def __init__(self,
                 in_channels: int,
                 out_channels: int,
                 edge_pos_emb=False,
                 aggr: str = 'softmax',
                 t: float = 1.0,
                 learn_t: bool = False,
                 p: float = 1.0,
                 learn_p: bool = False,
                 msg_norm: bool = False,
                 learn_msg_scale: bool = False,
                 norm: str = 'batch',
                 num_layers: int = 2,
                 eps: float = 1e-7,
                 **kwargs):

        kwargs.setdefault('aggr', None)
        super(GENConv, self).__init__(**kwargs)

        self.in_channels = in_channels
        self.out_channels = out_channels
        self.aggr = aggr
        self.eps = eps

        assert aggr in ['softmax', 'softmax_sg', 'power']

        channels = [in_channels]
        for i in range(num_layers - 1):
            channels.append(in_channels * 2)
        channels.append(out_channels)
        self.mlp = MLP(channels, norm=norm)

        self.msg_norm = MessageNorm(learn_msg_scale) if msg_norm else None

        self.initial_t = t
        self.initial_p = p

        if learn_t and aggr == 'softmax':
            self.t = Parameter(torch.Tensor([t]), requires_grad=True)
        else:
            self.t = t

        if learn_p:
            self.p = Parameter(torch.Tensor([p]), requires_grad=True)
        else:
            self.p = p

        if edge_pos_emb:
            self.edge_enc = TrajPositionalEncoding(d_model=out_channels,
                                                   max_len=110)
        else:
            self.edge_enc = None
Example #2
0
    def __init__(self,
                 in_channels: int,
                 out_channels: int,
                 aggr: str = 'softmax',
                 t: float = 1.0,
                 learn_t: bool = False,
                 p: float = 1.0,
                 learn_p: bool = False,
                 msg_norm: bool = False,
                 learn_msg_scale: bool = False,
                 norm: str = 'batch',
                 num_layers: int = 2,
                 eps: float = 1e-7,
                 **kwargs):

        super(GENConv, self).__init__(aggr=None, **kwargs)

        self.in_channels = in_channels
        self.out_channels = out_channels
        self.aggr = aggr
        self.eps = eps

        assert aggr in ['softmax', 'softmax_sg', 'power', 'stat']

        channels = [in_channels]
        for i in range(num_layers - 1):
            channels.append(in_channels * 2)
        channels.append(out_channels)
        self.mlp = MLP(channels, norm=norm)

        self.msg_norm = MessageNorm(learn_msg_scale) if msg_norm else None

        self.initial_t = t
        self.initial_p = p

        if learn_t and aggr == 'softmax':
            self.t = Parameter(torch.Tensor([t]), requires_grad=True)
        else:
            self.t = t

        if learn_p:
            self.p = Parameter(torch.Tensor([p]), requires_grad=True)
        else:
            self.p = p

        self.lin_stat = nn.Linear(4, 1)
Example #3
0
    def __init__(self,
                 in_channels: int,
                 out_channels: int,
                 aggr: str = 'softmax',
                 t: float = 1.0,
                 learn_t: bool = False,
                 p: float = 1.0,
                 learn_p: bool = False,
                 msg_norm: bool = False,
                 learn_msg_scale: bool = False,
                 norm: str = 'batch',
                 num_layers: int = 2,
                 eps: float = 1e-7,
                 **kwargs):

        # Backward compatibility:
        aggr = 'softmax' if aggr == 'softmax_sg' else aggr
        aggr = 'powermean' if aggr == 'power' else aggr

        aggr_kwargs = {}
        if aggr == 'softmax':
            aggr_kwargs = dict(t=t, learn=learn_t)
        elif aggr == 'powermean':
            aggr_kwargs = dict(p=p, learn=learn_p)

        super().__init__(aggr=aggr, aggr_kwargs=aggr_kwargs, **kwargs)

        self.in_channels = in_channels
        self.out_channels = out_channels
        self.eps = eps

        channels = [in_channels]
        for i in range(num_layers - 1):
            channels.append(in_channels * 2)
        channels.append(out_channels)
        self.mlp = MLP(channels, norm=norm)

        self.msg_norm = MessageNorm(learn_msg_scale) if msg_norm else None
Example #4
0
    def __init__(self, in_channels, out_channels, edge_channels=1, **kwargs):
        super(GateConv, self).__init__(aggr='add', **kwargs)

        self.in_channels = in_channels
        self.out_channels = out_channels
        self.edge_channels = edge_channels

        self.linear_n = nn.Parameter(torch.Tensor(in_channels, out_channels))
        self.linear_e = nn.Parameter(torch.Tensor(edge_channels, out_channels))

