# Chapter 3: Building GNN Modules¶

DGL NN module is the building block for your GNN model. It inherents from Pytorch’s NN Module, MXNet Gluon’s NN Block and TensorFlow’s Keras Layer, depending on the DNN framework backend in use. In DGL NN module, the parameter registration in construction function and tensor operation in forward function are the same with the backend framework. In this way, DGL code can be seamlessly integrated into the backend framework code. The major difference lies in the message passing operations that are unique in DGL.

DGL has integrated many commonly used Conv Layers, Dense Conv Layers, Global Pooling Layers, and Utility Modules. We welcome your contribution!

In this section, we will use
`SAGEConv`

with Pytorch backend as an example to introduce how to build your own
DGL NN Module.

## DGL NN Module Construction Function¶

The construction function will do the following:

Set options.

Register learnable paramesters or submodules.

Reset parameters.

```
import torch as th
from torch import nn
from torch.nn import init
from .... import function as fn
from ....base import DGLError
from ....utils import expand_as_pair, check_eq_shape
class SAGEConv(nn.Module):
def __init__(self,
in_feats,
out_feats,
aggregator_type,
bias=True,
norm=None,
activation=None):
super(SAGEConv, self).__init__()
self._in_src_feats, self._in_dst_feats = expand_as_pair(in_feats)
self._out_feats = out_feats
self._aggre_type = aggregator_type
self.norm = norm
self.activation = activation
```

In construction function, we first need to set the data dimensions. For general Pytorch module, the dimensions are usually input dimension, output dimension and hidden dimensions. For graph neural, the input dimension can be split into source node dimension and destination node dimension.

Besides data dimensions, a typical option for graph neural network is
aggregation type (`self._aggre_type`

). Aggregation type determines how
messages on different edges are aggregated for a certain destination
node. Commonly used aggregation types include `mean`

, `sum`

,
`max`

, `min`

. Some modules may apply more complicated aggregation
like a `lstm`

.

`norm`

here is a callable function for feature normalization. On the
SAGEConv paper, such normalization can be l2 norm:
\(h_v = h_v / \lVert h_v \rVert_2\).

```
# aggregator type: mean, max_pool, lstm, gcn
if aggregator_type not in ['mean', 'max_pool', 'lstm', 'gcn']:
raise KeyError('Aggregator type {} not supported.'.format(aggregator_type))
if aggregator_type == 'max_pool':
self.fc_pool = nn.Linear(self._in_src_feats, self._in_src_feats)
if aggregator_type == 'lstm':
self.lstm = nn.LSTM(self._in_src_feats, self._in_src_feats, batch_first=True)
if aggregator_type in ['mean', 'max_pool', 'lstm']:
self.fc_self = nn.Linear(self._in_dst_feats, out_feats, bias=bias)
self.fc_neigh = nn.Linear(self._in_src_feats, out_feats, bias=bias)
self.reset_parameters()
```

Register parameters and submodules. In SAGEConv, submodules vary
according to the aggregation type. Those modules are pure Pytorch nn
modules like `nn.Linear`

, `nn.LSTM`

, etc. At the end of construction
function, weight initialization is applied by calling
`reset_parameters()`

.

```
def reset_parameters(self):
"""Reinitialize learnable parameters."""
gain = nn.init.calculate_gain('relu')
if self._aggre_type == 'max_pool':
nn.init.xavier_uniform_(self.fc_pool.weight, gain=gain)
if self._aggre_type == 'lstm':
self.lstm.reset_parameters()
if self._aggre_type != 'gcn':
nn.init.xavier_uniform_(self.fc_self.weight, gain=gain)
nn.init.xavier_uniform_(self.fc_neigh.weight, gain=gain)
```

## DGL NN Module Forward Function¶

In NN module, `forward()`

function does the actual message passing and
computating. Compared with Pytorch’s NN module which usually takes
tensors as the parameters, DGL NN module takes an additional parameter
`dgl.DGLGraph`

. The
workload for `forward()`

function can be splitted into three parts:

Graph checking and graph type specification.

