"""Torch Module for Atomic Convolution Layer"""
# pylint: disable= no-member, arguments-differ, invalid-name
import numpy as np
import torch as th
import torch.nn as nn
class RadialPooling(nn.Module):
r"""Radial pooling from `Atomic Convolutional Networks for
Predicting Protein-Ligand Binding Affinity <https://arxiv.org/abs/1703.10603>`__
We denote the distance between atom :math:`i` and :math:`j` by :math:`r_{ij}`.
A radial pooling layer transforms distances with radial filters. For radial filter
indexed by :math:`k`, it projects edge distances with
.. math::
h_{ij}^{k} = \exp(-\gamma_{k}|r_{ij}-r_{k}|^2)
If :math:`r_{ij} < c_k`,
.. math::
f_{ij}^{k} = 0.5 * \cos(\frac{\pi r_{ij}}{c_k} + 1),
else,
.. math::
f_{ij}^{k} = 0.
Finally,
.. math::
e_{ij}^{k} = h_{ij}^{k} * f_{ij}^{k}
Parameters
----------
interaction_cutoffs : float32 tensor of shape (K)
:math:`c_k` in the equations above. Roughly they can be considered as learnable cutoffs
and two atoms are considered as connected if the distance between them is smaller than
the cutoffs. K for the number of radial filters.
rbf_kernel_means : float32 tensor of shape (K)
:math:`r_k` in the equations above. K for the number of radial filters.
rbf_kernel_scaling : float32 tensor of shape (K)
:math:`\gamma_k` in the equations above. K for the number of radial filters.
"""
def __init__(self, interaction_cutoffs, rbf_kernel_means, rbf_kernel_scaling):
super(RadialPooling, self).__init__()
self.interaction_cutoffs = nn.Parameter(
interaction_cutoffs.reshape(-1, 1, 1), requires_grad=True)
self.rbf_kernel_means = nn.Parameter(
rbf_kernel_means.reshape(-1, 1, 1), requires_grad=True)
self.rbf_kernel_scaling = nn.Parameter(
rbf_kernel_scaling.reshape(-1, 1, 1), requires_grad=True)
def forward(self, distances):
"""
Description
-----------
Apply the layer to transform edge distances.
Parameters
----------
distances : Float32 tensor of shape (E, 1)
Distance between end nodes of edges. E for the number of edges.
Returns
-------
Float32 tensor of shape (K, E, 1)
Transformed edge distances. K for the number of radial filters.
"""
scaled_euclidean_distance = - self.rbf_kernel_scaling * \
(distances - self.rbf_kernel_means) ** 2 # (K, E, 1)
rbf_kernel_results = th.exp(scaled_euclidean_distance) # (K, E, 1)
cos_values = 0.5 * (th.cos(np.pi * distances / self.interaction_cutoffs) + 1) # (K, E, 1)
cutoff_values = th.where(
distances <= self.interaction_cutoffs,
cos_values, th.zeros_like(cos_values)) # (K, E, 1)
# Note that there appears to be an inconsistency between the paper and
# DeepChem's implementation. In the paper, the scaled_euclidean_distance first
# gets multiplied by cutoff_values, followed by exponentiation. Here we follow
# the practice of DeepChem.
return rbf_kernel_results * cutoff_values
def msg_func(edges):
"""
Description
-----------
Send messages along edges.
Parameters
----------
edges : EdgeBatch
A batch of edges.
Returns
-------
dict mapping 'm' to Float32 tensor of shape (E, K * T)
Messages computed. E for the number of edges, K for the number of
radial filters and T for the number of features to use
(types of atomic number in the paper).
"""
return {'m': th.einsum(
'ij,ik->ijk', edges.src['hv'], edges.data['he']).view(len(edges), -1)}
def reduce_func(nodes):
"""
Description
-----------
Collect messages and update node representations.
Parameters
----------
nodes : NodeBatch
A batch of nodes.
Returns
-------
dict mapping 'hv_new' to Float32 tensor of shape (V, K * T)
Updated node representations. V for the number of nodes, K for the number of
radial filters and T for the number of features to use
(types of atomic number in the paper).
"""
return {'hv_new': nodes.mailbox['m'].sum(1)}
[docs]class AtomicConv(nn.Module):
r"""Atomic Convolution Layer from `Atomic Convolutional Networks for
Predicting Protein-Ligand Binding Affinity <https://arxiv.org/abs/1703.10603>`__
Denoting the type of atom :math:`i` by :math:`z_i` and the distance between atom
:math:`i` and :math:`j` by :math:`r_{ij}`.
**Distance Transformation**
An atomic convolution layer first transforms distances with radial filters and
then perform a pooling operation.