        # self.linear_attn = LinearMultiHeadedAttention(h=)
        self.tfm_encoder = make_transformer_encoder(num_layers=2,
                                                    hidden_size=out_channels *
                                                    2,
                                                    ff_size=out_channels * 2,
                                                    num_att_heads=8)

        self.msg_norm = MessageNorm(learn_scale=True)

        self.linear_msg = nn.Linear(out_channels * 2, out_channels)
        self.linear_aggr = nn.Linear(out_channels, out_channels)

        self.reset_parameters()
Example #5
0
class GENConv(MessagePassing):
    r"""The GENeralized Graph Convolution (GENConv) from the `"DeeperGCN: All
    You Need to Train Deeper GCNs" <https://arxiv.org/abs/2006.07739>`_ paper.
    Supports SoftMax & PowerMean aggregation. The message construction is:

    .. math::
        \mathbf{x}_i^{\prime} = \mathrm{MLP} \left( \mathbf{x}_i +
        \mathrm{AGG} \left( \left\{
        \mathrm{ReLU} \left( \mathbf{x}_j + \mathbf{e_{ji}} \right) +\epsilon
        : j \in \mathcal{N}(i) \right\} \right)
        \right)

    .. note::

        For an example of using :obj:`GENConv`, see
        `examples/ogbn_proteins_deepgcn.py
        <https://github.com/pyg-team/pytorch_geometric/blob/master/examples/
        ogbn_proteins_deepgcn.py>`_.

    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.
        aggr (str, optional): The aggregation scheme to use (:obj:`"softmax"`,
            :obj:`"softmax_sg"`, :obj:`"power"`, :obj:`"add"`, :obj:`"mean"`,
            :obj:`max`). (default: :obj:`"softmax"`)
        t (float, optional): Initial inverse temperature for softmax
            aggregation. (default: :obj:`1.0`)
        learn_t (bool, optional): If set to :obj:`True`, will learn the value
            :obj:`t` for softmax aggregation dynamically.
            (default: :obj:`False`)
        p (float, optional): Initial power for power mean aggregation.
            (default: :obj:`1.0`)
        learn_p (bool, optional): If set to :obj:`True`, will learn the value
            :obj:`p` for power mean aggregation dynamically.
            (default: :obj:`False`)
        msg_norm (bool, optional): If set to :obj:`True`, will use message
            normalization. (default: :obj:`False`)
        learn_msg_scale (bool, optional): If set to :obj:`True`, will learn the
            scaling factor of message normalization. (default: :obj:`False`)
        norm (str, optional): Norm layer of MLP layers (:obj:`"batch"`,
            :obj:`"layer"`, :obj:`"instance"`) (default: :obj:`batch`)
        num_layers (int, optional): The number of MLP layers.
            (default: :obj:`2`)
        eps (float, optional): The epsilon value of the message construction
            function. (default: :obj:`1e-7`)
        **kwargs (optional): Additional arguments of
            :class:`torch_geometric.nn.conv.GenMessagePassing`.
    """
    def __init__(self, in_channels: int, out_channels: int,
                 aggr: str = 'softmax', t: float = 1.0, learn_t: bool = False,
                 p: float = 1.0, learn_p: bool = False, msg_norm: bool = False,
                 learn_msg_scale: bool = False, norm: str = 'batch',
                 num_layers: int = 2, eps: float = 1e-7, **kwargs):

        kwargs.setdefault('aggr', None)
        super().__init__(**kwargs)

        self.in_channels = in_channels
        self.out_channels = out_channels
        self.aggr = aggr
        self.eps = eps

        assert aggr in ['softmax', 'softmax_sg', 'power', 'add', 'mean', 'max']

        channels = [in_channels]
        for i in range(num_layers - 1):
            channels.append(in_channels * 2)
        channels.append(out_channels)
        self.mlp = MLP(channels, norm=norm)

