)
>>> res
tensor([[-1.9441, -0.9343],
[-1.9441, -0.9343],
[-1.9441, -0.9343],
[-2.7709, -1.3316],
[-1.9297, -0.9273],

forward(graph, feat)[source]

Compute Simplifying Graph Convolution layer.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor) – The input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes.

Returns

The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is size of output feature.

Return type

torch.Tensor

Raises

DGLError – If there are 0-in-degree nodes in the input graph, it will raise DGLError since no message will be passed to those nodes. This will cause invalid output. The error can be ignored by setting allow_zero_in_degree parameter to True.

Note

If cache is set to True, feat and graph should not change during training, or you will get wrong results.

### APPNPConv¶

class dgl.nn.pytorch.conv.APPNPConv(k, alpha, edge_drop=0.0)[source]

Bases: torch.nn.modules.module.Module

Approximate Personalized Propagation of Neural Predictions layer from paper Predict then Propagate: Graph Neural Networks meet Personalized PageRank.

\begin{align}\begin{aligned}H^{0} &= X\\H^{l+1} &= (1-\alpha)\left(\tilde{D}^{-1/2} \tilde{A} \tilde{D}^{-1/2} H^{l}\right) + \alpha H^{0}\end{aligned}\end{align}

where $$\tilde{A}$$ is $$A$$ + $$I$$.

Parameters
• k (int) – The number of iterations $$K$$.

• alpha (float) – The teleport probability $$\alpha$$.

• edge_drop (float, optional) – The dropout rate on edges that controls the messages received by each node. Default: 0.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import APPNPConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = APPNPConv(k=3, alpha=0.5)
>>> res = conv(g, feat)
>>> res
tensor([[1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000],
[1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000],
[1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000],
[1.0303, 1.0303, 1.0303, 1.0303, 1.0303, 1.0303, 1.0303, 1.0303, 1.0303,
1.0303],
[0.8643, 0.8643, 0.8643, 0.8643, 0.8643, 0.8643, 0.8643, 0.8643, 0.8643,
0.8643],
[0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000,
0.5000]])

forward(graph, feat)[source]

Compute APPNP layer.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor) – The input feature of shape $$(N, *)$$. $$N$$ is the number of nodes, and $$*$$ could be of any shape.

Returns

The output feature of shape $$(N, *)$$ where $$*$$ should be the same as input shape.

Return type

torch.Tensor

### GINConv¶

class dgl.nn.pytorch.conv.GINConv(apply_func, aggregator_type, init_eps=0, learn_eps=False)[source]

Bases: torch.nn.modules.module.Module

Graph Isomorphism Network layer from paper How Powerful are Graph Neural Networks?.

$h_i^{(l+1)} = f_\Theta \left((1 + \epsilon) h_i^{l} + \mathrm{aggregate}\left(\left\{h_j^{l}, j\in\mathcal{N}(i) \right\}\right)\right)$

If a weight tensor on each edge is provided, the weighted graph convolution is defined as:

$h_i^{(l+1)} = f_\Theta \left((1 + \epsilon) h_i^{l} + \mathrm{aggregate}\left(\left\{e_{ji} h_j^{l}, j\in\mathcal{N}(i) \right\}\right)\right)$

where $$e_{ji}$$ is the weight on the edge from node $$j$$ to node $$i$$. Please make sure that e_{ji} is broadcastable with h_j^{l}.

Parameters
• apply_func (callable activation function/layer or None) – If not None, apply this function to the updated node feature, the $$f_\Theta$$ in the formula.

• aggregator_type (str) – Aggregator type to use (sum, max or mean).

• init_eps (float, optional) – Initial $$\epsilon$$ value, default: 0.

• learn_eps (bool, optional) – If True, $$\epsilon$$ will be a learnable parameter. Default: False.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import GINConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> lin = th.nn.Linear(10, 10)
>>> conv = GINConv(lin, 'max')
>>> res = conv(g, feat)
>>> res
tensor([[-0.4821,  0.0207, -0.7665,  0.5721, -0.4682, -0.2134, -0.5236,  1.2855,
0.8843, -0.8764],
[-0.4821,  0.0207, -0.7665,  0.5721, -0.4682, -0.2134, -0.5236,  1.2855,
0.8843, -0.8764],
[-0.4821,  0.0207, -0.7665,  0.5721, -0.4682, -0.2134, -0.5236,  1.2855,
0.8843, -0.8764],
[-0.4821,  0.0207, -0.7665,  0.5721, -0.4682, -0.2134, -0.5236,  1.2855,
0.8843, -0.8764],
[-0.4821,  0.0207, -0.7665,  0.5721, -0.4682, -0.2134, -0.5236,  1.2855,
0.8843, -0.8764],
[-0.1804,  0.0758, -0.5159,  0.3569, -0.1408, -0.1395, -0.2387,  0.7773,

forward(graph, feat, edge_weight=None)[source]

Compute Graph Isomorphism Network layer.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor or pair of torch.Tensor) – If a torch.Tensor is given, the input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes. If a pair of torch.Tensor is given, the pair must contain two tensors of shape $$(N_{in}, D_{in})$$ and $$(N_{out}, D_{in})$$. If apply_func is not None, $$D_{in}$$ should fit the input dimensionality requirement of apply_func.

• edge_weight (torch.Tensor, optional) – Optional tensor on the edge. If given, the convolution will weight with regard to the message.

Returns

The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is the output dimensionality of apply_func. If apply_func is None, $$D_{out}$$ should be the same as input dimensionality.

Return type

torch.Tensor

### GatedGraphConv¶

class dgl.nn.pytorch.conv.GatedGraphConv(in_feats, out_feats, n_steps, n_etypes, bias=True)[source]

Bases: torch.nn.modules.module.Module

Gated Graph Convolution layer from paper Gated Graph Sequence Neural Networks.

\begin{align}\begin{aligned}h_{i}^{0} &= [ x_i \| \mathbf{0} ]\\a_{i}^{t} &= \sum_{j\in\mathcal{N}(i)} W_{e_{ij}} h_{j}^{t}\\h_{i}^{t+1} &= \mathrm{GRU}(a_{i}^{t}, h_{i}^{t})\end{aligned}\end{align}
Parameters
• in_feats (int) – Input feature size; i.e, the number of dimensions of $$x_i$$.

• out_feats (int) – Output feature size; i.e., the number of dimensions of $$h_i^{(t+1)}$$.

• n_steps (int) – Number of recurrent steps; i.e, the $$t$$ in the above formula.

• n_etypes (int) – Number of edge types.

• bias (bool) – If True, adds a learnable bias to the output. Default: True.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import GatedGraphConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = GatedGraphConv(10, 10, 2, 3)
>>> etype = th.tensor([0,1,2,0,1,2])
>>> res = conv(g, feat, etype)
>>> res
tensor([[ 0.4652,  0.4458,  0.5169,  0.4126,  0.4847,  0.2303,  0.2757,  0.7721,
0.0523,  0.0857],
[ 0.0832,  0.1388, -0.5643,  0.7053, -0.2524, -0.3847,  0.7587,  0.8245,
0.9315,  0.4063],
[ 0.6340,  0.4096,  0.7692,  0.2125,  0.2106,  0.4542, -0.0580,  0.3364,
-0.1376,  0.4948],
[ 0.5551,  0.7946,  0.6220,  0.8058,  0.5711,  0.3063, -0.5454,  0.2272,
-0.6931, -0.1607],
[ 0.2644,  0.2469, -0.6143,  0.6008, -0.1516, -0.3781,  0.5878,  0.7993,
0.9241,  0.1835],
[ 0.6393,  0.3447,  0.3893,  0.4279,  0.3342,  0.3809,  0.0406,  0.5030,

forward(graph, feat, etypes=None)[source]

Compute Gated Graph Convolution layer.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor) – The input feature of shape $$(N, D_{in})$$ where $$N$$ is the number of nodes of the graph and $$D_{in}$$ is the input feature size.

• etypes (torch.LongTensor, or None) – The edge type tensor of shape $$(E,)$$ where $$E$$ is the number of edges of the graph. When there’s only one edge type, this argument can be skipped

Returns

The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is the output feature size.

Return type

torch.Tensor

### GMMConv¶

class dgl.nn.pytorch.conv.GMMConv(in_feats, out_feats, dim, n_kernels, aggregator_type='sum', residual=False, bias=True, allow_zero_in_degree=False)[source]

Bases: torch.nn.modules.module.Module

The Gaussian Mixture Model Convolution layer from Geometric Deep Learning on Graphs and Manifolds using Mixture Model CNNs.

\begin{align}\begin{aligned}u_{ij} &= f(x_i, x_j), x_j \in \mathcal{N}(i)\\w_k(u) &= \exp\left(-\frac{1}{2}(u-\mu_k)^T \Sigma_k^{-1} (u - \mu_k)\right)\\h_i^{l+1} &= \mathrm{aggregate}\left(\left\{\frac{1}{K} \sum_{k}^{K} w_k(u_{ij}), \forall j\in \mathcal{N}(i)\right\}\right)\end{aligned}\end{align}

where $$u$$ denotes the pseudo-coordinates between a vertex and one of its neighbor, computed using function $$f$$, $$\Sigma_k^{-1}$$ and $$\mu_k$$ are learnable parameters representing the covariance matrix and mean vector of a Gaussian kernel.

Parameters
• in_feats (int) – Number of input features; i.e., the number of dimensions of $$x_i$$.

• out_feats (int) – Number of output features; i.e., the number of dimensions of $$h_i^{(l+1)}$$.

• dim (int) – Dimensionality of pseudo-coordinte; i.e, the number of dimensions of $$u_{ij}$$.

• n_kernels (int) – Number of kernels $$K$$.

• aggregator_type (str) – Aggregator type (sum, mean, max). Default: sum.

• residual (bool) – If True, use residual connection inside this layer. Default: False.

• bias (bool) – If True, adds a learnable bias to the output. Default: True.

• allow_zero_in_degree (bool, optional) – If there are 0-in-degree nodes in the graph, output for those nodes will be invalid since no message will be passed to those nodes. This is harmful for some applications causing silent performance regression. This module will raise a DGLError if it detects 0-in-degree nodes in input graph. By setting True, it will suppress the check and let the users handle it by themselves. Default: False.

Note

Zero in-degree nodes will lead to invalid output value. This is because no message will be passed to those nodes, the aggregation function will be appied on empty input. A common practice to avoid this is to add a self-loop for each node in the graph if it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph


Calling add_self_loop will not work for some graphs, for example, heterogeneous graph since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree to True for those cases to unblock the code and handle zero-in-degree nodes manually. A common practise to handle this is to filter out the nodes with zero-in-degree when use after conv.

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import GMMConv

>>> # Case 1: Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = GMMConv(10, 2, 3, 2, 'mean')
>>> pseudo = th.ones(12, 3)
>>> res = conv(g, feat, pseudo)
>>> res
tensor([[-0.3462, -0.2654],
[-0.3462, -0.2654],
[-0.3462, -0.2654],
[-0.3462, -0.2654],
[-0.3462, -0.2654],

>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.bipartite((u, v))
>>> u_fea = th.rand(2, 5)
>>> v_fea = th.rand(4, 10)
>>> pseudo = th.ones(5, 3)
>>> conv = GMMConv((10, 5), 2, 3, 2, 'mean')
>>> res = conv(g, (u_fea, v_fea), pseudo)
>>> res
tensor([[-0.1107, -0.1559],
[-0.1646, -0.2326],
[-0.1377, -0.1943],

forward(graph, feat, pseudo)[source]

Compute Gaussian Mixture Model Convolution layer.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor) – If a single tensor is given, the input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes. If a pair of tensors are given, the pair must contain two tensors of shape $$(N_{in}, D_{in_{src}})$$ and $$(N_{out}, D_{in_{dst}})$$.

