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import torch, functools
from torch import nn
import torch.nn.functional as F
from torch_geometric.nn import MessagePassing
from torch_scatter import scatter_add
def tuple_sum(*args):
'''
Sums any number of tuples (s, V) elementwise.
'''
return tuple(map(sum, zip(*args)))
def tuple_cat(*args, dim=-1):
'''
Concatenates any number of tuples (s, V) elementwise.
:param dim: dimension along which to concatenate when viewed
as the `dim` index for the scalar-channel tensors.
This means that `dim=-1` will be applied as
`dim=-2` for the vector-channel tensors.
'''
dim %= len(args[0][0].shape)
s_args, v_args = list(zip(*args))
return torch.cat(s_args, dim=dim), torch.cat(v_args, dim=dim)
def tuple_index(x, idx):
'''
Indexes into a tuple (s, V) along the first dimension.
:param idx: any object which can be used to index into a `torch.Tensor`
'''
return x[0][idx], x[1][idx]
def randn(n, dims, device="cpu"):
'''
Returns random tuples (s, V) drawn elementwise from a normal distribution.
:param n: number of data points
:param dims: tuple of dimensions (n_scalar, n_vector)
:return: (s, V) with s.shape = (n, n_scalar) and
V.shape = (n, n_vector, 3)
'''
return torch.randn(n, dims[0], device=device), \
torch.randn(n, dims[1], 3, device=device)
def _norm_no_nan(x, axis=-1, keepdims=False, eps=1e-8, sqrt=True):
'''
L2 norm of tensor clamped above a minimum value `eps`.
:param sqrt: if `False`, returns the square of the L2 norm
'''
out = torch.clamp(torch.sum(torch.square(x), axis, keepdims), min=eps)
return torch.sqrt(out) if sqrt else out
def _split(x, nv):
'''
Splits a merged representation of (s, V) back into a tuple.
Should be used only with `_merge(s, V)` and only if the tuple
representation cannot be used.
:param x: the `torch.Tensor` returned from `_merge`
:param nv: the number of vector channels in the input to `_merge`
'''
v = torch.reshape(x[..., -3*nv:], x.shape[:-1] + (nv, 3))
s = x[..., :-3*nv]
return s, v
def _merge(s, v):
'''
Merges a tuple (s, V) into a single `torch.Tensor`, where the
vector channels are flattened and appended to the scalar channels.
Should be used only if the tuple representation cannot be used.
Use `_split(x, nv)` to reverse.
'''
v = torch.reshape(v, v.shape[:-2] + (3*v.shape[-2],))
return torch.cat([s, v], -1)
class GVP(nn.Module):
'''
Geometric Vector Perceptron. See manuscript and README.md
for more details.
:param in_dims: tuple (n_scalar, n_vector)
:param out_dims: tuple (n_scalar, n_vector)
:param h_dim: intermediate number of vector channels, optional
:param activations: tuple of functions (scalar_act, vector_act)
:param vector_gate: whether to use vector gating.
(vector_act will be used as sigma^+ in vector gating if `True`)
'''
def __init__(self, in_dims, out_dims, h_dim=None,
activations=(F.relu, torch.sigmoid), vector_gate=False):
super(GVP, self).__init__()
self.si, self.vi = in_dims
self.so, self.vo = out_dims
self.vector_gate = vector_gate
if self.vi:
self.h_dim = h_dim or max(self.vi, self.vo)
self.wh = nn.Linear(self.vi, self.h_dim, bias=False)
self.ws = nn.Linear(self.h_dim + self.si, self.so)
if self.vo:
self.wv = nn.Linear(self.h_dim, self.vo, bias=False)
if self.vector_gate: self.wsv = nn.Linear(self.so, self.vo)
else:
self.ws = nn.Linear(self.si, self.so)
self.scalar_act, self.vector_act = activations
self.dummy_param = nn.Parameter(torch.empty(0))
def forward(self, x):
'''
:param x: tuple (s, V) of `torch.Tensor`,
or (if vectors_in is 0), a single `torch.Tensor`
:return: tuple (s, V) of `torch.Tensor`,
or (if vectors_out is 0), a single `torch.Tensor`
'''
if self.vi:
s, v = x
v = torch.transpose(v, -1, -2)
vh = self.wh(v)
vn = _norm_no_nan(vh, axis=-2)
s = self.ws(torch.cat([s, vn], -1))
if self.vo:
v = self.wv(vh)
v = torch.transpose(v, -1, -2)
if self.vector_gate:
if self.vector_act:
gate = self.wsv(self.vector_act(s))
else:
gate = self.wsv(s)
v = v * torch.sigmoid(gate).unsqueeze(-1)
elif self.vector_act:
v = v * self.vector_act(
_norm_no_nan(v, axis=-1, keepdims=True))
else:
s = self.ws(x)
if self.vo:
v = torch.zeros(s.shape[0], self.vo, 3,
device=self.dummy_param.device)
if self.scalar_act:
s = self.scalar_act(s)
return (s, v) if self.vo else s
class _VDropout(nn.Module):
'''
Vector channel dropout where the elements of each
vector channel are dropped together.
