tg.nn.TransformerConv（）再分析

import math
from typing import Union, Tuple, Optional
from torch_geometric.typing import PairTensor, Adj, OptTensor

import torch
from torch import Tensor
import torch.nn.functional as F
from torch_sparse import SparseTensor

from torch_geometric.nn.conv import MessagePassing
from torch_geometric.nn.dense.linear import Linear
from torch_geometric.utils import softmax


class TransformerConv(MessagePassing):
    r"""The graph transformer operator from the `"Masked Label Prediction:
    Unified Message Passing Model for Semi-Supervised Classification"
    <https://arxiv.org/abs/2009.03509>`_ paper

    .. math::
        \mathbf{x}^{\prime}_i = \mathbf{W}_1 \mathbf{x}_i +
        \sum_{j \in \mathcal{N}(i)} \alpha_{i,j} \mathbf{W}_2 \mathbf{x}_{j},

    where the attention coefficients :math:`\alpha_{i,j}` are computed via
    multi-head dot product attention:

    .. math::
        \alpha_{i,j} = \textrm{softmax} \left(
        \frac{(\mathbf{W}_3\mathbf{x}_i)^{\top} (\mathbf{W}_4\mathbf{x}_j)}
        {\sqrt{d}} \right)

    Args:
        in_channels (int or tuple): Size of each input sample, or :obj:`-1` to
            derive the size from the first input(s) to the forward method.
            A tuple corresponds to the sizes of source and target
            dimensionalities.
        out_channels (int): Size of each output sample.
        heads (int, optional): Number of multi-head-attentions.
            (default: :obj:`1`)
        concat (bool, optional): If set to :obj:`False`, the multi-head
            attentions are averaged instead of concatenated.
            (default: :obj:`True`)
        beta (bool, optional): If set, will combine aggregation and
            skip information via

            .. math::
                \mathbf{x}^{\prime}_i = \beta_i \mathbf{W}_1 \mathbf{x}_i +
                (1 - \beta_i) \underbrace{\left(\sum_{j \in \mathcal{N}(i)}
                \alpha_{i,j} \mathbf{W}_2 \vec{x}_j \right)}_{=\mathbf{m}_i}

            with :math:`\beta_i = \textrm{sigmoid}(\mathbf{w}_5^{\top}
            [ \mathbf{x}_i, \mathbf{m}_i, \mathbf{x}_i - \mathbf{m}_i ])`
            (default: :obj:`False`)
        dropout (float, optional): Dropout probability of the normalized
            attention coefficients which exposes each node to a stochastically
            sampled neighborhood during training. (default: :obj:`0`)
        edge_dim (int, optional): Edge feature dimensionality (in case
            there are any). Edge features are added to the keys after
            linear transformation, that is, prior to computing the
            attention dot product. They are also added to final values
            after the same linear transformation. The model is:

            .. math::
                \mathbf{x}^{\prime}_i = \mathbf{W}_1 \mathbf{x}_i +
                \sum_{j \in \mathcal{N}(i)} \alpha_{i,j} \left(
                \mathbf{W}_2 \mathbf{x}_{j} + \mathbf{W}_6 \mathbf{e}_{ij}
                \right),

            where the attention coefficients :math:`\alpha_{i,j}` are now
            computed via:

            .. math::
                \alpha_{i,j} = \textrm{softmax} \left(
                \frac{(\mathbf{W}_3\mathbf{x}_i)^{\top}
                (\mathbf{W}_4\mathbf{x}_j + \mathbf{W}_6 \mathbf{e}_{ij})}
                {\sqrt{d}} \right)