• pseudo (torch.Tensor) – The pseudo coordinate tensor of shape $$(E, D_{u})$$ where $$E$$ is the number of edges of the graph and $$D_{u}$$ is the dimensionality of pseudo coordinate.

Returns

The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is the output feature size.

Return type

torch.Tensor

Raises

DGLError – If there are 0-in-degree nodes in the input graph, it will raise DGLError since no message will be passed to those nodes. This will cause invalid output. The error can be ignored by setting allow_zero_in_degree parameter to True.

### ChebConv¶

class dgl.nn.pytorch.conv.ChebConv(in_feats, out_feats, k, activation=<function relu>, bias=True)[source]

Bases: torch.nn.modules.module.Module

Chebyshev Spectral Graph Convolution layer from paper Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering.

\begin{align}\begin{aligned}h_i^{l+1} &= \sum_{k=0}^{K-1} W^{k, l}z_i^{k, l}\\Z^{0, l} &= H^{l}\\Z^{1, l} &= \tilde{L} \cdot H^{l}\\Z^{k, l} &= 2 \cdot \tilde{L} \cdot Z^{k-1, l} - Z^{k-2, l}\\\tilde{L} &= 2\left(I - \tilde{D}^{-1/2} \tilde{A} \tilde{D}^{-1/2}\right)/\lambda_{max} - I\end{aligned}\end{align}

where $$\tilde{A}$$ is $$A$$ + $$I$$, $$W$$ is learnable weight.

Parameters
• in_feats (int) – Dimension of input features; i.e, the number of dimensions of $$h_i^{(l)}$$.

• out_feats (int) – Dimension of output features $$h_i^{(l+1)}$$.

• k (int) – Chebyshev filter size $$K$$.

• activation (function, optional) – Activation function. Default ReLu.

• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import ChebConv
>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = ChebConv(10, 2, 2)
>>> res = conv(g, feat)
>>> res
tensor([[ 0.6163, -0.1809],
[ 0.6163, -0.1809],
[ 0.6163, -0.1809],
[ 0.9698, -1.5053],
[ 0.3664,  0.7556],

forward(graph, feat, lambda_max=None)[source]

Compute ChebNet layer.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor) – The input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes.

• lambda_max (list or tensor or None, optional.) –

A list(tensor) with length $$B$$, stores the largest eigenvalue of the normalized laplacian of each individual graph in graph, where $$B$$ is the batch size of the input graph. Default: None.

If None, this method would set the default value to 2. One can use dgl.laplacian_lambda_max() to compute this value.

Returns

The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is size of output feature.

Return type

torch.Tensor

### AGNNConv¶

class dgl.nn.pytorch.conv.AGNNConv(init_beta=1.0, learn_beta=True, allow_zero_in_degree=False)[source]

Bases: torch.nn.modules.module.Module

Attention-based Graph Neural Network layer from paper Attention-based Graph Neural Network for Semi-Supervised Learning.

$H^{l+1} = P H^{l}$

where $$P$$ is computed as:

$P_{ij} = \mathrm{softmax}_i ( \beta \cdot \cos(h_i^l, h_j^l))$

where $$\beta$$ is a single scalar parameter.

Parameters
• init_beta (float, optional) – The $$\beta$$ in the formula, a single scalar parameter.

• learn_beta (bool, optional) – If True, $$\beta$$ will be learnable parameter.

• allow_zero_in_degree (bool, optional) – If there are 0-in-degree nodes in the graph, output for those nodes will be invalid since no message will be passed to those nodes. This is harmful for some applications causing silent performance regression. This module will raise a DGLError if it detects 0-in-degree nodes in input graph. By setting True, it will suppress the check and let the users handle it by themselves. Default: False.

Note

Zero in-degree nodes will lead to invalid output value. This is because no message will be passed to those nodes, the aggregation function will be appied on empty input. A common practice to avoid this is to add a self-loop for each node in the graph if it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph


Calling add_self_loop will not work for some graphs, for example, heterogeneous graph since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree to True for those cases to unblock the code and handle zero-in-degree nodes manually. A common practise to handle this is to filter out the nodes with zero-in-degree when use after conv.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import AGNNConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = AGNNConv()
>>> res = conv(g, feat)
>>> res
tensor([[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]],

forward(graph, feat)[source]

Compute AGNN layer.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor) – The input feature of shape $$(N, *)$$ $$N$$ is the number of nodes, and $$*$$ could be of any shape. If a pair of torch.Tensor is given, the pair must contain two tensors of shape $$(N_{in}, *)$$ and $$(N_{out}, *)$$, the $$*$$ in the later tensor must equal the previous one.

Returns

The output feature of shape $$(N, *)$$ where $$*$$ should be the same as input shape.

Return type

torch.Tensor

Raises

DGLError – If there are 0-in-degree nodes in the input graph, it will raise DGLError since no message will be passed to those nodes. This will cause invalid output. The error can be ignored by setting allow_zero_in_degree parameter to True.

### NNConv¶

class dgl.nn.pytorch.conv.NNConv(in_feats, out_feats, edge_func, aggregator_type='mean', residual=False, bias=True)[source]

Bases: torch.nn.modules.module.Module

Graph Convolution layer introduced in Neural Message Passing for Quantum Chemistry.

$h_{i}^{l+1} = h_{i}^{l} + \mathrm{aggregate}\left(\left\{ f_\Theta (e_{ij}) \cdot h_j^{l}, j\in \mathcal{N}(i) \right\}\right)$

where $$e_{ij}$$ is the edge feature, $$f_\Theta$$ is a function with learnable parameters.

Parameters
• in_feats (int) – Input feature size; i.e, the number of dimensions of $$h_j^{(l)}$$. NNConv can be applied on homogeneous graph and unidirectional bipartite graph. If the layer is to be applied on a unidirectional bipartite graph, in_feats specifies the input feature size on both the source and destination nodes. If a scalar is given, the source and destination node feature size would take the same value.

• out_feats (int) – Output feature size; i.e., the number of dimensions of $$h_i^{(l+1)}$$.

• edge_func (callable activation function/layer) – Maps each edge feature to a vector of shape (in_feats * out_feats) as weight to compute messages. Also is the $$f_\Theta$$ in the formula.

• aggregator_type (str) – Aggregator type to use (sum, mean or max).

• residual (bool, optional) – If True, use residual connection. Default: False.

• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True.

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import NNConv

>>> # Case 1: Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> lin = th.nn.Linear(5, 20)
>>> def edge_func(efeat):
...     return lin(efeat)
>>> efeat = th.ones(6+6, 5)
>>> conv = NNConv(10, 2, edge_func, 'mean')
>>> res = conv(g, feat, efeat)
>>> res
tensor([[-1.5243, -0.2719],
[-1.5243, -0.2719],
[-1.5243, -0.2719],
[-1.5243, -0.2719],
[-1.5243, -0.2719],

>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.bipartite((u, v))
>>> u_feat = th.tensor(np.random.rand(2, 10).astype(np.float32))
>>> v_feat = th.tensor(np.random.rand(4, 10).astype(np.float32))
>>> conv = NNConv(10, 2, edge_func, 'mean')
>>> efeat = th.ones(5, 5)
>>> res = conv(g, (u_feat, v_feat), efeat)
>>> res
tensor([[-0.6568,  0.5042],
[ 0.9089, -0.5352],
[ 0.1261, -0.0155],

forward(graph, feat, efeat)[source]

Compute MPNN Graph Convolution layer.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor or pair of torch.Tensor) – The input feature of shape $$(N, D_{in})$$ where $$N$$ is the number of nodes of the graph and $$D_{in}$$ is the input feature size.

• efeat (torch.Tensor) – The edge feature of shape $$(E, *)$$, which should fit the input shape requirement of edge_func. $$E$$ is the number of edges of the graph.

Returns

The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is the output feature size.

Return type

torch.Tensor

### AtomicConv¶

class dgl.nn.pytorch.conv.AtomicConv(interaction_cutoffs, rbf_kernel_means, rbf_kernel_scaling, features_to_use=None)[source]

Bases: torch.nn.modules.module.Module

Atomic Convolution Layer from paper Atomic Convolutional Networks for Predicting Protein-Ligand Binding Affinity.

Denoting the type of atom $$i$$ by $$z_i$$ and the distance between atom $$i$$ and $$j$$ by $$r_{ij}$$.

Distance Transformation

An atomic convolution layer first transforms distances with radial filters and then perform a pooling operation.

For radial filter indexed by $$k$$, it projects edge distances with

$h_{ij}^{k} = \exp(-\gamma_{k}|r_{ij}-r_{k}|^2)$

If $$r_{ij} < c_k$$,

$f_{ij}^{k} = 0.5 * \cos(\frac{\pi r_{ij}}{c_k} + 1),$

else,

$f_{ij}^{k} = 0.$

Finally,

$e_{ij}^{k} = h_{ij}^{k} * f_{ij}^{k}$

Aggregation

For each type $$t$$, each atom collects distance information from all neighbor atoms of type $$t$$:

$p_{i, t}^{k} = \sum_{j\in N(i)} e_{ij}^{k} * 1(z_j == t)$

Then concatenate the results for all RBF kernels and atom types.

Parameters
• interaction_cutoffs (float32 tensor of shape (K)) – $$c_k$$ in the equations above. Roughly they can be considered as learnable cutoffs and two atoms are considered as connected if the distance between them is smaller than the cutoffs. K for the number of radial filters.

• rbf_kernel_means (float32 tensor of shape (K)) – $$r_k$$ in the equations above. K for the number of radial filters.

• rbf_kernel_scaling (float32 tensor of shape (K)) – $$\gamma_k$$ in the equations above. K for the number of radial filters.

• features_to_use (None or float tensor of shape (T)) – In the original paper, these are atomic numbers to consider, representing the types of atoms. T for the number of types of atomic numbers. Default to None.

Note

• This convolution operation is designed for molecular graphs in Chemistry, but it might be possible to extend it to more general graphs.

• There seems to be an inconsistency about the definition of $$e_{ij}^{k}$$ in the paper and the author’s implementation. We follow the author’s implementation. In the paper, $$e_{ij}^{k}$$ was defined as $$\exp(-\gamma_{k}|r_{ij}-r_{k}|^2 * f_{ij}^{k})$$.

• $$\gamma_{k}$$, $$r_k$$ and $$c_k$$ are all learnable.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import AtomicConv

>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 1)
>>> edist = th.ones(6, 1)
>>> interaction_cutoffs = th.ones(3).float() * 2
>>> rbf_kernel_means = th.ones(3).float()
>>> rbf_kernel_scaling = th.ones(3).float()
>>> conv = AtomicConv(interaction_cutoffs, rbf_kernel_means, rbf_kernel_scaling)
>>> res = conv(g, feat, edist)
>>> res
tensor([[0.5000, 0.5000, 0.5000],
[0.5000, 0.5000, 0.5000],
[0.5000, 0.5000, 0.5000],
[1.0000, 1.0000, 1.0000],
[0.5000, 0.5000, 0.5000],

forward(graph, feat, distances)[source]

Apply the atomic convolution layer.

Parameters
• graph (DGLGraph) – Topology based on which message passing is performed.

• feat (Float32 tensor of shape $$(V, 1)$$) – Initial node features, which are atomic numbers in the paper. $$V$$ for the number of nodes.

• distances (Float32 tensor of shape $$(E, 1)$$) – Distance between end nodes of edges. E for the number of edges.

Returns

Updated node representations. $$V$$ for the number of nodes, $$K$$ for the number of radial filters, and $$T$$ for the number of types of atomic numbers.

Return type

Float32 tensor of shape $$(V, K * T)$$

### CFConv¶

class dgl.nn.pytorch.conv.CFConv(node_in_feats, edge_in_feats, hidden_feats, out_feats)[source]

Bases: torch.nn.modules.module.Module

CFConv in SchNet.