        self.msg_norm = MessageNorm(learn_msg_scale) if msg_norm else None

        self.initial_t = t
        self.initial_p = p

        if learn_t and aggr == 'softmax':
            self.t = Parameter(torch.Tensor([t]), requires_grad=True)
        else:
            self.t = t

        if learn_p:
            self.p = Parameter(torch.Tensor([p]), requires_grad=True)
        else:
            self.p = p

    def reset_parameters(self):
        reset(self.mlp)
        if self.msg_norm is not None:
            self.msg_norm.reset_parameters()
        if self.t and isinstance(self.t, Tensor):
            self.t.data.fill_(self.initial_t)
        if self.p and isinstance(self.p, Tensor):
            self.p.data.fill_(self.initial_p)

    def forward(self, x: Union[Tensor, OptPairTensor], edge_index: Adj,
                edge_attr: OptTensor = None, size: Size = None) -> Tensor:
        """"""

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

        # Node and edge feature dimensionalites need to match.
        if isinstance(edge_index, Tensor):
            if edge_attr is not None:
                assert x[0].size(-1) == edge_attr.size(-1)
        elif isinstance(edge_index, SparseTensor):
            edge_attr = edge_index.storage.value()
            if edge_attr is not None:
                assert x[0].size(-1) == edge_attr.size(-1)

        # propagate_type: (x: OptPairTensor, edge_attr: OptTensor)
        out = self.propagate(edge_index, x=x, edge_attr=edge_attr, size=size)

        if self.msg_norm is not None:
            out = self.msg_norm(x[0], out)

        x_r = x[1]
        if x_r is not None:
            out += x_r

        return self.mlp(out)

    def message(self, x_j: Tensor, edge_attr: OptTensor) -> Tensor:
        msg = x_j if edge_attr is None else x_j + edge_attr
        return F.relu(msg) + self.eps

    def aggregate(self, inputs: Tensor, index: Tensor,
                  dim_size: Optional[int] = None) -> Tensor:

        if self.aggr == 'softmax':
            out = scatter_softmax(inputs * self.t, index, dim=self.node_dim)
            return scatter(inputs * out, index, dim=self.node_dim,
                           dim_size=dim_size, reduce='sum')

        elif self.aggr == 'softmax_sg':
            out = scatter_softmax(inputs * self.t, index,
                                  dim=self.node_dim).detach()
            return scatter(inputs * out, index, dim=self.node_dim,
                           dim_size=dim_size, reduce='sum')

        elif self.aggr == 'power':
            min_value, max_value = 1e-7, 1e1
            torch.clamp_(inputs, min_value, max_value)
            out = scatter(torch.pow(inputs, self.p), index, dim=self.node_dim,
                          dim_size=dim_size, reduce='mean')
            torch.clamp_(out, min_value, max_value)
            return torch.pow(out, 1 / self.p)

        else:
            return scatter(inputs, index, dim=self.node_dim, dim_size=dim_size,
                           reduce=self.aggr)

    def __repr__(self) -> str:
        return (f'{self.__class__.__name__}({self.in_channels}, '
                f'{self.out_channels}, aggr={self.aggr})')
Example #6
0
class GENConv(MessagePassing):
    r"""The GENeralized Graph Convolution (GENConv) from the `"DeeperGCN: All
    You Need to Train Deeper GCNs" <https://arxiv.org/abs/2006.07739>`_ paper.
    Supports SoftMax & PowerMean aggregation. The message construction is:

    .. math::
        \mathbf{x}_i^{\prime} = \mathrm{MLP} \left( \mathbf{x}_i +
        \mathrm{AGG} \left( \left\{
        \mathrm{ReLU} \left( \mathbf{x}_j + \mathbf{e_{ji}} \right) +\epsilon
        : j \in \mathcal{N}(i) \right\} \right)
        \right)

    .. note::

        For an example of using :obj:`GENConv`, see
        `examples/ogbn_proteins_deepgcn.py
        <https://github.com/pyg-team/pytorch_geometric/blob/master/examples/
        ogbn_proteins_deepgcn.py>`_.