            (default :obj:`None`)
        bias (bool, optional): If set to :obj:`False`, the layer will not learn
            an additive bias. (default: :obj:`True`)
        root_weight (bool, optional): If set to :obj:`False`, the layer will
            not add the transformed root node features to the output and the
            option  :attr:`beta` is set to :obj:`False`. (default: :obj:`True`)
        **kwargs (optional): Additional arguments of
            :class:`torch_geometric.nn.conv.MessagePassing`.
    """
    _alpha: OptTensor

    def __init__(
        self,
        in_channels: Union[int, Tuple[int, int]],
        out_channels: int,
        heads: int = 1,
        concat: bool = True,
        beta: bool = False,
        dropout: float = 0.,
        edge_dim: Optional[int] = None,
        bias: bool = True,
        root_weight: bool = True,
        **kwargs,
    ):
        kwargs.setdefault('aggr', 'add')
        super(TransformerConv, self).__init__(node_dim=0, **kwargs)

        self.in_channels = in_channels
        self.out_channels = out_channels
        self.heads = heads
        self.beta = beta and root_weight
        self.root_weight = root_weight
        self.concat = concat
        self.dropout = dropout
        self.edge_dim = edge_dim

        if isinstance(in_channels, int):
            in_channels = (in_channels, in_channels)

        self.lin_key = Linear(in_channels[0], heads * out_channels)
        self.lin_query = Linear(in_channels[1], heads * out_channels)
        self.lin_value = Linear(in_channels[0], heads * out_channels)
        if edge_dim is not None:
            self.lin_edge = Linear(edge_dim, heads * out_channels, bias=False)
        else:
            self.lin_edge = self.register_parameter('lin_edge', None)

        if concat:
            self.lin_skip = Linear(in_channels[1], heads * out_channels,
                                   bias=bias)
            if self.beta:
                self.lin_beta = Linear(3 * heads * out_channels, 1, bias=False)
            else:
                self.lin_beta = self.register_parameter('lin_beta', None)
        else:
            self.lin_skip = Linear(in_channels[1], out_channels, bias=bias)
            if self.beta:
                self.lin_beta = Linear(3 * out_channels, 1, bias=False)
            else:
                self.lin_beta = self.register_parameter('lin_beta', None)

        self.reset_parameters()

    def reset_parameters(self):
        self.lin_key.reset_parameters()
        self.lin_query.reset_parameters()
        self.lin_value.reset_parameters()
        if self.edge_dim:
            self.lin_edge.reset_parameters()
        self.lin_skip.reset_parameters()
        if self.beta:
            self.lin_beta.reset_parameters()

    def forward(self, x: Union[Tensor, PairTensor], edge_index: Adj,
                edge_attr: OptTensor = None, return_attention_weights=None):
        # type: (Union[Tensor, PairTensor], Tensor, OptTensor, NoneType) -> Tensor  # noqa
        # type: (Union[Tensor, PairTensor], SparseTensor, OptTensor, NoneType) -> Tensor  # noqa
        # type: (Union[Tensor, PairTensor], Tensor, OptTensor, bool) -> Tuple[Tensor, Tuple[Tensor, Tensor]]  # noqa
        # type: (Union[Tensor, PairTensor], SparseTensor, OptTensor, bool) -> Tuple[Tensor, SparseTensor]  # noqa
        r"""
        Args:
            return_attention_weights (bool, optional): If set to :obj:`True`,
                will additionally return the tuple
                :obj:`(edge_index, attention_weights)`, holding the computed
                attention weights for each edge. (default: :obj:`None`)
        """

        if isinstance(x, Tensor):
            x: PairTensor = (x, x)

        # propagate_type: (x: PairTensor, edge_attr: OptTensor)
        out = self.propagate(edge_index, x=x, edge_attr=edge_attr, size=None)

        alpha = self._alpha
        self._alpha = None

        if self.concat:
            out = out.view(-1, self.heads * self.out_channels)
        else:
            out = out.mean(dim=1)

        if self.root_weight:
            x_r = self.lin_skip(x[1])
            if self.lin_beta is not None:
                beta = self.lin_beta(torch.cat([out, x_r, out - x_r], dim=-1))
                beta = beta.sigmoid()
                out = beta * x_r + (1 - beta) * out
            else:
                out += x_r

        if isinstance(return_attention_weights, bool):
            assert alpha is not None
            if isinstance(edge_index, Tensor):
                return out, (edge_index, alpha)
            elif isinstance(edge_index, SparseTensor):
                return out, edge_index.set_value(alpha, layout='coo')
        else:
            return out

    def message(self, x_i: Tensor, x_j: Tensor, edge_attr: OptTensor,
                index: Tensor, ptr: OptTensor,
                size_i: Optional[int]) -> Tensor:

        query = self.lin_query(x_i).view(-1, self.heads, self.out_channels)
        key = self.lin_key(x_j).view(-1, self.heads, self.out_channels)

        if self.lin_edge is not None:
            assert edge_attr is not None
            edge_attr = self.lin_edge(edge_attr).view(-1, self.heads,
                                                      self.out_channels)
            key += edge_attr

        alpha = (query * key).sum(dim=-1) / math.sqrt(self.out_channels)
        alpha = softmax(alpha, index, ptr, size_i)
        self._alpha = alpha
        alpha = F.dropout(alpha, p=self.dropout, training=self.training)

        out = self.lin_value(x_j).view(-1, self.heads, self.out_channels)
        if edge_attr is not None:
            out += edge_attr

        out *= alpha.view(-1, self.heads, 1)
        return out

    def __repr__(self):
        return '{}({}, {}, heads={})'.format(self.__class__.__name__,
                                             self.in_channels,
                                             self.out_channels, self.heads)

我在debug的时候，查看了一下具体python里面的函数和官方的多少还是有点差别的。感觉现在应该是能够完全理解了吧！！

我遇到的代码是这样的：

self.gc1 = tg.nn.TransformerConv(params.feat_hidden2, params.gcn_hidden1, heads=1, dropout=params.p_drop)

然后这里的params.feat_hidden2=128 params.gcn_hidden1=128,对应着内置函数就是in_channels: Union[int, Tuple[int, int]], out_channels: int。

实例化之后，就是：

hidden1,atten = self.gc1(feat_x, adj,return_attention_weights=True)

feat_x,adj传入forward中，分别对应着的是x: Union[Tensor, PairTensor], edge_index: Adj。也就是节点特征x和边索引Adj。

out = self.propagate(edge_index, x=x, edge_attr=edge_attr, size=None)

这里最重要的就是self.propagate的这个函数了。具体参考一下这几个博客

PyG的MessagePassing基类中self.propagate函数的消息传递机制-CSDN博客

Torch geometric GCNConv 源码分析-CSDN博客

https://zhuanlan.zhihu.com/p/113862170

在这里主要提一下：在self.propagate函数中，会自动调用self.message函数、self.aggregate函数、self.update函数。我在这里主要讲一下self.message这个函数

    def message(self, x_i: Tensor, x_j: Tensor, edge_attr: OptTensor,
                index: Tensor, ptr: OptTensor,
                size_i: Optional[int]) -> Tensor:

        query = self.lin_query(x_i).view(-1, self.heads, self.out_channels)
        key = self.lin_key(x_j).view(-1, self.heads, self.out_channels)

        if self.lin_edge is not None:
            assert edge_attr is not None
            edge_attr = self.lin_edge(edge_attr).view(-1, self.heads,
                                                      self.out_channels)
            key += edge_attr

        alpha = (query * key).sum(dim=-1) / math.sqrt(self.out_channels)
        alpha = softmax(alpha, index, ptr, size_i)
        self._alpha = alpha
        alpha = F.dropout(alpha, p=self.dropout, training=self.training)

        out = self.lin_value(x_j).view(-1, self.heads, self.out_channels)
        if edge_attr is not None:
            out += edge_attr

        out *= alpha.view(-1, self.heads, 1)
        return out

python中是这样给出的

现在看一下propagate和message的对应关系。

propagate：

edge_index, x=x,这两个参数也就是图的边索引，前者edge_index是一个2*E的维度，E代表有多少条边。

这个应该上下对应着看01 10 12 20 分别连成不同的边。

• x_i : 源节点的特征张量。在 propagate 中，这对应于 x，即 x_i = x[edge_index[0]]。
• x_j : 目标节点的特征张量。在 propagate 中，这对应于 x，即 x_j = x[edge_index[1]]。
• edge_attr : 边特征张量。直接对应于 edge_attr 参数。
• index : 索引张量，用于定位当前消息的具体位置。在 propagate 中，PyTorch Geometric会自动处理这一部分。message最后返回的是out
• 后续的gc1的参数没什么了都是简单的维度变化之类的。
• 感觉终于把这个函数看明白了 好不容易