SchNet is introduced in SchNet: A continuous-filter convolutional neural network for modeling quantum interactions.

It combines node and edge features in message passing and updates node representations.

$h_i^{(l+1)} = \sum_{j\in \mathcal{N}(i)} h_j^{l} \circ W^{(l)}e_ij$

where $$\circ$$ represents element-wise multiplication and for $$\text{SPP}$$ :

$\text{SSP}(x) = \frac{1}{\beta} * \log(1 + \exp(\beta * x)) - \log(\text{shift})$
Parameters
• node_in_feats (int) – Size for the input node features $$h_j^{(l)}$$.

• edge_in_feats (int) – Size for the input edge features $$e_ij$$.

• hidden_feats (int) – Size for the hidden representations.

• out_feats (int) – Size for the output representations $$h_j^{(l+1)}$$.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import CFConv
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> nfeat = th.ones(6, 10)
>>> efeat = th.ones(6, 5)
>>> conv = CFConv(10, 5, 3, 2)
>>> res = conv(g, nfeat, efeat)
>>> res
tensor([[-0.1209, -0.2289],
[-0.1209, -0.2289],
[-0.1209, -0.2289],
[-0.1135, -0.2338],
[-0.1209, -0.2289],

forward(g, node_feats, edge_feats)[source]

Performs message passing and updates node representations.

Parameters
• g (DGLGraph) – The graph.

• node_feats (torch.Tensor or pair of torch.Tensor) – The input node features. If a torch.Tensor is given, it represents the input node feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes. If a pair of torch.Tensor is given, which is the case for bipartite graph, the pair must contain two tensors of shape $$(N_{src}, D_{in_{src}})$$ and $$(N_{dst}, D_{in_{dst}})$$ separately for the source and destination nodes.

• edge_feats (torch.Tensor) – The input edge feature of shape $$(E, edge_in_feats)$$ where $$E$$ is the number of edges.

Returns

The output node feature of shape $$(N_{out}, out_feats)$$ where $$N_{out}$$ is the number of destination nodes.

Return type

torch.Tensor

### DotGatConv¶

class dgl.nn.pytorch.conv.DotGatConv(in_feats, out_feats, num_heads, allow_zero_in_degree=False)[source]

Bases: torch.nn.modules.module.Module

Apply dot product version of self attention in GCN.

$h_i^{(l+1)} = \sum_{j\in \mathcal{N}(i)} \alpha_{i, j} h_j^{(l)}$

where $$\alpha_{ij}$$ is the attention score bewteen node $$i$$ and node $$j$$:

\begin{align}\begin{aligned}\alpha_{i, j} &= \mathrm{softmax_i}(e_{ij}^{l})\\e_{ij}^{l} &= ({W_i^{(l)} h_i^{(l)}})^T \cdot {W_j^{(l)} h_j^{(l)}}\end{aligned}\end{align}

where $$W_i$$ and $$W_j$$ transform node $$i$$’s and node $$j$$’s features into the same dimension, so that when compute note features’ similarity, it can use dot-product.

Parameters
• in_feats (int, or pair of ints) – Input feature size; i.e, the number of dimensions of $$h_i^{(l)}$$. DotGatConv can be applied on homogeneous graph and unidirectional bipartite graph. If the layer is to be applied to a unidirectional bipartite graph, in_feats specifies the input feature size on both the source and destination nodes. If a scalar is given, the source and destination node feature size would take the same value.

• out_feats (int) – Output feature size; i.e, the number of dimensions of $$h_i^{(l+1)}$$.

• allow_zero_in_degree (bool, optional) – If there are 0-in-degree nodes in the graph, output for those nodes will be invalid since no message will be passed to those nodes. This is harmful for some applications causing silent performance regression. This module will raise a DGLError if it detects 0-in-degree nodes in input graph. By setting True, it will suppress the check and let the users handle it by themselves. Default: False.

Note

Zero in-degree nodes will lead to invalid output value. This is because no message will be passed to those nodes, the aggregation function will be appied on empty input. A common practice to avoid this is to add a self-loop for each node in the graph if it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph


Calling add_self_loop will not work for some graphs, for example, heterogeneous graph since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree to True for those cases to unblock the code and handle zero-in-degree nodes manually. A common practise to handle this is to filter out the nodes with zero-in-degree when use after conv.

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import DotGatConv

>>> # Case 1: Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> dotgatconv = DotGatConv(10, 2, num_heads=3)
>>> res = dotgatconv(g, feat)
>>> res
tensor([[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],

>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.bipartite((u, v))
>>> u_feat = th.tensor(np.random.rand(2, 5).astype(np.float32))
>>> v_feat = th.tensor(np.random.rand(4, 10).astype(np.float32))
>>> dotgatconv = DotGatConv((5,10), 2, 3)
>>> res = dotgatconv(g, (u_feat, v_feat))
>>> res
tensor([[[-0.6066,  1.0268],
[-0.5945, -0.4801],
[ 0.1594,  0.3825]],
[[ 0.0268,  1.0783],
[ 0.5041, -1.3025],
[ 0.6568,  0.7048]],
[[-0.2688,  1.0543],
[-0.0315, -0.9016],
[ 0.3943,  0.5347]],
[[-0.6066,  1.0268],
[-0.5945, -0.4801],

forward(graph, feat, get_attention=False)[source]

Apply dot product version of self attention in GCN.

Parameters
• graph (DGLGraph or bi_partities graph) – The graph

• feat (torch.Tensor or pair of torch.Tensor) – If a torch.Tensor is given, the input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes. If a pair of torch.Tensor is given, the pair must contain two tensors of shape $$(N_{in}, D_{in_{src}})$$ and $$(N_{out}, D_{in_{dst}})$$.

• get_attention (bool, optional) – Whether to return the attention values. Default to False.

Returns

• torch.Tensor – The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is size of output feature.

• torch.Tensor, optional – The attention values of shape $$(E, 1)$$, where $$E$$ is the number of edges. This is returned only when get_attention is True.

Raises

DGLError – If there are 0-in-degree nodes in the input graph, it will raise DGLError since no message will be passed to those nodes. This will cause invalid output. The error can be ignored by setting allow_zero_in_degree parameter to True.

### TWIRLSConv¶

class dgl.nn.pytorch.conv.TWIRLSConv(input_d, output_d, hidden_d, prop_step, num_mlp_before=1, num_mlp_after=1, norm='none', precond=True, alp=0, lam=1, attention=False, tau=0.2, T=-1, p=1, use_eta=False, attn_bef=False, dropout=0.0, attn_dropout=0.0, inp_dropout=0.0)[source]

Bases: torch.nn.modules.module.Module

Together with iteratively reweighting least squre from paper Graph Neural Networks Inspired by Classical Iterative Algorithms.

Parameters
• input_d (int) – Number of input features.

• output_d (int) – Number of output features.

• hidden_d (int) – Size of hidden layers.

• prop_step (int) – Number of propagation steps

• num_mlp_before (int) – Number of mlp layers before propagation. Default: 1.

• num_mlp_after (int) – Number of mlp layers after propagation. Default: 1.

• norm (str) – The type of norm layers inside mlp layers. Can be 'batch', 'layer' or 'none'. Default: 'none'

• precond (str) – If True, use pre conditioning and unormalized laplacian, else not use pre conditioning and use normalized laplacian. Default: True

• alp (float) – The $$\alpha$$ in paper. If equal to $$0$$, will be automatically decided based on other hyper prameters. Default: 0.

• lam (float) – The $$\lambda$$ in paper. Default: 1.

• attention (bool) – If True, add an attention layer inside propagations. Default: False.

• tau (float) – The $$\tau$$ in paper. Default: 0.2.

• T (float) – The $$T$$ in paper. If < 0, $$T$$ will be set to infty. Default: -1.

• p (float) – The $$p$$ in paper. Default: 1.

• use_eta (bool) – If True, add a learnable weight on each dimension in attention. Default: False.

• attn_bef (bool) – If True, add another attention layer before propagation. Default: False.

• dropout (float) – The dropout rate in mlp layers. Default: 0.0.

• attn_dropout (float) – The dropout rate of attention values. Default: 0.0.

• inp_dropout (float) – The dropout rate on input features. Default: 0.0.

Note

add_self_loop will be automatically called before propagation.

Example

>>> import dgl
>>> from dgl.nn import TWIRLSConv
>>> import torch as th

>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = TWIRLSConv(10, 2, 128, prop_step = 64)
>>> res = conv(g , feat)
>>> res
tensor([[ 0.4556, -2.6692],
[ 0.4556, -2.6692],
[ 0.4556, -2.6692],
[ 1.0112, -5.9241],
[ 0.8011, -4.6935],

forward(graph, feat)[source]

Run TWIRLS forward.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor) – The initial node features.

Returns

The output feature

Return type

torch.Tensor

Note

• Input shape: $$(N, \text{input_d})$$ where $$N$$ is the number of nodes.

• Output shape: $$(N, \text{output_d})$$.

### TWIRLSUnfoldingAndAttention¶

class dgl.nn.pytorch.conv.TWIRLSUnfoldingAndAttention(d, alp, lam, prop_step, attn_aft=-1, tau=0.2, T=-1, p=1, use_eta=False, init_att=False, attn_dropout=0, precond=True)[source]

Bases: torch.nn.modules.module.Module

Combine propagation and attention together.

Parameters
• d (int) – Size of graph feature.

• alp (float) – Step size. $$\alpha$$ in ther paper.

• lam (int) – Coefficient of graph smooth term. $$\lambda$$ in ther paper.

• prop_step (int) – Number of propagation steps

• attn_aft (int) – Where to put attention layer. i.e. number of propagation steps before attention. If set to -1, then no attention.

• tau (float) – The lower thresholding parameter. Correspond to $$\tau$$ in the paper.

• T (float) – The upper thresholding parameter. Correspond to $$T$$ in the paper.

• p (float) – Correspond to $$\rho$$ in the paper..

• use_eta (bool) – If True, learn a weight vector for each dimension when doing attention.

• init_att (bool) – If True, add an extra attention layer before propagation.

• attn_dropout (float) – the dropout rate of attention value. Default: 0.0.

• precond (bool) – If True, use pre-conditioned & reparameterized version propagation (eq.28), else use normalized laplacian (eq.30).

Example

>>> import dgl
>>> from dgl.nn import TWIRLSUnfoldingAndAttention
>>> import torch as th

>>> g = dgl.graph(([0, 1, 2, 3, 2, 5], [1, 2, 3, 4, 0, 3])).add_self_loop()
>>> feat = th.ones(6,5)
>>> prop = TWIRLSUnfoldingAndAttention(10, 1, 1, prop_step=3)
>>> res = prop(g,feat)
>>> res
tensor([[2.5000, 2.5000, 2.5000, 2.5000, 2.5000],
[2.5000, 2.5000, 2.5000, 2.5000, 2.5000],
[2.5000, 2.5000, 2.5000, 2.5000, 2.5000],
[3.7656, 3.7656, 3.7656, 3.7656, 3.7656],
[2.5217, 2.5217, 2.5217, 2.5217, 2.5217],
[4.0000, 4.0000, 4.0000, 4.0000, 4.0000]])

forward(g, X)[source]

Compute forward pass of propagation & attention.

Parameters
• g (DGLGraph) – The graph.

• X (torch.Tensor) – Init features.

Returns

The graph.

