from typing import Optional
import torch
from torch import Tensor
from torch_geometric.nn.aggr import Aggregation
from torch_geometric.utils import softmax
[docs]class Set2Set(Aggregation):
r"""The Set2Set aggregation operator based on iterative content-based
attention, as described in the `"Order Matters: Sequence to sequence for
Sets" <https://arxiv.org/abs/1511.06391>`_ paper
.. math::
\mathbf{q}_t &= \mathrm{LSTM}(\mathbf{q}^{*}_{t-1})
\alpha_{i,t} &= \mathrm{softmax}(\mathbf{x}_i \cdot \mathbf{q}_t)
\mathbf{r}_t &= \sum_{i=1}^N \alpha_{i,t} \mathbf{x}_i
\mathbf{q}^{*}_t &= \mathbf{q}_t \, \Vert \, \mathbf{r}_t,
where :math:`\mathbf{q}^{*}_T` defines the output of the layer with twice
the dimensionality as the input.
Args:
in_channels (int): Size of each input sample.
processing_steps (int): Number of iterations :math:`T`.
**kwargs (optional): Additional arguments of :class:`torch.nn.LSTM`.
"""
def __init__(self, in_channels: int, processing_steps: int, **kwargs):
super().__init__()
self.in_channels = in_channels
self.out_channels = 2 * in_channels
self.processing_steps = processing_steps
self.lstm = torch.nn.LSTM(self.out_channels, in_channels, **kwargs)
self.reset_parameters()
def reset_parameters(self):
self.lstm.reset_parameters()
def forward(self, x: Tensor, index: Optional[Tensor] = None,
ptr: Optional[Tensor] = None, dim_size: Optional[int] = None,
dim: int = -2) -> Tensor:
# TODO Currently, `to_dense_batch` can only operate on `index`:
self.assert_index_present(index)
self.assert_two_dimensional_input(x, dim)
h = (x.new_zeros((self.lstm.num_layers, dim_size, x.size(-1))),
x.new_zeros((self.lstm.num_layers, dim_size, x.size(-1))))
q_star = x.new_zeros(dim_size, self.out_channels)
for _ in range(self.processing_steps):
q, h = self.lstm(q_star.unsqueeze(0), h)
q = q.view(dim_size, self.in_channels)
e = (x * q[index]).sum(dim=-1, keepdim=True)
a = softmax(e, index, ptr, dim_size, dim)
r = self.reduce(a * x, index, ptr, dim_size, dim, reduce='add')
q_star = torch.cat([q, r], dim=-1)
return q_star
def __repr__(self) -> str:
return (f'{self.__class__.__name__}({self.in_channels}, '
f'{self.out_channels})')