"""Torch Module for Directional Graph Networks Convolution Layer"""
# pylint: disable= no-member, arguments-differ, invalid-name
from functools import partial
import torch
import torch.nn as nn
from .pnaconv import AGGREGATORS, PNAConv, PNAConvTower, SCALERS
def aggregate_dir_av(h, eig_s, eig_d, eig_idx):
"""directional average aggregation"""
h_mod = torch.mul(
h,
(
torch.abs(eig_s[:, :, eig_idx] - eig_d[:, :, eig_idx])
/ (
torch.sum(
torch.abs(eig_s[:, :, eig_idx] - eig_d[:, :, eig_idx]),
keepdim=True,
dim=1,
)
+ 1e-30
)
).unsqueeze(-1),
)
return torch.sum(h_mod, dim=1)
def aggregate_dir_dx(h, eig_s, eig_d, h_in, eig_idx):
"""directional derivative aggregation"""
eig_w = (
(eig_s[:, :, eig_idx] - eig_d[:, :, eig_idx])
/ (
torch.sum(
torch.abs(eig_s[:, :, eig_idx] - eig_d[:, :, eig_idx]),
keepdim=True,
dim=1,
)
+ 1e-30
)
).unsqueeze(-1)
h_mod = torch.mul(h, eig_w)
return torch.abs(torch.sum(h_mod, dim=1) - torch.sum(eig_w, dim=1) * h_in)
for k in range(1, 4):
AGGREGATORS[f"dir{k}-av"] = partial(aggregate_dir_av, eig_idx=k - 1)
AGGREGATORS[f"dir{k}-dx"] = partial(aggregate_dir_dx, eig_idx=k - 1)
class DGNConvTower(PNAConvTower):
"""A single DGN tower with modified reduce function"""
def message(self, edges):
"""message function for DGN layer"""
if self.edge_feat_size > 0:
f = torch.cat(
[edges.src["h"], edges.dst["h"], edges.data["a"]], dim=-1
)
else:
f = torch.cat([edges.src["h"], edges.dst["h"]], dim=-1)
return {
"msg": self.M(f),
"eig_s": edges.src["eig"],
"eig_d": edges.dst["eig"],
}
def reduce_func(self, nodes):
"""reduce function for DGN layer"""
h_in = nodes.data["h"]
eig_s = nodes.mailbox["eig_s"]
eig_d = nodes.mailbox["eig_d"]
msg = nodes.mailbox["msg"]
degree = msg.size(1)
h = []
for agg in self.aggregators:
if agg.startswith("dir"):
if agg.endswith("av"):
h.append(AGGREGATORS[agg](msg, eig_s, eig_d))
else:
h.append(AGGREGATORS[agg](msg, eig_s, eig_d, h_in))
else:
h.append(AGGREGATORS[agg](msg))
h = torch.cat(h, dim=1)
h = torch.cat(
[
SCALERS[scaler](h, D=degree, delta=self.delta)
if scaler != "identity"
else h
for scaler in self.scalers
],
dim=1,
)
return {"h_neigh": h}
[docs]class DGNConv(PNAConv):
r"""Directional Graph Network Layer from `Directional Graph Networks
<https://arxiv.org/abs/2010.02863>`__
DGN introduces two special directional aggregators according to the vector field
:math:`F`, which is defined as the gradient of the low-frequency eigenvectors of graph
laplacian.
The directional average aggregator is defined as
:math:`h_i' = \sum_{j\in\mathcal{N}(i)}\frac{|F_{i,j}|\cdot h_j}{||F_{i,:}||_1+\epsilon}`
The directional derivative aggregator is defined as
:math:`h_i' = \sum_{j\in\mathcal{N}(i)}\frac{F_{i,j}\cdot h_j}{||F_{i,:}||_1+\epsilon}
-h_i\cdot\sum_{j\in\mathcal{N}(i)}\frac{F_{i,j}}{||F_{i,:}||_1+\epsilon}`
:math:`\epsilon` is the infinitesimal to keep the computation numerically stable.