Return type

torch.Tensor

### GCN2Conv¶

class dgl.nn.pytorch.conv.GCN2Conv(in_feats, layer, alpha=0.1, lambda_=1, project_initial_features=True, allow_zero_in_degree=False, bias=True, activation=None)[source]

Bases: torch.nn.modules.module.Module

The Graph Convolutional Network via Initial residual and Identity mapping (GCNII) was introduced in “Simple and Deep Graph Convolutional Networks” paper. It is mathematically is defined as follows:

$\mathbf{h}^{(l+1)} =\left( (1 - \alpha)(\mathbf{D}^{-1/2} \mathbf{\hat{A}} \mathbf{D}^{-1/2})\mathbf{h}^{(l)} + \alpha {\mathbf{h}^{(0)}} \right) \left( (1 - \beta_l) \mathbf{I} + \beta_l \mathbf{W} \right)$

where $$\mathbf{\hat{A}}$$ is the adjacency matrix with self-loops, $$\mathbf{D}_{ii} = \sum_{j=0} \mathbf{A}_{ij}$$ is its diagonal degree matrix, $$\mathbf{h}^{(0)}$$ is the initial node features, $$\mathbf{h}^{(l)}$$ is the feature of layer $$l$$, $$\alpha$$ is the fraction of initial node features, and $$\beta_l$$ is the hyperparameter to tune the strength of identity mapping. It is defined by $$\beta_l = \log(\frac{\lambda}{l}+1)\approx\frac{\lambda}{l}$$, where $$\lambda$$ is a hyperparameter. :math: beta ensures that the decay of the weight matrix adaptively increases as we stack more layers.

Parameters
• in_feats (int) – Input feature size; i.e, the number of dimensions of $$h_j^{(l)}$$.

• layer (int) – the index of current layer.

• alpha (float) – The fraction of the initial input features. Default: 0.1

• lambda_ (float) – The hyperparameter to ensure the decay of the weight matrix adaptively increases. Default: 1

• project_initial_features (bool) – Whether to share a weight matrix between initial features and smoothed features. Default: True

• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True.

• activation (callable activation function/layer or None, optional) – If not None, applies an activation function to the updated node features. Default: None.

• allow_zero_in_degree (bool, optional) – If there are 0-in-degree nodes in the graph, output for those nodes will be invalid since no message will be passed to those nodes. This is harmful for some applications causing silent performance regression. This module will raise a DGLError if it detects 0-in-degree nodes in input graph. By setting True, it will suppress the check and let the users handle it by themselves. Default: False.

Note

Zero in-degree nodes will lead to invalid output value. This is because no message will be passed to those nodes, the aggregation function will be appied on empty input. A common practice to avoid this is to add a self-loop for each node in the graph if it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph


Calling add_self_loop will not work for some graphs, for example, heterogeneous graph since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree to True for those cases to unblock the code and handle zero-in-degree nodes manually. A common practise to handle this is to filter out the nodes with zero-in-degree when use after conv.

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import GCN2Conv

>>> # Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 3)
>>> conv1 = GCN2Conv(3, layer=1, alpha=0.5, \
...         project_initial_features=True, allow_zero_in_degree=True)
>>> conv2 = GCN2Conv(3, layer=2, alpha=0.5, \
...         project_initial_features=True, allow_zero_in_degree=True)
>>> res = feat
>>> res = conv1(g, res, feat)
>>> res = conv2(g, res, feat)
>>> print(res)
tensor([[1.3803, 3.3191, 2.9572],
[1.3803, 3.3191, 2.9572],
[1.3803, 3.3191, 2.9572],
[1.4770, 3.8326, 3.2451],
[1.3623, 3.2102, 2.8679],

forward(graph, feat, feat_0)[source]

Compute graph convolution.

Parameters
• graph (DGLGraph) – The graph.

• feat (torch.Tensor) – The input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is the size of input feature and $$N$$ is the number of nodes.

• feat_0 (torch.Tensor) – The initial feature of shape $$(N, D_{in})$$

Returns

The output feature

Return type

torch.Tensor

Raises

DGLError – If there are 0-in-degree nodes in the input graph, it will raise DGLError since no message will be passed to those nodes. This will cause invalid output. The error can be ignored by setting allow_zero_in_degree parameter to True.

Note

• Input shape: $$(N, *, \text{in_feats})$$ where * means any number of additional dimensions, $$N$$ is the number of nodes.

• Output shape: $$(N, *, \text{out_feats})$$ where all but the last dimension are the same shape as the input.

• Weight shape: $$(\text{in_feats}, \text{out_feats})$$.

## Dense Conv Layers¶

### DenseGraphConv¶

class dgl.nn.pytorch.conv.DenseGraphConv(in_feats, out_feats, norm='both', bias=True, activation=None)[source]

Bases: torch.nn.modules.module.Module

Graph Convolutional Network layer where the graph structure is given by an adjacency matrix. We recommend user to use this module when applying graph convolution on dense graphs.

Parameters
• in_feats (int) – Input feature size; i.e, the number of dimensions of $$h_j^{(l)}$$.

• out_feats (int) – Output feature size; i.e., the number of dimensions of $$h_i^{(l+1)}$$.

• norm (str, optional) – How to apply the normalizer. If is ‘right’, divide the aggregated messages by each node’s in-degrees, which is equivalent to averaging the received messages. If is ‘none’, no normalization is applied. Default is ‘both’, where the $$c_{ij}$$ in the paper is applied.

• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True.

• activation (callable activation function/layer or None, optional) – If not None, applies an activation function to the updated node features. Default: None.

Notes

Zero in-degree nodes will lead to all-zero output. A common practice to avoid this is to add a self-loop for each node in the graph, which can be achieved by setting the diagonal of the adjacency matrix to be 1.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import DenseGraphConv
>>>
>>> feat = th.ones(6, 10)
>>> adj = th.tensor([[0., 0., 1., 0., 0., 0.],
...         [1., 0., 0., 0., 0., 0.],
...         [0., 1., 0., 0., 0., 0.],
...         [0., 0., 1., 0., 0., 1.],
...         [0., 0., 0., 1., 0., 0.],
...         [0., 0., 0., 0., 0., 0.]])
>>> conv = DenseGraphConv(10, 2)
>>> res
tensor([[0.2159, 1.9027],
[0.3053, 2.6908],
[0.3053, 2.6908],
[0.3685, 3.2481],
[0.3053, 2.6908],


GraphConv

forward(adj, feat)[source]

Compute (Dense) Graph Convolution layer.

Parameters
• adj (torch.Tensor) – The adjacency matrix of the graph to apply Graph Convolution on, when applied to a unidirectional bipartite graph, adj should be of shape should be of shape $$(N_{out}, N_{in})$$; when applied to a homo graph, adj should be of shape $$(N, N)$$. In both cases, a row represents a destination node while a column represents a source node.

• feat (torch.Tensor) – The input feature.

Returns

The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is size of output feature.

Return type

torch.Tensor

### DenseSAGEConv¶

class dgl.nn.pytorch.conv.DenseSAGEConv(in_feats, out_feats, feat_drop=0.0, bias=True, norm=None, activation=None)[source]

Bases: torch.nn.modules.module.Module

GraphSAGE layer where the graph structure is given by an adjacency matrix. We recommend to use this module when appying GraphSAGE on dense graphs.

Note that we only support gcn aggregator in DenseSAGEConv.

Parameters
• in_feats (int) – Input feature size; i.e, the number of dimensions of $$h_i^{(l)}$$.

• out_feats (int) – Output feature size; i.e, the number of dimensions of $$h_i^{(l+1)}$$.

• feat_drop (float, optional) – Dropout rate on features. Default: 0.

• bias (bool) – If True, adds a learnable bias to the output. Default: True.

• norm (callable activation function/layer or None, optional) – If not None, applies normalization to the updated node features.

• activation (callable activation function/layer or None, optional) – If not None, applies an activation function to the updated node features. Default: None.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import DenseSAGEConv
>>>
>>> feat = th.ones(6, 10)
>>> adj = th.tensor([[0., 0., 1., 0., 0., 0.],
...         [1., 0., 0., 0., 0., 0.],
...         [0., 1., 0., 0., 0., 0.],
...         [0., 0., 1., 0., 0., 1.],
...         [0., 0., 0., 1., 0., 0.],
...         [0., 0., 0., 0., 0., 0.]])
>>> conv = DenseSAGEConv(10, 2)
>>> res
tensor([[1.0401, 2.1008],
[1.0401, 2.1008],
[1.0401, 2.1008],
[1.0401, 2.1008],
[1.0401, 2.1008],


SAGEConv

forward(adj, feat)[source]

Compute (Dense) Graph SAGE layer.

Parameters
• adj (torch.Tensor) – The adjacency matrix of the graph to apply SAGE Convolution on, when applied to a unidirectional bipartite graph, adj should be of shape should be of shape $$(N_{out}, N_{in})$$; when applied to a homo graph, adj should be of shape $$(N, N)$$. In both cases, a row represents a destination node while a column represents a source node.

• feat (torch.Tensor or a pair of torch.Tensor) – If a torch.Tensor is given, the input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes. If a pair of torch.Tensor is given, the pair must contain two tensors of shape $$(N_{in}, D_{in})$$ and $$(N_{out}, D_{in})$$.

Returns

The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is size of output feature.

Return type

torch.Tensor

### DenseChebConv¶

class dgl.nn.pytorch.conv.DenseChebConv(in_feats, out_feats, k, bias=True)[source]

Bases: torch.nn.modules.module.Module

Chebyshev Spectral Graph Convolution layer from paper Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering.

We recommend to use this module when applying ChebConv on dense graphs.

Parameters
• in_feats (int) – Dimension of input features $$h_i^{(l)}$$.

• out_feats (int) – Dimension of output features $$h_i^{(l+1)}$$.

• k (int) – Chebyshev filter size.

• activation (function, optional) – Activation function, default is ReLu.

• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True.

Example

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import DenseChebConv
>>>
>>> feat = th.ones(6, 10)
>>> adj = th.tensor([[0., 0., 1., 0., 0., 0.],
...         [1., 0., 0., 0., 0., 0.],
...         [0., 1., 0., 0., 0., 0.],
...         [0., 0., 1., 0., 0., 1.],
...         [0., 0., 0., 1., 0., 0.],
...         [0., 0., 0., 0., 0., 0.]])
>>> conv = DenseChebConv(10, 2, 2)
>>> res
tensor([[-3.3516, -2.4797],
[-3.3516, -2.4797],
[-3.3516, -2.4797],
[-4.5192, -3.0835],
[-2.5259, -2.0527],


ChebConv

forward(adj, feat, lambda_max=None)[source]

Compute (Dense) Chebyshev Spectral Graph Convolution layer.

Parameters
• adj (torch.Tensor) – The adjacency matrix of the graph to apply Graph Convolution on, should be of shape $$(N, N)$$, where a row represents the destination and a column represents the source.

• feat (torch.Tensor) – The input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes.

• lambda_max (float or None, optional) – A float value indicates the largest eigenvalue of given graph. Default: None.

Returns

The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is size of output feature.

Return type

torch.Tensor

## Global Pooling Layers¶

Torch modules for graph global pooling.

### SumPooling¶

class dgl.nn.pytorch.glob.SumPooling[source]

Bases: torch.nn.modules.module.Module

Apply sum pooling over the nodes in a graph .

$r^{(i)} = \sum_{k=1}^{N_i} x^{(i)}_k$

Notes

Input: Could be one graph, or a batch of graphs. If using a batch of graphs, make sure nodes in all graphs have the same feature size, and concatenate nodes’ feature together as the input.

Examples

The following example uses PyTorch backend.

