from neuralogic.core.constructs.metadata import Metadata
from neuralogic.core.constructs.function import Transformation, Aggregation
from neuralogic.core.constructs.factories import R, V
from neuralogic.nn.module.module import Module
[docs]
class SGConv(Module):
r"""
Simple Graph Convolutional layer from `"Simplifying Graph Convolutional Networks" <https://arxiv.org/abs/1902.07153>`_.
Which can be expressed as:
.. math::
\mathbf{x}^{\prime}_i = act(\mathbf{W} \cdot {agg}_{j \in \mathcal{N}^k(i)}(\mathbf{x}_j))
Where *act* is an activation function, *agg* aggregation function, *W* is a learnable parameter
and :math:`\mathcal{N}^k(i)` denotes nodes that are *k* hops away from the node *i*.
This equation is translated into the logic form as:
.. code:: logtalk
(R.<output_name>(V.I)[<W>] <= (
R.<feature_name>(V.I<k>),
R.<edge_name>(V.I<1>, V.I<0>), R.<edge_name>(V.I<2>, V.I<1>), ..., R.<edge_name>(V.I<k>, V.I<k-1>),
)) | [<aggregation>, Transformation.IDENTITY]
R.<output_name> / 1 | [<activation>]
Examples
--------
The whole computation of this module (parametrized as :code:`SGConv(2, 3, "h1", "h0", "_edge", 2)`) is as follows:
.. code:: logtalk
(R.h1(V.I0)[3, 2] <= (R.h0(V.I2), R._edge(V.I1, V.I0), R._edge(V.I2, V.I1))) | [Transformation.IDENTITY, Aggregation.SUM]
R.h1 / 1 | [Transformation.IDENTITY]
Module parametrized as :code:`SGConv(2, 3, "h1", "h0", "_edge", 1)` translates into:
.. code:: logtalk
(R.h1(V.I0)[3, 2] <= (R.h0(V.I1), R._edge(V.I1, V.I0))) | [Transformation.IDENTITY, Aggregation.SUM]
R.h1 / 1 | [Transformation.IDENTITY]
Parameters
----------
in_channels : int
Input feature size.
out_channels : int
Output feature size.
output_name : str
Output (head) predicate name of the module.
feature_name : str
Feature predicate name to get features from.
edge_name : str
Edge predicate name to use for neighborhood relations.
k : int
Number of hops.
Default: ``1``
activation : Transformation
Activation function of the output.
Default: ``Transformation.IDENTITY``
aggregation : Aggregation
Aggregation function of nodes' neighbors.
Default: ``Aggregation.SUM``
"""
def __init__(
self,
in_channels: int,
out_channels: int,
output_name: str,
feature_name: str,
edge_name: str,
k: int = 1,
activation: Transformation = Transformation.IDENTITY,
aggregation: Aggregation = Aggregation.SUM,
):
self.output_name = output_name
self.feature_name = feature_name
self.edge_name = edge_name
self.in_channels = in_channels
self.out_channels = out_channels
self.k = k
self.aggregation = aggregation
self.activation = activation
def __call__(self):
head = R.get(self.output_name)(V.I0)[self.out_channels, self.in_channels]
metadata = Metadata(
transformation=Transformation.IDENTITY, aggregation=self.aggregation, duplicit_grounding=True
)
edge = R.get(self.edge_name)
feature = R.get(self.feature_name)
return [
(
head
<= (
feature(f"I{self.k}"),
*(edge(f"I{b}", f"I{a}") for a, b in zip(range(self.k), range(1, self.k + 1))),
)
)
| metadata,
R.get(self.output_name) / 1 | Metadata(transformation=self.activation),
]