def forward(self,
q: QTensor,
edge_index: Adj,
edge_attr: QTensor,
size: Size = None) -> QTensor:
assert edge_attr.__class__.__name__ == "QTensor"
x = q.clone()
# "cast" QTensor back to torch.Tensor
q = q.stack(dim=1) # (batch_num_nodes, 4, feature_dim)
q = q.reshape(q.size(0), -1) # (batch_num_nodes, 4*feature_dim)
edge_attr = edge_attr.stack(dim=1)
edge_attr = edge_attr.reshape(edge_attr.size(0), -1)
# propagate
agg = self.propagate(edge_index=edge_index,
x=q,
edge_attr=edge_attr,
size=size)
agg = agg.reshape(agg.size(0), 4, -1).permute(1, 0, 2)
q = QTensor(*agg)
if self.same_dim: # aggregate messages -> linearly transform -> add self-loops.
q = self.transform(q)
if self.add_self_loops:
q += x
else:
if self.add_self_loops: # aggregate messages -> add self-loops -> linearly transform.
q += x
q = self.transform(q)
return q
def forward(self,
q: QTensor,
edge_index: Adj,
edge_attr: QTensor,
size: Size = None) -> QTensor:
assert edge_attr.__class__.__name__ == "QTensor"
x = q.clone()
# "cast" QTensor back to torch.Tensor
q = q.stack(dim=1) # (batch_num_nodes, 4, feature_dim)
q = q.reshape(q.size(0), -1) # (batch_num_nodes, 4*feature_dim)
edge_attr = edge_attr.stack(dim=1)
edge_attr = edge_attr.reshape(edge_attr.size(0), -1)
# propagate
agg = self.propagate(edge_index=edge_index,
x=q,
edge_attr=edge_attr,
size=size)
agg = agg.reshape(agg.size(0), 4, -1).permute(1, 0, 2)
agg = QTensor(*agg)
if self.add_self_loops:
x += agg
# transform aggregated node embeddings
q = self.transform(x)
return q
def test_quaternion_dropout(self):
batch_size = 128
in_features = 32
same = False
p = 0.3
q = QTensor(*torch.randn(4, batch_size, in_features))
q_dropped = quaternion_dropout(q=q, p=p, training=True, same=same)
q_tensor = q.stack(dim=0)
q_dropped_tensor = q_dropped.stack(dim=0)
# check that "on"-indices are the same when retrieving the data
ids = (q_dropped_tensor != 0.0)
q_on = q_tensor[ids]
q_dropped_on = q_dropped_tensor[ids]
q_dropped_on *= (1-p) # rescaling
assert torch.allclose(q_on, q_dropped_on)
same = True
q = QTensor(*torch.randn(4, batch_size, in_features))
q_dropped = quaternion_dropout(q=q, p=p, training=True, same=same)
q_tensor = q.stack(dim=0)
q_dropped_tensor = q_dropped.stack(dim=0)
# rescaling
q_dropped_tensor *= (1-p)
# check if quaternion-component axis is really 0 among all components
ids = [(x != 0.0).to(torch.float32) for x in q_dropped_tensor]
for a, b in permutations(ids, 2):
assert torch.allclose(a, b)
def test_qtensor_scatter_idx(self):
row_ids = 1024
idx = torch.randint(low=0,
high=256,
size=(row_ids, ),
dtype=torch.int64)
p = 64
x = QTensor(*torch.randn(4, row_ids, p))
x_tensor = x.stack(dim=1)
assert x_tensor.size() == torch.Size([row_ids, 4, p])
x_aggr = scatter_sum(src=x_tensor,
index=idx,
dim=0,
dim_size=x_tensor.size(0))
assert x_aggr.size() == x_tensor.size()
x_aggr = x_aggr.permute(1, 0, 2)
q_aggr = QTensor(*x_aggr)
r = scatter_sum(x.r, idx, dim=0, dim_size=x.size(0))
i = scatter_sum(x.i, idx, dim=0, dim_size=x.size(0))
j = scatter_sum(x.j, idx, dim=0, dim_size=x.size(0))
k = scatter_sum(x.k, idx, dim=0, dim_size=x.size(0))
q_aggr2 = QTensor(r, i, j, k)
assert q_aggr == q_aggr2
def forward(self, x: QTensor, idx: torch.Tensor, dim: int, dim_size: Optional[int] = None) -> QTensor:
x = x.stack(dim=1) # (num_nodes_batch, 4, feature_dim)
weights = torch_scatter.composite.scatter_softmax(src=self.beta * x, index=idx, dim=dim)
x = weights * x
x = torch_scatter.scatter(src=x, index=idx, dim=dim, dim_size=dim_size, reduce="sum")
# (num_nodes_batch, 4, feature_dim)
x = x.permute(1, 0, 2) # (4, num_nodes_batch, feature_dim)
return QTensor(*x)
def quaternion_batch_norm(
qtensor: QTensor,
running_mean,
running_var,
weight=None,
bias=None,
training=True,
momentum=0.1,
eps=1e-05,
) -> QTensor:
""" Functional implementation of quaternion batch normalization """
# check arguments
assert ((running_mean is None and running_var is None)
or (running_mean is not None and running_var is not None))
assert ((weight is None and bias is None)
or (weight is not None and bias is not None))
# stack qtensor along the first dimension
x = qtensor.stack(dim=0)
# whiten and apply affine transformation
z = whiten4x4(q=x,
training=training,
running_mean=running_mean,
running_cov=running_var,