>>> import dgl
>>> import torch as th
>>> from dgl.nn import SumPooling
>>>
>>> g1 = dgl.rand_graph(3, 4)  # g1 is a random graph with 3 nodes and 4 edges
>>> g1_node_feats = th.rand(3, 5)  # feature size is 5
>>> g1_node_feats
tensor([[0.8948, 0.0699, 0.9137, 0.7567, 0.3637],
[0.8137, 0.8938, 0.8377, 0.4249, 0.6118],
[0.5197, 0.9030, 0.6825, 0.5725, 0.4755]])
>>>
>>> g2 = dgl.rand_graph(4, 6)  # g2 is a random graph with 4 nodes and 6 edges
>>> g2_node_feats = th.rand(4, 5)  # feature size is 5
>>> g2_node_feats
tensor([[0.2053, 0.2426, 0.4111, 0.9028, 0.5658],
[0.5278, 0.6365, 0.9990, 0.2351, 0.8945],
[0.3134, 0.0580, 0.4349, 0.7949, 0.3891],
[0.0142, 0.2709, 0.3330, 0.8521, 0.6925]])
>>>
>>> sumpool = SumPooling()  # create a sum pooling layer


Case 1: Input a single graph

>>> sumpool(g1, g1_node_feats)
tensor([[2.2282, 1.8667, 2.4338, 1.7540, 1.4511]])


Case 2: Input a batch of graphs

Build a batch of DGL graphs and concatenate all graphs’ node features into one tensor.

>>> batch_g = dgl.batch([g1, g2])
>>> batch_f = th.cat([g1_node_feats, g2_node_feats])
>>>
>>> sumpool(batch_g, batch_f)
tensor([[2.2282, 1.8667, 2.4338, 1.7540, 1.4511],
[1.0608, 1.2080, 2.1780, 2.7849, 2.5420]])

forward(graph, feat)[source]

Compute sum pooling.

Parameters
• graph (DGLGraph) – a DGLGraph or a batch of DGLGraphs

• feat (torch.Tensor) – The input feature with shape $$(N, D)$$, where $$N$$ is the number of nodes in the graph, and $$D$$ means the size of features.

Returns

The output feature with shape $$(B, D)$$, where $$B$$ refers to the batch size of input graphs.

Return type

torch.Tensor

### AvgPooling¶

class dgl.nn.pytorch.glob.AvgPooling[source]

Bases: torch.nn.modules.module.Module

Apply average pooling over the nodes in a graph.

$r^{(i)} = \frac{1}{N_i}\sum_{k=1}^{N_i} x^{(i)}_k$

Notes

Input: Could be one graph, or a batch of graphs. If using a batch of graphs, make sure nodes in all graphs have the same feature size, and concatenate nodes’ feature together as the input.

Examples

The following example uses PyTorch backend.

>>> import dgl
>>> import torch as th
>>> from dgl.nn import AvgPooling
>>>
>>> g1 = dgl.rand_graph(3, 4)  # g1 is a random graph with 3 nodes and 4 edges
>>> g1_node_feats = th.rand(3, 5)  # feature size is 5
>>> g1_node_feats
tensor([[0.8948, 0.0699, 0.9137, 0.7567, 0.3637],
[0.8137, 0.8938, 0.8377, 0.4249, 0.6118],
[0.5197, 0.9030, 0.6825, 0.5725, 0.4755]])
>>>
>>> g2 = dgl.rand_graph(4, 6)  # g2 is a random graph with 4 nodes and 6 edges
>>> g2_node_feats = th.rand(4, 5)  # feature size is 5
>>> g2_node_feats
tensor([[0.2053, 0.2426, 0.4111, 0.9028, 0.5658],
[0.5278, 0.6365, 0.9990, 0.2351, 0.8945],
[0.3134, 0.0580, 0.4349, 0.7949, 0.3891],
[0.0142, 0.2709, 0.3330, 0.8521, 0.6925]])
>>>
>>> avgpool = AvgPooling()  # create an average pooling layer


Case 1: Input single graph

>>> avgpool(g1, g1_node_feats)
tensor([[0.7427, 0.6222, 0.8113, 0.5847, 0.4837]])


Case 2: Input a batch of graphs

Build a batch of DGL graphs and concatenate all graphs’ note features into one tensor.

>>> batch_g = dgl.batch([g1, g2])
>>> batch_f = th.cat([g1_node_feats, g2_node_feats])
>>>
>>> avgpool(batch_g, batch_f)
tensor([[0.7427, 0.6222, 0.8113, 0.5847, 0.4837],
[0.2652, 0.3020, 0.5445, 0.6962, 0.6355]])

forward(graph, feat)[source]

Compute average pooling.

Parameters
• graph (DGLGraph) – A DGLGraph or a batch of DGLGraphs.

• feat (torch.Tensor) – The input feature with shape $$(N, D)$$, where $$N$$ is the number of nodes in the graph, and $$D$$ means the size of features.

Returns

The output feature with shape $$(B, D)$$, where $$B$$ refers to the batch size of input graphs.

Return type

torch.Tensor

### MaxPooling¶

class dgl.nn.pytorch.glob.MaxPooling[source]

Bases: torch.nn.modules.module.Module

Apply max pooling over the nodes in a graph.

$r^{(i)} = \max_{k=1}^{N_i}\left( x^{(i)}_k \right)$

Notes

Input: Could be one graph, or a batch of graphs. If using a batch of graphs, make sure nodes in all graphs have the same feature size, and concatenate nodes’ feature together as the input.

Examples

The following example uses PyTorch backend.

>>> import dgl
>>> import torch as th
>>> from dgl.nn import MaxPooling
>>>
>>> g1 = dgl.rand_graph(3, 4)  # g1 is a random graph with 3 nodes and 4 edges
>>> g1_node_feats = th.rand(3, 5)  # feature size is 5
>>> g1_node_feats
tensor([[0.8948, 0.0699, 0.9137, 0.7567, 0.3637],
[0.8137, 0.8938, 0.8377, 0.4249, 0.6118],
[0.5197, 0.9030, 0.6825, 0.5725, 0.4755]])
>>>
>>> g2 = dgl.rand_graph(4, 6)  # g2 is a random graph with 4 nodes and 6 edges
>>> g2_node_feats = th.rand(4, 5)  # feature size is 5
>>> g2_node_feats
tensor([[0.2053, 0.2426, 0.4111, 0.9028, 0.5658],
[0.5278, 0.6365, 0.9990, 0.2351, 0.8945],
[0.3134, 0.0580, 0.4349, 0.7949, 0.3891],
[0.0142, 0.2709, 0.3330, 0.8521, 0.6925]])
>>>
>>> maxpool = MaxPooling()  # create a max pooling layer


Case 1: Input a single graph

>>> maxpool(g1, g1_node_feats)
tensor([[0.8948, 0.9030, 0.9137, 0.7567, 0.6118]])


Case 2: Input a batch of graphs

Build a batch of DGL graphs and concatenate all graphs’ node features into one tensor.

>>> batch_g = dgl.batch([g1, g2])
>>> batch_f = th.cat([g1_node_feats, g2_node_feats])
>>>
>>> maxpool(batch_g, batch_f)
tensor([[0.8948, 0.9030, 0.9137, 0.7567, 0.6118],
[0.5278, 0.6365, 0.9990, 0.9028, 0.8945]])

forward(graph, feat)[source]

Compute max pooling.

Parameters
• graph (DGLGraph) – A DGLGraph or a batch of DGLGraphs.

• feat (torch.Tensor) – The input feature with shape $$(N, *)$$, where $$N$$ is the number of nodes in the graph.

Returns

The output feature with shape $$(B, *)$$, where $$B$$ refers to the batch size.

Return type

torch.Tensor

### SortPooling¶

class dgl.nn.pytorch.glob.SortPooling(k)[source]

Bases: torch.nn.modules.module.Module

Apply Sort Pooling (An End-to-End Deep Learning Architecture for Graph Classification) over the nodes in a graph. Sort Pooling first sorts the node features in ascending order along the feature dimension, and selects the sorted features of top-k nodes (ranked by the largest value of each node).

Parameters

k (int) – The number of nodes to hold for each graph.

Notes

Input: Could be one graph, or a batch of graphs. If using a batch of graphs, make sure nodes in all graphs have the same feature size, and concatenate nodes’ feature together as the input.

Examples

>>> import dgl
>>> import torch as th
>>> from dgl.nn import SortPooling
>>>
>>> g1 = dgl.rand_graph(3, 4)  # g1 is a random graph with 3 nodes and 4 edges
>>> g1_node_feats = th.rand(3, 5)  # feature size is 5
>>> g1_node_feats
tensor([[0.8948, 0.0699, 0.9137, 0.7567, 0.3637],
[0.8137, 0.8938, 0.8377, 0.4249, 0.6118],
[0.5197, 0.9030, 0.6825, 0.5725, 0.4755]])
>>>
>>> g2 = dgl.rand_graph(4, 6)  # g2 is a random graph with 4 nodes and 6 edges
>>> g2_node_feats = th.rand(4, 5)  # feature size is 5
>>> g2_node_feats
tensor([[0.2053, 0.2426, 0.4111, 0.9028, 0.5658],
[0.5278, 0.6365, 0.9990, 0.2351, 0.8945],
[0.3134, 0.0580, 0.4349, 0.7949, 0.3891],
[0.0142, 0.2709, 0.3330, 0.8521, 0.6925]])
>>>
>>> sortpool = SortPooling(k=2)  # create a sort pooling layer


Case 1: Input a single graph

>>> sortpool(g1, g1_node_feats)
tensor([[0.0699, 0.3637, 0.7567, 0.8948, 0.9137, 0.4755, 0.5197, 0.5725, 0.6825,
0.9030]])


Case 2: Input a batch of graphs

Build a batch of DGL graphs and concatenate all graphs’ node features into one tensor.

>>> batch_g = dgl.batch([g1, g2])
>>> batch_f = th.cat([g1_node_feats, g2_node_feats])
>>>
>>> sortpool(batch_g, batch_f)
tensor([[0.0699, 0.3637, 0.7567, 0.8948, 0.9137, 0.4755, 0.5197, 0.5725, 0.6825,
0.9030],
[0.2351, 0.5278, 0.6365, 0.8945, 0.9990, 0.2053, 0.2426, 0.4111, 0.5658,
0.9028]])

forward(graph, feat)[source]

Compute sort pooling.

Parameters
• graph (DGLGraph) – A DGLGraph or a batch of DGLGraphs.

• feat (torch.Tensor) – The input feature with shape $$(N, D)$$, where $$N$$ is the number of nodes in the graph, and $$D$$ means the size of features.

Returns

The output feature with shape $$(B, k * D)$$, where $$B$$ refers to the batch size of input graphs.

Return type

torch.Tensor

### WeightAndSum¶

class dgl.nn.pytorch.glob.WeightAndSum(in_feats)[source]

Bases: torch.nn.modules.module.Module

Compute importance weights for atoms and perform a weighted sum.

Parameters

in_feats (int) – Input atom feature size

Examples

The following example uses PyTorch backend.

>>> import dgl
>>> import torch as th
>>> from dgl.nn import WeightAndSum
>>>
>>> g1 = dgl.rand_graph(3, 4)  # g1 is a random graph with 3 nodes and 4 edges
>>> g1_node_feats = th.rand(3, 5)  # feature size is 5
>>> g1_node_feats
tensor([[0.8948, 0.0699, 0.9137, 0.7567, 0.3637],
[0.8137, 0.8938, 0.8377, 0.4249, 0.6118],
[0.5197, 0.9030, 0.6825, 0.5725, 0.4755]])
>>>
>>> g2 = dgl.rand_graph(4, 6)  # g2 is a random graph with 4 nodes and 6 edges
>>> g2_node_feats = th.rand(4, 5)  # feature size is 5
>>> g2_node_feats
tensor([[0.2053, 0.2426, 0.4111, 0.9028, 0.5658],
[0.5278, 0.6365, 0.9990, 0.2351, 0.8945],
[0.3134, 0.0580, 0.4349, 0.7949, 0.3891],
[0.0142, 0.2709, 0.3330, 0.8521, 0.6925]])
>>>
>>> weight_and_sum = WeightAndSum(5)  # create a weight and sum layer(in_feats=16)


Case 1: Input a single graph

>>> weight_and_sum(g1, g1_node_feats)
tensor([[1.2194, 0.9490, 1.3235, 0.9609, 0.7710]],


Case 2: Input a batch of graphs

Build a batch of DGL graphs and concatenate all graphs’ node features into one tensor.