Message passing and reducing.

Update feature after reducing for output.

Let’s dive deep into the `forward()`

function in SAGEConv example.

### Graph checking and graph type specification¶

```
def forward(self, graph, feat):
with graph.local_scope():
# Specify graph type then expand input feature according to graph type
feat_src, feat_dst = expand_as_pair(feat, graph)
```

`forward()`

needs to handle many corner cases on the input that can
lead to invalid values in computing and message passing. One typical check in conv modules like `GraphConv`

is to verify no 0-in-degree node in the input graph. When a node has 0-in-degree, the `mailbox`

will be empty and the reduce function will produce all-zero values. This may cause silent regression in model performance. However, in `SAGEConv`

module, the aggregated representation will be concatenated with the original node feature, the output of `forward()`

will not be all-zero. No such check is needed in this case.

DGL NN module should be reusable across different types of graph input including: homogeneous graph, heterogeneous graph (1.5 Heterogeneous Graphs), subgraph block (Chapter 6: Stochastic Training on Large Graphs).

The math formulas for SAGEConv are:

We need to specify the source node feature `feat_src`

and destination
node feature `feat_dst`

according to the graph type. The function to
specify the graph type and expand `feat`

into `feat_src`

and
`feat_dst`

is
`expand_as_pair()`

.
The detail of this function is shown below.

```
def expand_as_pair(input_, g=None):
if isinstance(input_, tuple):
# Bipartite graph case
return input_
elif g is not None and g.is_block:
# Subgraph block case
if isinstance(input_, Mapping):
input_dst = {
k: F.narrow_row(v, 0, g.number_of_dst_nodes(k))
for k, v in input_.items()}
else:
input_dst = F.narrow_row(input_, 0, g.number_of_dst_nodes())
return input_, input_dst
else:
# Homograph case
return input_, input_
```

For homogeneous whole graph training, source nodes and destination nodes are the same. They are all the nodes in the graph.

For heterogeneous case, the graph can be splitted into several bipartite
graphs, one for each relation. The relations are represented as
`(src_type, edge_type, dst_dtype)`

. When we identify the input feature
`feat`

is a tuple, we will treat the graph as bipartite. The first
element in the tuple will be the source node feature and the second
element will be the destination node feature.

In mini-batch training, the computing is applied on a subgraph sampled
by given a bunch of destination nodes. The subgraph is called as
`block`

in DGL. After message passing, only those destination nodes
will be updated since they have the same neighborhood as the one they
have in the original full graph. In the block creation phase,
`dst nodes`

are in the front of the node list. We can find the
`feat_dst`

by the index `[0:g.number_of_dst_nodes()]`

.

After determining `feat_src`

and `feat_dst`

, the computing for the
above three graph types are the same.

### Message passing and reducing¶

```
if self._aggre_type == 'mean':
graph.srcdata['h'] = feat_src
graph.update_all(fn.copy_u('h', 'm'), fn.mean('m', 'neigh'))
h_neigh = graph.dstdata['neigh']
elif self._aggre_type == 'gcn':
check_eq_shape(feat)
graph.srcdata['h'] = feat_src
graph.dstdata['h'] = feat_dst # same as above if homogeneous
graph.update_all(fn.copy_u('h', 'm'), fn.sum('m', 'neigh'))
# divide in_degrees
degs = graph.in_degrees().to(feat_dst)
h_neigh = (graph.dstdata['neigh'] + graph.dstdata['h']) / (degs.unsqueeze(-1) + 1)
elif self._aggre_type == 'max_pool':
graph.srcdata['h'] = F.relu(self.fc_pool(feat_src))
graph.update_all(fn.copy_u('h', 'm'), fn.max('m', 'neigh'))
h_neigh = graph.dstdata['neigh']
else:
raise KeyError('Aggregator type {} not recognized.'.format(self._aggre_type))
# GraphSAGE GCN does not require fc_self.
if self._aggre_type == 'gcn':
rst = self.fc_neigh(h_neigh)
else:
rst = self.fc_self(h_self) + self.fc_neigh(h_neigh)
```

The code actually does message passing and reducing computing. This part
of code varies module by module. Note that all the message passings in
the above code are implemented using `update_all()`

API and
`built-in`

message/reduce functions to fully utilize DGL’s performance
optimization as described in Chapter 2: Message Passing.

