Source code for dgl.nn.pytorch.conv.dgnconv

"""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(
            torch.abs(eig_s[:, :, eig_idx] - eig_d[:, :, eig_idx])
            / (
                    torch.abs(eig_s[:, :, eig_idx] - eig_d[:, :, eig_idx]),
                + 1e-30
    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.abs(eig_s[:, :, eig_idx] - eig_d[:, :, eig_idx]),
            + 1e-30
    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 =
                [edges.src["h"], edges.dst["h"],["a"]], dim=-1
            f =[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 =["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))
                    h.append(AGGREGATORS[agg](msg, eig_s, eig_d, h_in))
        h =, dim=1)
        h =
                SCALERS[scaler](h, D=degree,
                if scaler != "identity"
                else h
                for scaler in self.scalers
        return {"h_neigh": h}

[docs]class DGNConv(PNAConv): r"""Directional Graph Network Layer from `Directional Graph Networks <>`__ 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)