    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.
        aggr (str, optional): The aggregation scheme to use (:obj:`"softmax"`,
            :obj:`"powermean"`, :obj:`"add"`, :obj:`"mean"`, :obj:`max`).
            (default: :obj:`"softmax"`)
        t (float, optional): Initial inverse temperature for softmax
            aggregation. (default: :obj:`1.0`)
        learn_t (bool, optional): If set to :obj:`True`, will learn the value
            :obj:`t` for softmax aggregation dynamically.
            (default: :obj:`False`)
        p (float, optional): Initial power for power mean aggregation.
            (default: :obj:`1.0`)
        learn_p (bool, optional): If set to :obj:`True`, will learn the value
            :obj:`p` for power mean aggregation dynamically.
            (default: :obj:`False`)
        msg_norm (bool, optional): If set to :obj:`True`, will use message
            normalization. (default: :obj:`False`)
        learn_msg_scale (bool, optional): If set to :obj:`True`, will learn the
            scaling factor of message normalization. (default: :obj:`False`)
        norm (str, optional): Norm layer of MLP layers (:obj:`"batch"`,
            :obj:`"layer"`, :obj:`"instance"`) (default: :obj:`batch`)
        num_layers (int, optional): The number of MLP layers.
            (default: :obj:`2`)
        eps (float, optional): The epsilon value of the message construction
            function. (default: :obj:`1e-7`)
        **kwargs (optional): Additional arguments of
            :class:`torch_geometric.nn.conv.GenMessagePassing`.

    Shapes:
        - **input:**
          node features :math:`(|\mathcal{V}|, F_{in})` or
          :math:`((|\mathcal{V_s}|, F_{in}), (|\mathcal{V_t}|, F_{t})`
          if bipartite,
          edge indices :math:`(2, |\mathcal{E}|)`,
          edge attributes :math:`(|\mathcal{E}|, D)` *(optional)*
        - **output:** node features :math:`(|\mathcal{V}|, F_{out})` or
          :math:`(|\mathcal{V}_t|, F_{out})` if bipartite
    """
    def __init__(self,
                 in_channels: int,
                 out_channels: int,
                 aggr: str = 'softmax',
                 t: float = 1.0,
                 learn_t: bool = False,
                 p: float = 1.0,
                 learn_p: bool = False,
                 msg_norm: bool = False,
                 learn_msg_scale: bool = False,
                 norm: str = 'batch',
                 num_layers: int = 2,
                 eps: float = 1e-7,
                 **kwargs):

        # Backward compatibility:
        aggr = 'softmax' if aggr == 'softmax_sg' else aggr
        aggr = 'powermean' if aggr == 'power' else aggr

        aggr_kwargs = {}
        if aggr == 'softmax':
            aggr_kwargs = dict(t=t, learn=learn_t)
        elif aggr == 'powermean':
            aggr_kwargs = dict(p=p, learn=learn_p)

        super().__init__(aggr=aggr, aggr_kwargs=aggr_kwargs, **kwargs)

        self.in_channels = in_channels
        self.out_channels = out_channels
        self.eps = eps

        channels = [in_channels]
        for i in range(num_layers - 1):
            channels.append(in_channels * 2)
        channels.append(out_channels)
        self.mlp = MLP(channels, norm=norm)

        self.msg_norm = MessageNorm(learn_msg_scale) if msg_norm else None

    def reset_parameters(self):
        reset(self.mlp)
        self.aggr_module.reset_parameters()
        if self.msg_norm is not None:
            self.msg_norm.reset_parameters()

    def forward(self,
                x: Union[Tensor, OptPairTensor],
                edge_index: Adj,
                edge_attr: OptTensor = None,
                size: Size = None) -> Tensor:
        """"""
        if isinstance(x, Tensor):
            x: OptPairTensor = (x, x)

        # Node and edge feature dimensionalites need to match.
        if isinstance(edge_index, Tensor):
            if edge_attr is not None:
                assert x[0].size(-1) == edge_attr.size(-1)
        elif isinstance(edge_index, SparseTensor):
            edge_attr = edge_index.storage.value()
            if edge_attr is not None:
                assert x[0].size(-1) == edge_attr.size(-1)