>>> batch_g = dgl.batch([g1, g2])
>>> batch_f = th.cat([g1_node_feats, g2_node_feats])
>>>
>>> weight_and_sum(batch_g, batch_f)
tensor([[1.2194, 0.9490, 1.3235, 0.9609, 0.7710],
[0.5322, 0.5840, 1.0729, 1.3665, 1.2360]],


Notes

WeightAndSum module was commonly used in molecular property prediction networks, see the GCN predictor in dgl-lifesci to understand how to use WeightAndSum layer to get the graph readout output.

forward(g, feats)[source]

Compute molecule representations out of atom representations

Parameters
• g (DGLGraph) – DGLGraph with batch size B for processing multiple molecules in parallel

• feats (FloatTensor of shape (N, self.in_feats)) – Representations for all atoms in the molecules * N is the total number of atoms in all molecules

Returns

Representations for B molecules

Return type

FloatTensor of shape (B, self.in_feats)

### GlobalAttentionPooling¶

class dgl.nn.pytorch.glob.GlobalAttentionPooling(gate_nn, feat_nn=None)[source]

Bases: torch.nn.modules.module.Module

Apply Global Attention Pooling (Gated Graph Sequence Neural Networks) over the nodes in a graph.

$r^{(i)} = \sum_{k=1}^{N_i}\mathrm{softmax}\left(f_{gate} \left(x^{(i)}_k\right)\right) f_{feat}\left(x^{(i)}_k\right)$
Parameters
• gate_nn (torch.nn.Module) – A neural network that computes attention scores for each feature.

• feat_nn (torch.nn.Module, optional) – A neural network applied to each feature before combining them with attention scores.

Examples

The following example uses PyTorch backend.

>>> import dgl
>>> import torch as th
>>> from dgl.nn import GlobalAttentionPooling
>>>
>>> g1 = dgl.rand_graph(3, 4)  # g1 is a random graph with 3 nodes and 4 edges
>>> g1_node_feats = th.rand(3, 5)  # feature size is 5
>>> g1_node_feats
tensor([[0.8948, 0.0699, 0.9137, 0.7567, 0.3637],
[0.8137, 0.8938, 0.8377, 0.4249, 0.6118],
[0.5197, 0.9030, 0.6825, 0.5725, 0.4755]])
>>>
>>> g2 = dgl.rand_graph(4, 6)  # g2 is a random graph with 4 nodes and 6 edges
>>> g2_node_feats = th.rand(4, 5)  # feature size is 5
>>> g2_node_feats
tensor([[0.2053, 0.2426, 0.4111, 0.9028, 0.5658],
[0.5278, 0.6365, 0.9990, 0.2351, 0.8945],
[0.3134, 0.0580, 0.4349, 0.7949, 0.3891],
[0.0142, 0.2709, 0.3330, 0.8521, 0.6925]])
>>>
>>> gate_nn = th.nn.Linear(5, 1)  # the gate layer that maps node feature to scalar
>>> gap = GlobalAttentionPooling(gate_nn)  # create a Global Attention Pooling layer


Case 1: Input a single graph

>>> gap(g1, g1_node_feats)
tensor([[0.7410, 0.6032, 0.8111, 0.5942, 0.4762]],


Case 2: Input a batch of graphs

Build a batch of DGL graphs and concatenate all graphs’ node features into one tensor.

>>> batch_g = dgl.batch([g1, g2])
>>> batch_f = th.cat([g1_node_feats, g2_node_feats], 0)
>>>
>>> gap(batch_g, batch_f)
tensor([[0.7410, 0.6032, 0.8111, 0.5942, 0.4762],
[0.2417, 0.2743, 0.5054, 0.7356, 0.6146]],


Notes

See our GGNN example on how to use GatedGraphConv and GlobalAttentionPooling layer to build a Graph Neural Networks that can solve Soduku.

forward(graph, feat)[source]

Compute global attention pooling.

Parameters
• graph (DGLGraph) – A DGLGraph or a batch of DGLGraphs.

• feat (torch.Tensor) – The input feature with shape $$(N, D)$$ where $$N$$ is the number of nodes in the graph, and $$D$$ means the size of features.

Returns

The output feature with shape $$(B, D)$$, where $$B$$ refers to the batch size.

Return type

torch.Tensor

### Set2Set¶

class dgl.nn.pytorch.glob.Set2Set(input_dim, n_iters, n_layers)[source]

Bases: torch.nn.modules.module.Module

For each individual graph in the batch, set2set computes

\begin{align}\begin{aligned}q_t &= \mathrm{LSTM} (q^*_{t-1})\\\alpha_{i,t} &= \mathrm{softmax}(x_i \cdot q_t)\\r_t &= \sum_{i=1}^N \alpha_{i,t} x_i\\q^*_t &= q_t \Vert r_t\end{aligned}\end{align}

for this graph.

Parameters
• input_dim (int) – The size of each input sample.

• n_iters (int) – The number of iterations.

• n_layers (int) – The number of recurrent layers.

Examples

The following example uses PyTorch backend.

>>> import dgl
>>> import torch as th
>>> from dgl.nn import Set2Set
>>>
>>> g1 = dgl.rand_graph(3, 4)  # g1 is a random graph with 3 nodes and 4 edges
>>> g1_node_feats = th.rand(3, 5)  # feature size is 5
>>> g1_node_feats
tensor([[0.8948, 0.0699, 0.9137, 0.7567, 0.3637],
[0.8137, 0.8938, 0.8377, 0.4249, 0.6118],
[0.5197, 0.9030, 0.6825, 0.5725, 0.4755]])
>>>
>>> g2 = dgl.rand_graph(4, 6)  # g2 is a random graph with 4 nodes and 6 edges
>>> g2_node_feats = th.rand(4, 5)  # feature size is 5
>>> g2_node_feats
tensor([[0.2053, 0.2426, 0.4111, 0.9028, 0.5658],
[0.5278, 0.6365, 0.9990, 0.2351, 0.8945],
[0.3134, 0.0580, 0.4349, 0.7949, 0.3891],
[0.0142, 0.2709, 0.3330, 0.8521, 0.6925]])
>>>
>>> s2s = Set2Set(5, 2, 1)  # create a Set2Set layer(n_iters=2, n_layers=1)


Case 1: Input a single graph

>>> s2s(g1, g1_node_feats)
tensor([[-0.0235, -0.2291,  0.2654,  0.0376,  0.1349,  0.7560,  0.5822,  0.8199,


Case 2: Input a batch of graphs

Build a batch of DGL graphs and concatenate all graphs’ node features into one tensor.

>>> batch_g = dgl.batch([g1, g2])
>>> batch_f = th.cat([g1_node_feats, g2_node_feats], 0)
>>>
>>> s2s(batch_g, batch_f)
tensor([[-0.0235, -0.2291,  0.2654,  0.0376,  0.1349,  0.7560,  0.5822,  0.8199,
0.5960,  0.4760],
[-0.0483, -0.2010,  0.2324,  0.0145,  0.1361,  0.2703,  0.3078,  0.5529,


Notes

Set2Set is widely used in molecular property predictions, see dgl-lifesci’s MPNN example on how to use DGL’s Set2Set layer in graph property prediction applications.

forward(graph, feat)[source]

Compute set2set pooling.

Parameters
• graph (DGLGraph) – The input graph.

• feat (torch.Tensor) – The input feature with shape $$(N, D)$$ where $$N$$ is the number of nodes in the graph, and $$D$$ means the size of features.

Returns

The output feature with shape $$(B, D)$$, where $$B$$ refers to the batch size, and $$D$$ means the size of features.

Return type

torch.Tensor

### SetTransformerEncoder¶

class dgl.nn.pytorch.glob.SetTransformerEncoder(d_model, n_heads, d_head, d_ff, n_layers=1, block_type='sab', m=None, dropouth=0.0, dropouta=0.0)[source]

Bases: torch.nn.modules.module.Module

The Encoder module in Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks.

Parameters
• d_model (int) – The hidden size of the model.

• d_ff (int) – The kernel size in FFN (Positionwise Feed-Forward Network) layer.

• n_layers (int) – The number of layers.

• block_type (str) – Building block type: ‘sab’ (Set Attention Block) or ‘isab’ (Induced Set Attention Block).

• m (int or None) – The number of induced vectors in ISAB Block. Set to None if block type is ‘sab’.

• dropouth (float) – The dropout rate of each sublayer.

• dropouta (float) – The dropout rate of attention heads.

Examples

>>> import dgl
>>> import torch as th
>>> from dgl.nn import SetTransformerEncoder
>>>
>>> g1 = dgl.rand_graph(3, 4)  # g1 is a random graph with 3 nodes and 4 edges
>>> g1_node_feats = th.rand(3, 5)  # feature size is 5
>>> g1_node_feats
tensor([[0.8948, 0.0699, 0.9137, 0.7567, 0.3637],
[0.8137, 0.8938, 0.8377, 0.4249, 0.6118],
[0.5197, 0.9030, 0.6825, 0.5725, 0.4755]])
>>>
>>> g2 = dgl.rand_graph(4, 6)  # g2 is a random graph with 4 nodes and 6 edges
>>> g2_node_feats = th.rand(4, 5)  # feature size is 5
>>> g2_node_feats
tensor([[0.2053, 0.2426, 0.4111, 0.9028, 0.5658],
[0.5278, 0.6365, 0.9990, 0.2351, 0.8945],
[0.3134, 0.0580, 0.4349, 0.7949, 0.3891],
[0.0142, 0.2709, 0.3330, 0.8521, 0.6925]])
>>>
>>> set_trans_enc = SetTransformerEncoder(5, 4, 4, 20)  # create a settrans encoder.


Case 1: Input a single graph

>>> set_trans_enc(g1, g1_node_feats)
tensor([[ 0.1262, -1.9081,  0.7287,  0.1678,  0.8854],
[-0.0634, -1.1996,  0.6955, -0.9230,  1.4904],
[-0.9972, -0.7924,  0.6907, -0.5221,  1.6211]],


Case 2: Input a batch of graphs

Build a batch of DGL graphs and concatenate all graphs’ node features into one tensor.

>>> batch_g = dgl.batch([g1, g2])
>>> batch_f = th.cat([g1_node_feats, g2_node_feats])
>>>
>>> set_trans_enc(batch_g, batch_f)
tensor([[ 0.1262, -1.9081,  0.7287,  0.1678,  0.8854],
[-0.0634, -1.1996,  0.6955, -0.9230,  1.4904],
[-0.9972, -0.7924,  0.6907, -0.5221,  1.6211],
[-0.7973, -1.3203,  0.0634,  0.5237,  1.5306],
[-0.4497, -1.0920,  0.8470, -0.8030,  1.4977],
[-0.4940, -1.6045,  0.2363,  0.4885,  1.3737],
[-0.9840, -1.0913, -0.0099,  0.4653,  1.6199]],


Notes

SetTransformerEncoder is not a readout layer, the tensor it returned is nodewise representation instead out graphwise representation, and the SetTransformerDecoder would return a graph readout tensor.

forward(graph, feat)[source]

Compute the Encoder part of Set Transformer.

Parameters
• graph (DGLGraph) – The input graph.

• feat (torch.Tensor) – The input feature with shape $$(N, D)$$, where $$N$$ is the number of nodes in the graph.

Returns

The output feature with shape $$(N, D)$$.