momentum=momentum,
nugget=eps)
p = x.size(-1)
if weight is not None and bias is not None:
shape = (1, p)
weight = weight.reshape(4, 4, *shape)
""" this is just the scaling formula
x_r_BN = gamma_rr * x_r + gamma_ri * x_i + gamma_rj * x_j + gamma_rk * x_k + beta_r
x_i_BN = gamma_ir * x_r + gamma_ii * x_i + gamma_ij * x_j + gamma_ik * x_k + beta_i
x_j_BN = gamma_jr * x_r + gamma_ji * x_i + gamma_jj * x_j + gamma_jk * x_k + beta_j
x_k_BN = gamma_kr * x_r + gamma_ki * x_i + gamma_kj * x_j + gamma_kk * x_k + beta_k
"""
z = torch.stack([
z[0] * weight[0, 0] + z[1] * weight[0, 1] + z[2] * weight[0, 2] +
z[3] * weight[0, 3],
z[0] * weight[1, 0] + z[1] * weight[1, 1] + z[2] * weight[1, 2] +
z[3] * weight[1, 3],
z[0] * weight[2, 0] + z[1] * weight[2, 1] + z[2] * weight[2, 2] +
z[3] * weight[2, 3],
z[0] * weight[3, 0] + z[1] * weight[3, 1] + z[2] * weight[3, 2] +
z[3] * weight[3, 3],
],
dim=0) + bias.reshape(4, *shape)
return QTensor(z[0], z[1], z[2], z[3])
def qrelu_naive(q: QTensor) -> QTensor:
r"""
quaternion relu activation function f(z), where z = a + b*i + c*j + d*k
a,b,c,d are real scalars where the last three scalars correspond to the vectorial part of the quaternion number
f(z) returns z, iif a + b + c + d > 0.
Otherwise it returns 0
Note that f(z) is applied for each dimensionality of q, as in real-valued fashion.
:param q: quaternion tensor of shape (b, d) where b is the batch-size and d the dimensionality
:return: activated quaternion tensor
"""
q = q.stack(dim=0)
sum = q.sum(dim=0)
a = torch.heaviside(sum, values=torch.zeros(sum.size()).to(q.device))
a = a.expand_as(q)
q = q * a
return QTensor(*q)
def quaternion_dropout(q: QTensor, p: float = 0.2, training: bool = True, same: bool = False) -> QTensor:
assert 0.0 <= p <= 1.0, f"dropout rate must be in [0.0 ; 1.0]. {p} was inserted!"
r"""
Applies the same dropout mask for each quaternion component tensor of size [num_batch_nodes, d]
along the same dimension d for the real and three hypercomplex parts.
:param q: quaternion tensor with real part r and three hypercomplex parts i,j,k
:param p: dropout rate. Must be within [0.0 ; 1.0]. If p=0.0, this function returns the input tensors
:param training: boolean flag if the dropout is used in training mode
Only if this is True, the dropout will be applied. Otherwise it will return the input tensors
:return: (droped-out) quaternion q
"""
if training and p > 0.0:
q = q.stack(dim=0)
if same:
mask = get_bernoulli_mask(x=q[0], p=p).unsqueeze(dim=0)
q = torch_dropout(x=q, p=p, mask=mask)
else:
q = F.dropout(q, p=p, training=training)
return QTensor(*q)
else:
return q
def test_scatter_batch_idx(self):
n_graphs = 128
n_nodes = 2048
idx = torch.randint(low=0,
high=n_graphs,
size=(n_nodes, ),
dtype=torch.int64)
p = 64
x = QTensor(*torch.randn(4, n_nodes, p))
x_tensor = x.stack(dim=1)
assert x_tensor.size() == torch.Size([n_nodes, 4, p])
x_aggr = scatter_sum(src=x_tensor, index=idx, dim=0)
x_aggr2 = global_add_pool(x_tensor, batch=idx)
assert torch.allclose(x_aggr, x_aggr2)
x_aggr = x_aggr.permute(1, 0, 2)
q_aggr = QTensor(*x_aggr)
r = scatter_sum(x.r, idx, dim=0)
i = scatter_sum(x.i, idx, dim=0)
j = scatter_sum(x.j, idx, dim=0)
k = scatter_sum(x.k, idx, dim=0)
q_aggr2 = QTensor(r, i, j, k)
assert q_aggr == q_aggr2
assert torch.allclose(x_aggr[0], r)
assert torch.allclose(x_aggr[1], i)
assert torch.allclose(x_aggr[2], j)
assert torch.allclose(x_aggr[3], k)
r1 = global_add_pool(x.r, idx)
i1 = global_add_pool(x.i, idx)
j1 = global_add_pool(x.j, idx)
k1 = global_add_pool(x.k, idx)
q_aggr3 = QTensor(r1, i1, j1, k1)
assert q_aggr == q_aggr2 == q_aggr3
def __call__(self, x: QTensor, batch: Batch) -> QTensor:
x_tensor = x.stack(dim=1) # transform to torch.Tensor
pooled = self.module(x=x_tensor, batch=batch) # apply global pooling
pooled = pooled.permute(1, 0, 2) # permute such that first dimension is (4,*,*)
return QTensor(*pooled)
def forward(self, x: QTensor, idx: torch.Tensor, dim: int, dim_size: Optional[int] = None) -> QTensor:
x_tensor = x.stack(dim=1) # transform to torch.Tensor (*, 4, *)
aggr = torch_scatter.scatter(src=x_tensor, index=idx, dim=dim, dim_size=dim_size, reduce=self.reduce)
aggr = aggr.permute(1, 0, 2) # permute such that first dimension is (4,*,*)
return QTensor(*aggr)