        # propagate_type: (x: OptPairTensor, edge_attr: OptTensor)
        out = self.propagate(edge_index, x=x, edge_attr=edge_attr, size=size)

        if self.msg_norm is not None:
            out = self.msg_norm(x[0], out)

        x_r = x[1]
        if x_r is not None:
            out += x_r

        return self.mlp(out)

    def message(self, x_j: Tensor, edge_attr: OptTensor) -> Tensor:
        msg = x_j if edge_attr is None else x_j + edge_attr
        return msg.relu() + self.eps

    def __repr__(self) -> str:
        return (f'{self.__class__.__name__}({self.in_channels}, '
                f'{self.out_channels}, aggr={self.aggr})')
class GENConv(MessagePassing):
    r"""The GENeralized Graph Convolution (GENConv) from the `"DeeperGCN: All
    You Need to Train Deeper GCNs" <https://arxiv.org/abs/2006.07739>`_ paper.
    Supports SoftMax & PowerMean aggregation. The message construction is:

    .. math::
        \mathbf{x}_i^{\prime} = \mathrm{MLP} \left( \mathbf{x}_i +
        \mathrm{AGG} \left( \left\{
        \mathrm{ReLU} \left( \mathbf{x}_j + \mathbf{e_{ji}} \right) +\epsilon
        : j \in \mathcal{N}(i) \right\} \right)
        \right)

    .. note::

        For an example of using :obj:`GENConv`, see
        `examples/ogbn_proteins_deepgcn.py
        <https://github.com/rusty1s/pytorch_geometric/blob/master/examples/
        ogbn_proteins_deepgcn.py>`_.

    Args:
        in_channels (int): Size of each input sample.
        out_channels (int): Size of each output sample.
        aggr (str, optional): The aggregation scheme to use (:obj:`"softmax"`,
            :obj:`"softmax_sg"`, :obj:`"power"`, :obj:`"add"`, :obj:`"mean"`,
            :obj:`max`). (default: :obj:`"softmax"`)
        t (float, optional): Initial inverse temperature for softmax
            aggregation. (default: :obj:`1.0`)
        learn_t (bool, optional): If set to :obj:`True`, will learn the value
            :obj:`t` for softmax aggregation dynamically.
            (default: :obj:`False`)
        p (float, optional): Initial power for power mean aggregation.
            (default: :obj:`1.0`)
        learn_p (bool, optional): If set to :obj:`True`, will learn the value
            :obj:`p` for power mean aggregation dynamically.
            (default: :obj:`False`)
        msg_norm (bool, optional): If set to :obj:`True`, will use message
            normalization. (default: :obj:`False`)
        learn_msg_scale (bool, optional): If set to :obj:`True`, will learn the
            scaling factor of message normalization. (default: :obj:`False`)
        norm (str, optional): Norm layer of MLP layers (:obj:`"batch"`,
            :obj:`"layer"`, :obj:`"instance"`) (default: :obj:`batch`)
        num_layers (int, optional): The number of MLP layers.
            (default: :obj:`2`)
        eps (float, optional): The epsilon value of the message construction
            function. (default: :obj:`1e-7`)
        **kwargs (optional): Additional arguments of
            :class:`torch_geometric.nn.conv.GenMessagePassing`.
    """
    def __init__(self,
                 in_channels: int,
                 out_channels: int,
                 edge_pos_emb=False,
                 aggr: str = 'softmax',
                 t: float = 1.0,
                 learn_t: bool = False,
                 p: float = 1.0,
                 learn_p: bool = False,
                 msg_norm: bool = False,
                 learn_msg_scale: bool = False,
                 norm: str = 'batch',
                 num_layers: int = 2,
                 eps: float = 1e-7,
                 **kwargs):

        kwargs.setdefault('aggr', None)
        super(GENConv, self).__init__(**kwargs)

        self.in_channels = in_channels
        self.out_channels = out_channels
        self.aggr = aggr
        self.eps = eps

        assert aggr in ['softmax', 'softmax_sg', 'power']

        channels = [in_channels]
        for i in range(num_layers - 1):
            channels.append(in_channels * 2)
        channels.append(out_channels)
        self.mlp = MLP(channels, norm=norm)

        self.msg_norm = MessageNorm(learn_msg_scale) if msg_norm else None

        self.initial_t = t
        self.initial_p = p

        if learn_t and aggr == 'softmax':
            self.t = Parameter(torch.Tensor([t]), requires_grad=True)
        else:
            self.t = t

        if learn_p:
            self.p = Parameter(torch.Tensor([p]), requires_grad=True)
        else:
            self.p = p