'''
def __init__(self, drop_rate):
super(_VDropout, self).__init__()
self.drop_rate = drop_rate
self.dummy_param = nn.Parameter(torch.empty(0))
def forward(self, x):
'''
:param x: `torch.Tensor` corresponding to vector channels
'''
device = self.dummy_param.device
if not self.training:
return x
mask = torch.bernoulli(
(1 - self.drop_rate) * torch.ones(x.shape[:-1], device=device)
).unsqueeze(-1)
x = mask * x / (1 - self.drop_rate)
return x
class Dropout(nn.Module):
'''
Combined dropout for tuples (s, V).
Takes tuples (s, V) as input and as output.
'''
def __init__(self, drop_rate):
super(Dropout, self).__init__()
self.sdropout = nn.Dropout(drop_rate)
self.vdropout = _VDropout(drop_rate)
def forward(self, x):
'''
:param x: tuple (s, V) of `torch.Tensor`,
or single `torch.Tensor`
(will be assumed to be scalar channels)
'''
if type(x) is torch.Tensor:
return self.sdropout(x)
s, v = x
return self.sdropout(s), self.vdropout(v)
class LayerNorm(nn.Module):
'''
Combined LayerNorm for tuples (s, V).
Takes tuples (s, V) as input and as output.
'''
def __init__(self, dims):
super(LayerNorm, self).__init__()
self.s, self.v = dims
self.scalar_norm = nn.LayerNorm(self.s)
def forward(self, x):
'''
:param x: tuple (s, V) of `torch.Tensor`,
or single `torch.Tensor`
(will be assumed to be scalar channels)
'''
if not self.v:
return self.scalar_norm(x)
s, v = x
vn = _norm_no_nan(v, axis=-1, keepdims=True, sqrt=False)
vn = torch.sqrt(torch.mean(vn, dim=-2, keepdim=True))
return self.scalar_norm(s), v / vn
class GVPConv(MessagePassing):
'''
Graph convolution / message passing with Geometric Vector Perceptrons.
Takes in a graph with node and edge embeddings,
and returns new node embeddings.
This does NOT do residual updates and pointwise feedforward layers
---see `GVPConvLayer`.
:param in_dims: input node embedding dimensions (n_scalar, n_vector)
:param out_dims: output node embedding dimensions (n_scalar, n_vector)
:param edge_dims: input edge embedding dimensions (n_scalar, n_vector)
:param n_layers: number of GVPs in the message function
:param module_list: preconstructed message function, overrides n_layers
:param aggr: should be "add" if some incoming edges are masked, as in
a masked autoregressive decoder architecture, otherwise "mean"
:param activations: tuple of functions (scalar_act, vector_act) to use in GVPs
:param vector_gate: whether to use vector gating.
(vector_act will be used as sigma^+ in vector gating if `True`)
'''
def __init__(self, in_dims, out_dims, edge_dims,
n_layers=3, module_list=None, aggr="mean",
activations=(F.relu, torch.sigmoid), vector_gate=False):
super(GVPConv, self).__init__(aggr=aggr)
self.si, self.vi = in_dims
self.so, self.vo = out_dims
self.se, self.ve = edge_dims
GVP_ = functools.partial(GVP,
activations=activations, vector_gate=vector_gate)
module_list = module_list or []
if not module_list:
if n_layers == 1:
module_list.append(
GVP_((2*self.si + self.se, 2*self.vi + self.ve),
(self.so, self.vo), activations=(None, None)))
else:
module_list.append(
GVP_((2*self.si + self.se, 2*self.vi + self.ve), out_dims)
)
for i in range(n_layers - 2):
module_list.append(GVP_(out_dims, out_dims))
module_list.append(GVP_(out_dims, out_dims,
activations=(None, None)))
self.message_func = nn.Sequential(*module_list)
def forward(self, x, edge_index, edge_attr):
'''
:param x: tuple (s, V) of `torch.Tensor`
:param edge_index: array of shape [2, n_edges]
:param edge_attr: tuple (s, V) of `torch.Tensor`
'''
x_s, x_v = x
message = self.propagate(edge_index,
s=x_s, v=x_v.reshape(x_v.shape[0], 3*x_v.shape[1]),
edge_attr=edge_attr)
return _split(message, self.vo)
def message(self, s_i, v_i, s_j, v_j, edge_attr):
v_j = v_j.view(v_j.shape[0], v_j.shape[1]//3, 3)
v_i = v_i.view(v_i.shape[0], v_i.shape[1]//3, 3)
message = tuple_cat((s_j, v_j), edge_attr, (s_i, v_i))
message = self.message_func(message)
return _merge(*message)
class GVPConvLayer(nn.Module):
'''
Full graph convolution / message passing layer with
Geometric Vector Perceptrons. Residually updates node embeddings with
aggregated incoming messages, applies a pointwise feedforward
network to node embeddings, and returns updated node embeddings.