Parameters
----------
in_size : int
Input feature size; i.e. the size of :math:`h_i^l`.
out_size : int
Output feature size; i.e. the size of :math:`h_i^{l+1}`.
aggregators : list of str
List of aggregation function names(each aggregator specifies a way to aggregate
messages from neighbours), selected from:
* ``mean``: the mean of neighbour messages
* ``max``: the maximum of neighbour messages
* ``min``: the minimum of neighbour messages
* ``std``: the standard deviation of neighbour messages
* ``var``: the variance of neighbour messages
* ``sum``: the sum of neighbour messages
* ``moment3``, ``moment4``, ``moment5``: the normalized moments aggregation
:math:`(E[(X-E[X])^n])^{1/n}`
* ``dir{k}-av``: directional average aggregation with directions defined by the k-th
smallest eigenvectors. k can be selected from 1, 2, 3.
* ``dir{k}-dx``: directional derivative aggregation with directions defined by the k-th
smallest eigenvectors. k can be selected from 1, 2, 3.
Note that using directional aggregation requires the LaplacianPE transform on the input
graph for eigenvector computation (the PE size must be >= k above).
scalers: list of str
List of scaler function names, selected from:
* ``identity``: no scaling
* ``amplification``: multiply the aggregated message by :math:`\log(d+1)/\delta`,
where :math:`d` is the in-degree of the node.
* ``attenuation``: multiply the aggregated message by :math:`\delta/\log(d+1)`
delta: float
The in-degree-related normalization factor computed over the training set, used by scalers
for normalization. :math:`E[\log(d+1)]`, where :math:`d` is the in-degree for each node
in the training set.
dropout: float, optional
The dropout ratio. Default: 0.0.
num_towers: int, optional
The number of towers used. Default: 1. Note that in_size and out_size must be divisible
by num_towers.
edge_feat_size: int, optional
The edge feature size. Default: 0.
residual : bool, optional
The bool flag that determines whether to add a residual connection for the
output. Default: True. If in_size and out_size of the DGN conv layer are not
the same, this flag will be set as False forcibly.
Example
-------
>>> import dgl
>>> import torch as th
>>> from dgl.nn import DGNConv
>>> from dgl import LaplacianPE
>>>
>>> # DGN requires precomputed eigenvectors, with 'eig' as feature name.
>>> transform = LaplacianPE(k=3, feat_name='eig')
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> g = transform(g)
>>> eig = g.ndata['eig']
>>> feat = th.ones(6, 10)
>>> conv = DGNConv(10, 10, ['dir1-av', 'dir1-dx', 'sum'], ['identity', 'amplification'], 2.5)
>>> ret = conv(g, feat, eig_vec=eig)
"""
def __init__(
self,
in_size,
out_size,
aggregators,
scalers,
delta,
dropout=0.0,
num_towers=1,
edge_feat_size=0,
residual=True,
):
super(DGNConv, self).__init__(
in_size,
out_size,
aggregators,
scalers,
delta,
dropout,
num_towers,
edge_feat_size,
residual,
)
self.towers = nn.ModuleList(
[
DGNConvTower(
self.tower_in_size,
self.tower_out_size,
aggregators,
scalers,
delta,
dropout=dropout,
edge_feat_size=edge_feat_size,
)
for _ in range(num_towers)
]
)
self.use_eig_vec = False
for aggr in aggregators:
if aggr.startswith("dir"):
self.use_eig_vec = True
break
[docs] def forward(self, graph, node_feat, edge_feat=None, eig_vec=None):
r"""
Description
-----------
Compute DGN layer.
Parameters
----------
graph : DGLGraph
The graph.
node_feat : torch.Tensor
The input feature of shape :math:`(N, h_n)`. :math:`N` is the number of
nodes, and :math:`h_n` must be the same as in_size.
edge_feat : torch.Tensor, optional
The edge feature of shape :math:`(M, h_e)`. :math:`M` is the number of
edges, and :math:`h_e` must be the same as edge_feat_size.
eig_vec : torch.Tensor, optional
K smallest non-trivial eigenvectors of Graph Laplacian of shape :math:`(N, K)`.
It is only required when :attr:`aggregators` contains directional aggregators.
Returns
-------
torch.Tensor
The output node feature of shape :math:`(N, h_n')` where :math:`h_n'`
should be the same as out_size.
"""
with graph.local_scope():
if self.use_eig_vec:
graph.ndata["eig"] = eig_vec
return super().forward(graph, node_feat, edge_feat)