        if edge_pos_emb:
            self.edge_enc = TrajPositionalEncoding(d_model=out_channels,
                                                   max_len=110)
        else:
            self.edge_enc = None

    def reset_parameters(self):
        reset(self.mlp)
        if self.msg_norm is not None:
            self.msg_norm.reset_parameters()
        if self.t and isinstance(self.t, Tensor):
            self.t.data.fill_(self.initial_t)
        if self.p and isinstance(self.p, Tensor):
            self.p.data.fill_(self.initial_p)

    def forward(self,
                x: Union[Tensor, OptPairTensor],
                edge_index: Adj,
                edge_attr: OptTensor = None,
                edge_attr_len: OptTensor = None,
                size: Size = None,
                tm_index=None,
                duplicates_idx=None) -> Tensor:
        """"""

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

        # add_self_loops
        if tm_index is not None:
            edge_index = add_self_loops(edge_index, tm_index, verbose=False)

        # propagate_type: (x: OptPairTensor, edge_attr: OptTensor)
        out = self.propagate(edge_index,
                             x=x,
                             edge_attr=edge_attr,
                             edge_attr_len=edge_attr_len,
                             size=size,
                             duplicates_idx=duplicates_idx)

        if self.msg_norm is not None:
            out = self.msg_norm(x[0], out)

        x_r = x[1]
        if x_r is not None:
            out += x_r

        return self.mlp(out)

    def message(self, x_j: Tensor, edge_attr: OptTensor,
                edge_attr_len: OptTensor, duplicates_idx: OptTensor) -> Tensor:
        #         print('in message')
        #         print('x_j.size(), edge_attr.size()', x_j.size(), edge_attr.size())
        just_made_dup = False

        if duplicates_idx is None:  # 1st layer, so make duplicates_idx
            just_made_dup = True
            edge_indice, cnt_ = torch.unique(
                edge_attr,
                return_counts=True,
            )
            duplicates_idx = [
                [idx] * (c - 1)
                for idx, c in zip(edge_indice[cnt_ != 1], cnt_[cnt_ != 1])
            ]
            duplicates_idx = [_ for li in duplicates_idx for _ in li]

        # duplicates_idx is not None
        x_j = torch.cat((x_j, x_j[duplicates_idx, ]),
                        dim=0)  # ((E+num_duplicates),H)
        #         print("duplicates_idx: ", duplicates_idx)
        #         print("x_j: ", x_j)

        if just_made_dup:
            for i, idx in enumerate(duplicates_idx):
                edge_attr[torch.arange(edge_attr.size(0))[edge_attr == idx]
                          [-1]] = x_j.size(0) - len(duplicates_idx) + i

#         print('x_j.size(), edge_attr.size()', x_j.size(), edge_attr.size())

        if self.edge_enc:
            #             print("Adding edge_enc ... ")
            edge_pos_emb = self.edge_enc(edge_attr_len)
            #             print(edge_pos_emb.size())
            x_j[edge_attr] += edge_pos_emb.squeeze()


#         print("x_j size", x_j.size())
        self.duplicates_idx = duplicates_idx

        return F.relu(x_j) + self.eps, duplicates_idx

    def aggregate(self,
                  inputs,
                  index: Tensor,
                  dim_size: Optional[int] = None) -> Tensor:

        inputs, duplicates_idx = inputs
        index = torch.cat((index, index[duplicates_idx, ]), dim=0)
        #         print('duplicates_idx: ',duplicates_idx)

        if self.aggr == 'softmax':
            out = scatter_softmax(inputs * self.t, index, dim=self.node_dim)
            return scatter(inputs * out,
                           index,
                           dim=self.node_dim,
                           dim_size=dim_size,
                           reduce='sum')

        elif self.aggr == 'softmax_sg':
            out = scatter_softmax(inputs * self.t, index,
                                  dim=self.node_dim).detach()
            return scatter(inputs * out,
                           index,
                           dim=self.node_dim,
                           dim_size=dim_size,
                           reduce='sum')

        else:
            min_value, max_value = 1e-7, 1e1
            torch.clamp_(inputs, min_value, max_value)
            out = scatter(torch.pow(inputs, self.p),
                          index,
                          dim=self.node_dim,
                          dim_size=dim_size,
                          reduce='mean')
            torch.clamp_(out, min_value, max_value)
            return torch.pow(out, 1 / self.p)

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