# 3.2 DGL NN Module Forward Functionο

In NN module, `forward()`

function does the actual message passing and
computation. Compared with PyTorchβs 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 split into three parts:

Graph checking and graph type specification.

Message passing.

Feature update.

The rest of the section takes a deep dive into the `forward()`

function in SAGEConv example.

## Graph checking and graph type specificationο

```
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 that the input graph has no 0-in-degree nodes.
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:

One needs to specify the source node feature `feat_src`

and destination
node feature `feat_dst`

according to the graph type.
`expand_as_pair()`

is a function that specifies the graph
type and expand `feat`

into `feat_src`

and `feat_dst`

.
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:
# Homogeneous graph 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 split into several bipartite
graphs, one for each relation. The relations are represented as
`(src_type, edge_type, dst_dtype)`

. When it identifies that the input feature
`feat`

is a tuple, it 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
based on a bunch of destination nodes. The subgraph is called as
`block`

in DGL. In the block creation phase,
`dst nodes`

are in the front of the node list. One 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 reducingο

```
import dgl.function as fn
import torch.nn.functional as F
from dgl.utils import check_eq_shape
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
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 == '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 passing in
the above code are implemented using `update_all()`

API and
`built-in`

message/reduce functions to fully utilize DGLβs performance
optimization as described in 2.2 Writing Efficient Message Passing Code.

## Update feature after reducing for outputο

```
# 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.