To only compute the aggregated messages, see `GVPConv`.
:param node_dims: node embedding dimensions (n_scalar, n_vector)
:param edge_dims: input edge embedding dimensions (n_scalar, n_vector)
:param n_message: number of GVPs to use in message function
:param n_feedforward: number of GVPs to use in feedforward function
:param drop_rate: drop probability in all dropout layers
:param autoregressive: if `True`, this `GVPConvLayer` will be used
with a different set of input node embeddings for messages
where src >= dst
:param activations: tuple of functions (scalar_act, vector_act) to use in GVPs
:param vector_gate: whether to use vector gating.
(vector_act will be used as sigma^+ in vector gating if `True`)
'''
def __init__(self, node_dims, edge_dims,
n_message=3, n_feedforward=2, drop_rate=.1,
autoregressive=False,
activations=(F.relu, torch.sigmoid), vector_gate=False):
super(GVPConvLayer, self).__init__()
self.conv = GVPConv(node_dims, node_dims, edge_dims, n_message,
aggr="add" if autoregressive else "mean",
activations=activations, vector_gate=vector_gate)
GVP_ = functools.partial(GVP,
activations=activations, vector_gate=vector_gate)
self.norm = nn.ModuleList([LayerNorm(node_dims) for _ in range(2)])
self.dropout = nn.ModuleList([Dropout(drop_rate) for _ in range(2)])
ff_func = []
if n_feedforward == 1:
ff_func.append(GVP_(node_dims, node_dims, activations=(None, None)))
else:
hid_dims = 4*node_dims[0], 2*node_dims[1]
ff_func.append(GVP_(node_dims, hid_dims))
for i in range(n_feedforward-2):
ff_func.append(GVP_(hid_dims, hid_dims))
ff_func.append(GVP_(hid_dims, node_dims, activations=(None, None)))
self.ff_func = nn.Sequential(*ff_func)
def forward(self, x, edge_index, edge_attr,
autoregressive_x=None, node_mask=None):
'''
:param x: tuple (s, V) of `torch.Tensor`
:param edge_index: array of shape [2, n_edges]
:param edge_attr: tuple (s, V) of `torch.Tensor`
:param autoregressive_x: tuple (s, V) of `torch.Tensor`.
If not `None`, will be used as src node embeddings
for forming messages where src >= dst. The corrent node
embeddings `x` will still be the base of the update and the
pointwise feedforward.
:param node_mask: array of type `bool` to index into the first
dim of node embeddings (s, V). If not `None`, only
these nodes will be updated.
'''
if autoregressive_x is not None:
src, dst = edge_index
mask = src < dst
edge_index_forward = edge_index[:, mask]
edge_index_backward = edge_index[:, ~mask]
edge_attr_forward = tuple_index(edge_attr, mask)
edge_attr_backward = tuple_index(edge_attr, ~mask)
dh = tuple_sum(
self.conv(x, edge_index_forward, edge_attr_forward),
self.conv(autoregressive_x, edge_index_backward, edge_attr_backward)
)
count = scatter_add(torch.ones_like(dst), dst,
dim_size=dh[0].size(0)).clamp(min=1).unsqueeze(-1)
dh = dh[0] / count, dh[1] / count.unsqueeze(-1)
else:
dh = self.conv(x, edge_index, edge_attr)
if node_mask is not None:
x_ = x
x, dh = tuple_index(x, node_mask), tuple_index(dh, node_mask)
x = self.norm[0](tuple_sum(x, self.dropout[0](dh)))
dh = self.ff_func(x)
x = self.norm[1](tuple_sum(x, self.dropout[1](dh)))
if node_mask is not None:
x_[0][node_mask], x_[1][node_mask] = x[0], x[1]
x = x_
return x |