Return type

torch.Tensor

### SetTransformerDecoder¶

class dgl.nn.pytorch.glob.SetTransformerDecoder(d_model, num_heads, d_head, d_ff, n_layers, k, dropouth=0.0, dropouta=0.0)[source]

Bases: torch.nn.modules.module.Module

The Decoder module in Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks.

Parameters
• d_model (int) – Hidden size of the model.

• d_ff (int) – Kernel size in FFN (Positionwise Feed-Forward Network) layer.

• n_layers (int) – The number of layers.

• k (int) – The number of seed vectors in PMA (Pooling by Multihead Attention) layer.

• dropouth (float) – Dropout rate of each sublayer.

• dropouta (float) – Dropout rate of attention heads.

Examples

>>> import dgl
>>> import torch as th
>>> from dgl.nn import SetTransformerDecoder
>>>
>>> g1 = dgl.rand_graph(3, 4)  # g1 is a random graph with 3 nodes and 4 edges
>>> g1_node_feats = th.rand(3, 5)  # feature size is 5
>>> g1_node_feats
tensor([[0.8948, 0.0699, 0.9137, 0.7567, 0.3637],
[0.8137, 0.8938, 0.8377, 0.4249, 0.6118],
[0.5197, 0.9030, 0.6825, 0.5725, 0.4755]])
>>>
>>> g2 = dgl.rand_graph(4, 6)  # g2 is a random graph with 4 nodes and 6 edges
>>> g2_node_feats = th.rand(4, 5)  # feature size is 5
>>> g2_node_feats
tensor([[0.2053, 0.2426, 0.4111, 0.9028, 0.5658],
[0.5278, 0.6365, 0.9990, 0.2351, 0.8945],
[0.3134, 0.0580, 0.4349, 0.7949, 0.3891],
[0.0142, 0.2709, 0.3330, 0.8521, 0.6925]])
>>>
>>> set_trans_dec = SetTransformerDecoder(5, 4, 4, 20, 1, 3)  # define the layer


Case 1: Input a single graph

>>> set_trans_dec(g1, g1_node_feats)
tensor([[-0.5538,  1.8726, -1.0470,  0.0276, -0.2994, -0.6317,  1.6754, -1.3189,
0.2291,  0.0461, -0.4042,  0.8387, -1.7091,  1.0845,  0.1902]],


Case 2: Input a batch of graphs

Build a batch of DGL graphs and concatenate all graphs’ node features into one tensor.

>>> batch_g = dgl.batch([g1, g2])
>>> batch_f = th.cat([g1_node_feats, g2_node_feats])
>>>
>>> set_trans_dec(batch_g, batch_f)
tensor([[-0.5538,  1.8726, -1.0470,  0.0276, -0.2994, -0.6317,  1.6754, -1.3189,
0.2291,  0.0461, -0.4042,  0.8387, -1.7091,  1.0845,  0.1902],
[-0.5511,  1.8869, -1.0156,  0.0028, -0.3231, -0.6305,  1.6845, -1.3105,
0.2136,  0.0428, -0.3820,  0.8043, -1.7138,  1.1126,  0.1789]],

forward(graph, feat)[source]

Compute the decoder part of Set Transformer.

Parameters
• graph (DGLGraph) – The input graph.

• feat (torch.Tensor) – The input feature with shape $$(N, D)$$, where $$N$$ is the number of nodes in the graph, and $$D$$ means the size of features.

Returns

The output feature with shape $$(B, D)$$, where $$B$$ refers to the batch size.

Return type

torch.Tensor

## Heterogeneous Graph Convolution Module¶

### HeteroGraphConv¶

class dgl.nn.pytorch.HeteroGraphConv(mods, aggregate='sum')[source]

Bases: torch.nn.modules.module.Module

A generic module for computing convolution on heterogeneous graphs.

The heterograph convolution applies sub-modules on their associating relation graphs, which reads the features from source nodes and writes the updated ones to destination nodes. If multiple relations have the same destination node types, their results are aggregated by the specified method. If the relation graph has no edge, the corresponding module will not be called.

Pseudo-code:

outputs = {nty : [] for nty in g.dsttypes}
# Apply sub-modules on their associating relation graphs in parallel
for relation in g.canonical_etypes:
stype, etype, dtype = relation
dstdata = relation_submodule(g[relation], ...)
outputs[dtype].append(dstdata)

# Aggregate the results for each destination node type
rsts = {}
for ntype, ntype_outputs in outputs.items():
if len(ntype_outputs) != 0:
rsts[ntype] = aggregate(ntype_outputs)
return rsts


Examples

Create a heterograph with three types of relations and nodes.

>>> import dgl
>>> g = dgl.heterograph({
...     ('user', 'follows', 'user') : edges1,
...     ('user', 'plays', 'game') : edges2,
...     ('store', 'sells', 'game')  : edges3})


Create a HeteroGraphConv that applies different convolution modules to different relations. Note that the modules for 'follows' and 'plays' do not share weights.

>>> import dgl.nn.pytorch as dglnn
>>> conv = dglnn.HeteroGraphConv({
...     'follows' : dglnn.GraphConv(...),
...     'plays' : dglnn.GraphConv(...),
...     'sells' : dglnn.SAGEConv(...)},
...     aggregate='sum')


Call forward with some 'user' features. This computes new features for both 'user' and 'game' nodes.

>>> import torch as th
>>> h1 = {'user' : th.randn((g.number_of_nodes('user'), 5))}
>>> h2 = conv(g, h1)
>>> print(h2.keys())
dict_keys(['user', 'game'])


Call forward with both 'user' and 'store' features. Because both the 'plays' and 'sells' relations will update the 'game' features, their results are aggregated by the specified method (i.e., summation here).

>>> f1 = {'user' : ..., 'store' : ...}
>>> f2 = conv(g, f1)
>>> print(f2.keys())
dict_keys(['user', 'game'])


Call forward with some 'store' features. This only computes new features for 'game' nodes.

>>> g1 = {'store' : ...}
>>> g2 = conv(g, g1)
>>> print(g2.keys())
dict_keys(['game'])


Call forward with a pair of inputs is allowed and each submodule will also be invoked with a pair of inputs.

>>> x_src = {'user' : ..., 'store' : ...}
>>> x_dst = {'user' : ..., 'game' : ...}
>>> y_dst = conv(g, (x_src, x_dst))
>>> print(y_dst.keys())
dict_keys(['user', 'game'])

Parameters
• mods (dict[str, nn.Module]) – Modules associated with every edge types. The forward function of each module must have a DGLHeteroGraph object as the first argument, and its second argument is either a tensor object representing the node features or a pair of tensor object representing the source and destination node features.

• aggregate (str, callable, optional) –

Method for aggregating node features generated by different relations. Allowed string values are ‘sum’, ‘max’, ‘min’, ‘mean’, ‘stack’. The ‘stack’ aggregation is performed along the second dimension, whose order is deterministic. User can also customize the aggregator by providing a callable instance. For example, aggregation by summation is equivalent to the follows:

def my_agg_func(tensors, dsttype):
# tensors: is a list of tensors to aggregate
# dsttype: string name of the destination node type for which the
#          aggregation is performed
stacked = torch.stack(tensors, dim=0)


mods

Modules associated with every edge types.

Type

dict[str, nn.Module]

forward(g, inputs, mod_args=None, mod_kwargs=None)[source]

Forward computation

Invoke the forward function with each module and aggregate their results.

Parameters
• g (DGLHeteroGraph) – Graph data.

• inputs (dict[str, Tensor] or pair of dict[str, Tensor]) – Input node features.

• mod_args (dict[str, tuple[any]], optional) – Extra positional arguments for the sub-modules.

• mod_kwargs (dict[str, dict[str, any]], optional) – Extra key-word arguments for the sub-modules.

Returns

Output representations for every types of nodes.

Return type

dict[str, Tensor]

## Utility Modules¶

### Sequential¶

class dgl.nn.pytorch.utils.Sequential(*args)[source]

Bases: torch.nn.modules.container.Sequential

A sequential container for stacking graph neural network modules.

DGL supports two modes: sequentially apply GNN modules on 1) the same graph or 2) a list of given graphs. In the second case, the number of graphs equals the number of modules inside this container.

Parameters

*args – Sub-modules of torch.nn.Module that will be added to the container in the order by which they are passed in the constructor.

Examples

The following example uses PyTorch backend.

Mode 1: sequentially apply GNN modules on the same graph

>>> import torch
>>> import dgl
>>> import torch.nn as nn
>>> import dgl.function as fn
>>> from dgl.nn.pytorch import Sequential
>>> class ExampleLayer(nn.Module):
>>>     def __init__(self):
>>>         super().__init__()
>>>     def forward(self, graph, n_feat, e_feat):
>>>         with graph.local_scope():
>>>             graph.ndata['h'] = n_feat
>>>             graph.update_all(fn.copy_u('h', 'm'), fn.sum('m', 'h'))
>>>             n_feat += graph.ndata['h']
>>>             e_feat += graph.edata['e']
>>>             return n_feat, e_feat
>>>
>>> g = dgl.DGLGraph()
>>> g.add_edges([0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2])
>>> net = Sequential(ExampleLayer(), ExampleLayer(), ExampleLayer())
>>> n_feat = torch.rand(3, 4)
>>> e_feat = torch.rand(9, 4)
>>> net(g, n_feat, e_feat)
(tensor([[39.8597, 45.4542, 25.1877, 30.8086],
[40.7095, 45.3985, 25.4590, 30.0134],
[40.7894, 45.2556, 25.5221, 30.4220]]),
tensor([[80.3772, 89.7752, 50.7762, 60.5520],
[80.5671, 89.3736, 50.6558, 60.6418],
[80.4620, 89.5142, 50.3643, 60.3126],
[80.4817, 89.8549, 50.9430, 59.9108],
[80.2284, 89.6954, 50.0448, 60.1139],
[79.7846, 89.6882, 50.5097, 60.6213],
[80.2654, 90.2330, 50.2787, 60.6937],
[80.3468, 90.0341, 50.2062, 60.2659],
[80.0556, 90.2789, 50.2882, 60.5845]]))


Mode 2: sequentially apply GNN modules on different graphs

>>> import torch
>>> import dgl
>>> import torch.nn as nn
>>> import dgl.function as fn
>>> import networkx as nx
>>> from dgl.nn.pytorch import Sequential
>>> class ExampleLayer(nn.Module):
>>>     def __init__(self):
>>>         super().__init__()
>>>     def forward(self, graph, n_feat):
>>>         with graph.local_scope():
>>>             graph.ndata['h'] = n_feat
>>>             graph.update_all(fn.copy_u('h', 'm'), fn.sum('m', 'h'))
>>>             n_feat += graph.ndata['h']
>>>             return n_feat.view(graph.number_of_nodes() // 2, 2, -1).sum(1)
>>>
>>> g1 = dgl.DGLGraph(nx.erdos_renyi_graph(32, 0.05))
>>> g2 = dgl.DGLGraph(nx.erdos_renyi_graph(16, 0.2))
>>> g3 = dgl.DGLGraph(nx.erdos_renyi_graph(8, 0.8))
>>> net = Sequential(ExampleLayer(), ExampleLayer(), ExampleLayer())
>>> n_feat = torch.rand(32, 4)
>>> net([g1, g2, g3], n_feat)
tensor([[209.6221, 225.5312, 193.8920, 220.1002],
[250.0169, 271.9156, 240.2467, 267.7766],
[220.4007, 239.7365, 213.8648, 234.9637],
[196.4630, 207.6319, 184.2927, 208.7465]])

forward(graph, *feats)[source]

Sequentially apply modules to the input.

Parameters
• graph (DGLGraph or list of DGLGraphs) – The graph(s) to apply modules on.

• *feats – Input features. The output of the $$i$$-th module should match the input of the $$(i+1)$$-th module in the sequential.