For radial filter indexed by :math:`k`, it projects edge distances with
.. math::
h_{ij}^{k} = \exp(-\gamma_{k}|r_{ij}-r_{k}|^2)
If :math:`r_{ij} < c_k`,
.. math::
f_{ij}^{k} = 0.5 * \cos(\frac{\pi r_{ij}}{c_k} + 1),
else,
.. math::
f_{ij}^{k} = 0.
Finally,
.. math::
e_{ij}^{k} = h_{ij}^{k} * f_{ij}^{k}
**Aggregation**
For each type :math:`t`, each atom collects distance information from all neighbor atoms
of type :math:`t`:
.. math::
p_{i, t}^{k} = \sum_{j\in N(i)} e_{ij}^{k} * 1(z_j == t)
Then concatenate the results for all RBF kernels and atom types.
Parameters
----------
interaction_cutoffs : float32 tensor of shape (K)
:math:`c_k` in the equations above. Roughly they can be considered as learnable cutoffs
and two atoms are considered as connected if the distance between them is smaller than
the cutoffs. K for the number of radial filters.
rbf_kernel_means : float32 tensor of shape (K)
:math:`r_k` in the equations above. K for the number of radial filters.
rbf_kernel_scaling : float32 tensor of shape (K)
:math:`\gamma_k` in the equations above. K for the number of radial filters.
features_to_use : None or float tensor of shape (T)
In the original paper, these are atomic numbers to consider, representing the types
of atoms. T for the number of types of atomic numbers. Default to None.
Note
----
* This convolution operation is designed for molecular graphs in Chemistry, but it might
be possible to extend it to more general graphs.
* There seems to be an inconsistency about the definition of :math:`e_{ij}^{k}` in the
paper and the author's implementation. We follow the author's implementation. In the
paper, :math:`e_{ij}^{k}` was defined as
:math:`\exp(-\gamma_{k}|r_{ij}-r_{k}|^2 * f_{ij}^{k})`.
* :math:`\gamma_{k}`, :math:`r_k` and :math:`c_k` are all learnable.
Example
-------
>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import AtomicConv
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 1)
>>> edist = th.ones(6, 1)
>>> interaction_cutoffs = th.ones(3).float() * 2
>>> rbf_kernel_means = th.ones(3).float()
>>> rbf_kernel_scaling = th.ones(3).float()
>>> conv = AtomicConv(interaction_cutoffs, rbf_kernel_means, rbf_kernel_scaling)
>>> res = conv(g, feat, edist)
>>> res
tensor([[0.5000, 0.5000, 0.5000],
[0.5000, 0.5000, 0.5000],
[0.5000, 0.5000, 0.5000],
[1.0000, 1.0000, 1.0000],
[0.5000, 0.5000, 0.5000],
[0.0000, 0.0000, 0.0000]], grad_fn=<ViewBackward>)
"""
def __init__(self, interaction_cutoffs, rbf_kernel_means,
rbf_kernel_scaling, features_to_use=None):
super(AtomicConv, self).__init__()
self.radial_pooling = RadialPooling(interaction_cutoffs=interaction_cutoffs,
rbf_kernel_means=rbf_kernel_means,
rbf_kernel_scaling=rbf_kernel_scaling)
if features_to_use is None:
self.num_channels = 1
self.features_to_use = None
else:
self.num_channels = len(features_to_use)
self.features_to_use = nn.Parameter(features_to_use, requires_grad=False)
[docs] def forward(self, graph, feat, distances):
"""
Description
-----------
Apply the atomic convolution layer.
Parameters
----------
graph : DGLGraph
Topology based on which message passing is performed.
feat : Float32 tensor of shape :math:`(V, 1)`
Initial node features, which are atomic numbers in the paper.
:math:`V` for the number of nodes.
distances : Float32 tensor of shape :math:`(E, 1)`
Distance between end nodes of edges. E for the number of edges.
Returns
-------
Float32 tensor of shape :math:`(V, K * T)`
Updated node representations. :math:`V` for the number of nodes, :math:`K` for the
number of radial filters, and :math:`T` for the number of types of atomic numbers.
"""
with graph.local_scope():
radial_pooled_values = self.radial_pooling(distances) # (K, E, 1)
if self.features_to_use is not None:
feat = (feat == self.features_to_use).float() # (V, T)
graph.ndata['hv'] = feat
graph.edata['he'] = radial_pooled_values.transpose(1, 0).squeeze(-1) # (E, K)
graph.update_all(msg_func, reduce_func)
return graph.ndata['hv_new'].view(graph.number_of_nodes(), -1) # (V, K * T)