### Update feature after reducing for output¶

```
# activation
if self.activation is not None:
rst = self.activation(rst)
# normalization
if self.norm is not None:
rst = self.norm(rst)
return rst
```

The last part of `forward()`

function is to update the feature after
the `reduce function`

. Common update operations are applying
activation function and normalization according to the option set in the
object construction phase.

## Heterogeneous GraphConv Module¶

`dgl.nn.pytorch.HeteroGraphConv`

is a module-level encapsulation to run DGL NN module on heterogeneous
graph. The implementation logic is the same as message passing level API
`multi_update_all()`

:

DGL NN module within each relation \(r\).

Reduction that merges the results on the same node type from multiple relationships.

This can be formulated as:

where \(f_r\) is the NN module for each relation \(r\), \(AGG\) is the aggregation function.

### HeteroGraphConv implementation logic:¶

```
class HeteroGraphConv(nn.Module):
def __init__(self, mods, aggregate='sum'):
super(HeteroGraphConv, self).__init__()
self.mods = nn.ModuleDict(mods)
if isinstance(aggregate, str):
self.agg_fn = get_aggregate_fn(aggregate)
else:
self.agg_fn = aggregate
```

The heterograph convolution takes a dictonary `mods`

that maps each
relation to a nn module. And set the function that aggregates results on
the same node type from multiple relations.

```
def forward(self, g, inputs, mod_args=None, mod_kwargs=None):
if mod_args is None:
mod_args = {}
if mod_kwargs is None:
mod_kwargs = {}
outputs = {nty : [] for nty in g.dsttypes}
```

Besides input graph and input tensors, the `forward()`

function takes
two additional dictionary parameters `mod_args`

and `mod_kwargs`

.
These two dictionaries have the same keys as `self.mods`

. They are
used as customized parameters when calling their corresponding NN
modules in `self.mods`

for different types of relations.

An output dictionary is created to hold output tensor for each
destination type`nty`

. Note that the value for each `nty`

is a
list, indicating a single node type may get multiple outputs if more
than one relations have `nty`

as the destination type. We will hold
them in list for further aggregation.

```
if g.is_block:
src_inputs = inputs
dst_inputs = {k: v[:g.number_of_dst_nodes(k)] for k, v in inputs.items()}
else:
src_inputs = dst_inputs = inputs
for stype, etype, dtype in g.canonical_etypes:
rel_graph = g[stype, etype, dtype]
if rel_graph.number_of_edges() == 0:
continue
if stype not in src_inputs or dtype not in dst_inputs:
continue
dstdata = self.mods[etype](
rel_graph,
(src_inputs[stype], dst_inputs[dtype]),
*mod_args.get(etype, ()),
**mod_kwargs.get(etype, {}))
outputs[dtype].append(dstdata)
```

The input `g`

can be a heterogeneous graph or a subgraph block from a
heterogeneous graph. As in ordinary NN module, the `forward()`

function need to handle different input graph types separately.

Each relation is represented as a `canonical_etype`

, which is
`(stype, etype, dtype)`

. Using `canonical_etype`

as the key, we can
extract out a bipartite graph `rel_graph`

. For bipartite graph, the
input feature will be organized as a tuple
`(src_inputs[stype], dst_inputs[dtype])`

. The NN module for each
relation is called and the output is saved. To avoid unnecessary call,
relations with no edge or no node with the its src type will be skipped.

```
rsts = {}
for nty, alist in outputs.items():
if len(alist) != 0:
rsts[nty] = self.agg_fn(alist, nty)
```

Finally, the results on the same destination node type from multiple
relationships are aggregated using `self.agg_fn`

function. Examples can be found in the API Doc for `dgl.nn.pytorch.HeteroGraphConv`

.