### WeightBasis¶

class dgl.nn.pytorch.utils.WeightBasis(shape, num_bases, num_outputs)[source]

Bases: torch.nn.modules.module.Module

Basis decomposition module.

Basis decomposition is introduced in “Modeling Relational Data with Graph Convolutional Networks” and can be described as below:

$W_o = \sum_{b=1}^B a_{ob} V_b$

Each weight output $$W_o$$ is essentially a linear combination of basis transformations $$V_b$$ with coefficients $$a_{ob}$$.

If is useful as a form of regularization on a large parameter matrix. Thus, the number of weight outputs is usually larger than the number of bases.

Parameters
• shape (tuple[int]) – Shape of the basis parameter.

• num_bases (int) – Number of bases.

• num_outputs (int) – Number of outputs.

forward()[source]

Forward computation

Returns

weight – Composed weight tensor of shape (num_outputs,) + shape

Return type

torch.Tensor

### KNNGraph¶

class dgl.nn.pytorch.factory.KNNGraph(k)[source]

Bases: torch.nn.modules.module.Module

Layer that transforms one point set into a graph, or a batch of point sets with the same number of points into a union of those graphs.

The KNNGraph is implemented in the following steps:

1. Compute an NxN matrix of pairwise distance for all points.

2. Pick the k points with the smallest distance for each point as their k-nearest neighbors.

3. Construct a graph with edges to each point as a node from its k-nearest neighbors.

The overall computational complexity is $$O(N^2(logN + D)$$.

If a batch of point sets is provided, the point $$j$$ in point set $$i$$ is mapped to graph node ID: $$i \times M + j$$, where $$M$$ is the number of nodes in each point set.

The predecessors of each node are the k-nearest neighbors of the corresponding point.

Parameters

k (int) – The number of neighbors.

Notes

The nearest neighbors found for a node include the node itself.

Examples

The following example uses PyTorch backend.

>>> import torch
>>> from dgl.nn.pytorch.factory import KNNGraph
>>>
>>> kg = KNNGraph(2)
>>> x = torch.tensor([[0,1],
[1,2],
[1,3],
[100, 101],
[101, 102],
[50, 50]])
>>> g = kg(x)
>>> print(g.edges())
(tensor([0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5]),
tensor([0, 0, 1, 2, 1, 2, 5, 3, 4, 3, 4, 5]))

forward(x, algorithm='bruteforce-blas', dist='euclidean')[source]

Forward computation.

Parameters
• x (Tensor) – $$(M, D)$$ or $$(N, M, D)$$ where $$N$$ means the number of point sets, $$M$$ means the number of points in each point set, and $$D$$ means the size of features.

• algorithm (str, optional) –

Algorithm used to compute the k-nearest neighbors.

• ’bruteforce-blas’ will first compute the distance matrix using BLAS matrix multiplication operation provided by backend frameworks. Then use topk algorithm to get k-nearest neighbors. This method is fast when the point set is small but has $$O(N^2)$$ memory complexity where $$N$$ is the number of points.

• ’bruteforce’ will compute distances pair by pair and directly select the k-nearest neighbors during distance computation. This method is slower than ‘bruteforce-blas’ but has less memory overhead (i.e., $$O(Nk)$$ where $$N$$ is the number of points, $$k$$ is the number of nearest neighbors per node) since we do not need to store all distances.

• ’bruteforce-sharemem’ (CUDA only) is similar to ‘bruteforce’ but use shared memory in CUDA devices for buffer. This method is faster than ‘bruteforce’ when the dimension of input points is not large. This method is only available on CUDA device.

• ’kd-tree’ will use the kd-tree algorithm (CPU only). This method is suitable for low-dimensional data (e.g. 3D point clouds)

• ’nn-descent’ is a approximate approach from paper Efficient k-nearest neighbor graph construction for generic similarity measures. This method will search for nearest neighbor candidates in “neighbors’ neighbors”.

(default: ‘bruteforce-blas’)

• dist (str, optional) –

The distance metric used to compute distance between points. It can be the following metrics: * ‘euclidean’: Use Euclidean distance (L2 norm)

$$\sqrt{\sum_{i} (x_{i} - y_{i})^{2}}$$.

• ’cosine’: Use cosine distance.

(default: ‘euclidean’)

Returns

A DGLGraph without features.

Return type

DGLGraph

### SegmentedKNNGraph¶

class dgl.nn.pytorch.factory.SegmentedKNNGraph(k)[source]

Bases: torch.nn.modules.module.Module

Layer that transforms one point set into a graph, or a batch of point sets with different number of points into a union of those graphs.

If a batch of point sets is provided, then the point $$j$$ in the point set $$i$$ is mapped to graph node ID: $$\sum_{p<i} |V_p| + j$$, where $$|V_p|$$ means the number of points in the point set $$p$$.

The predecessors of each node are the k-nearest neighbors of the corresponding point.

Parameters

k (int) – The number of neighbors.

Notes

The nearest neighbors found for a node include the node itself.

Examples

The following example uses PyTorch backend.

>>> import torch
>>> from dgl.nn.pytorch.factory import SegmentedKNNGraph
>>>
>>> kg = SegmentedKNNGraph(2)
>>> x = torch.tensor([[0,1],
...                   [1,2],
...                   [1,3],
...                   [100, 101],
...                   [101, 102],
...                   [50, 50],
...                   [24,25],
...                   [25,24]])
>>> g = kg(x, [3,3,2])
>>> print(g.edges())
(tensor([0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 7]),
tensor([0, 0, 1, 2, 1, 2, 3, 4, 5, 3, 4, 5, 6, 7, 6, 7]))
>>>

forward(x, segs, algorithm='bruteforce-blas', dist='euclidean')[source]

Forward computation.

Parameters
• x (Tensor) – $$(M, D)$$ where $$M$$ means the total number of points in all point sets, and $$D$$ means the size of features.

• segs (iterable of int) – $$(N)$$ integers where $$N$$ means the number of point sets. The number of elements must sum up to $$M$$. And any $$N$$ should $$\ge k$$

• algorithm (str, optional) –

Algorithm used to compute the k-nearest neighbors.

• ’bruteforce-blas’ will first compute the distance matrix using BLAS matrix multiplication operation provided by backend frameworks. Then use topk algorithm to get k-nearest neighbors. This method is fast when the point set is small but has $$O(N^2)$$ memory complexity where $$N$$ is the number of points.

• ’bruteforce’ will compute distances pair by pair and directly select the k-nearest neighbors during distance computation. This method is slower than ‘bruteforce-blas’ but has less memory overhead (i.e., $$O(Nk)$$ where $$N$$ is the number of points, $$k$$ is the number of nearest neighbors per node) since we do not need to store all distances.

• ’bruteforce-sharemem’ (CUDA only) is similar to ‘bruteforce’ but use shared memory in CUDA devices for buffer. This method is faster than ‘bruteforce’ when the dimension of input points is not large. This method is only available on CUDA device.

• ’kd-tree’ will use the kd-tree algorithm (CPU only). This method is suitable for low-dimensional data (e.g. 3D point clouds)

• ’nn-descent’ is a approximate approach from paper Efficient k-nearest neighbor graph construction for generic similarity measures. This method will search for nearest neighbor candidates in “neighbors’ neighbors”.

(default: ‘bruteforce-blas’)

• dist (str, optional) –

The distance metric used to compute distance between points. It can be the following metrics: * ‘euclidean’: Use Euclidean distance (L2 norm)

$$\sqrt{\sum_{i} (x_{i} - y_{i})^{2}}$$.

• ’cosine’: Use cosine distance.

(default: ‘euclidean’)

Returns

A DGLGraph without features.

Return type

DGLGraph

## NodeEmbedding Module¶

### NodeEmbedding¶

class dgl.nn.pytorch.sparse_emb.NodeEmbedding(num_embeddings, embedding_dim, name, init_func=None, device=None, partition=None)[source]

Bases: object

Class for storing node embeddings.

The class is optimized for training large-scale node embeddings. It updates the embedding in a sparse way and can scale to graphs with millions of nodes. It also supports partitioning to multiple GPUs (on a single machine) for more acceleration. It does not support partitioning across machines.

Currently, DGL provides two optimizers that work with this NodeEmbedding class: SparseAdagrad and SparseAdam.

The implementation is based on torch.distributed package. It depends on the pytorch default distributed process group to collect multi-process information and uses torch.distributed.TCPStore to share meta-data information across multiple gpu processes. It use the local address of ‘127.0.0.1:12346’ to initialize the TCPStore.

NOTE: The support of NodeEmbedding is experimental.

Parameters
• num_embeddings (int) – The number of embeddings. Currently, the number of embeddings has to be the same as the number of nodes.

• embedding_dim (int) – The dimension size of embeddings.

• name (str) – The name of the embeddings. The name should uniquely identify the embeddings in the system.

• init_func (callable, optional) – The function to create the initial data. If the init function is not provided, the values of the embeddings are initialized to zero.

• device (th.device) – Device to store the embeddings on.

• parittion (NDArrayPartition) – The partition to use to distributed the embeddings between processes.

Examples

Before launching multiple gpu processes

>>> def initializer(emb):
th.nn.init.xavier_uniform_(emb)
return emb


In each training process

>>> emb = dgl.nn.NodeEmbedding(g.number_of_nodes(), 10, 'emb', init_func=initializer)
...     ...
...     feats = emb(nids, gpu_0)
...     loss = F.sum(feats + 1, 0)
...     loss.backward()
...     optimizer.step()

all_get_embedding()[source]

Return a copy of the embedding stored in CPU memory. If this is a multi-processing instance, the tensor will be returned in shared memory. If the embedding is currently stored on multiple GPUs, all processes must call this method in the same order.

NOTE: This method must be called by all processes sharing the embedding, or it may result in a deadlock.

Returns

The tensor storing the node embeddings.

Return type

torch.Tensor

all_set_embedding(values)[source]

Set the values of the embedding. This method must be called by all processes sharing the embedding with identical tensors for values.

NOTE: This method must be called by all processes sharing the embedding, or it may result in a deadlock.

Parameters

values (Tensor) – The global tensor to pull values from.

property comm

Return dgl.cuda.nccl.Communicator for data sharing across processes.

Returns

Communicator used for data sharing.

Return type

dgl.cuda.nccl.Communicator

property emb_tensor

Return the tensor storing the node embeddings

DEPRECATED: renamed weight

Returns

The tensor storing the node embeddings

Return type

torch.Tensor

property embedding_dim

Return the dimension of embeddings.

Returns

The dimension of embeddings.

Return type

int

property name

Return the name of NodeEmbedding.

Returns

The name of NodeEmbedding.

Return type

str

property num_embeddings

Return the number of embeddings.

Returns

The number of embeddings.

Return type

int

property optm_state

Return the optimizer related state tensor.

Returns

The optimizer related state.

Return type

tuple of torch.Tensor

property partition

Return the partition identifying how the tensor is split across processes.

Returns

The mode.

Return type

String

property rank

Return rank of current process.

Returns

The rank of current process.

Return type

int

reset_trace()[source]

Clean up the trace of the indices of embeddings used in the training step(s).

set_optm_state(state)[source]

Store the optimizer related state tensor.

Parameters

state (tuple of torch.Tensor) – Optimizer related state.

property store

Returns

KVStore used for meta data sharing.

Return type

torch.distributed.TCPStore

property trace

Return a trace of the indices of embeddings used in the training step(s).

Returns

The indices of embeddings used in the training step(s).

Return type

[torch.Tensor]

property weight

Return the tensor storing the node embeddings

Returns

The tensor storing the node embeddings

Return type

torch.Tensor

property world_size

Return world size of the pytorch distributed training env.

Returns

The world size of the pytorch distributed training env.

Return type

int