import itertools
import torch
import torch.nn.functional as F
[docs]def NCE_loss(zs=None, zs_n=None, batch=None, sigma=None, **kwargs):
'''The InfoNCE (NT-XENT) loss in contrastive learning.
Args:
zs (list, optipnal): List of tensors of shape [batch_size, z_dim].
zs_n (list, optional): List of tensors of shape [nodes, z_dim].
batch (Tensor, optional): Required when both :obj:`zs` and :obj:`zs_n` are given.
sigma (ndarray, optional): A 2D-array of shape [:obj:`n_views`, :obj:`n_views`] with boolean
values, indicating contrast between which two views are computed. Only required
when number of views is greater than 2. If :obj:`sigma[i][j]` = :obj:`True`,
infoNCE between :math:`view_i` and :math:`view_j` will be computed.
tau (int, optional): The temperature used in NT-XENT.
:rtype: :class:`Tensor`
'''
assert zs is not None or zs_n is not None
if 'tau' in kwargs:
tau = kwargs['tau']
else:
tau = 0.5
if 'norm' in kwargs:
norm = kwargs['norm']
else:
norm = True
if zs_n is not None:
if zs is None:
# InfoNCE in GRACE
assert len(zs_n)==2
return (infoNCE_local_intra_node(zs_n[0], zs_n[1], tau, norm)+
infoNCE_local_intra_node(zs_n[1], zs_n[0], tau, norm))*0.5
else:
assert len(zs_n)==len(zs)
assert batch is not None
if len(zs)==1:
return infoNCE_local_global(zs[0], zs_n[0], batch, tau, norm)
elif len(zs)==2:
return (infoNCE_local_global(zs[0], zs_n[1], batch, tau, norm)+
infoNCE_local_global(zs[1], zs_n[0], batch, tau, norm))
else:
assert len(zs)==len(sigma)
loss = 0
for (i, j) in itertools.combinations(range(len(zs)), 2):
if sigma[i][j]:
loss += (infoNCE_local_global(zs[i], zs_n[j], batch, tau, norm)+
infoNCE_local_global(zs[j], zs_n[i], batch, tau, norm))
return loss
if len(zs)==2:
return NT_Xent(zs[0], zs[1], tau, norm)
elif len(zs)>2:
assert len(zs)==len(sigma)
loss = 0
for (i, j) in itertools.combinations(range(len(zs)), 2):
if sigma[i][j]:
loss += NT_Xent(zs[i], zs[j], tau, norm)
return loss
def infoNCE_local_intra_node(z1_n, z2_n, tau=0.5, norm=True):
'''
Args:
z1_n: Tensor of shape [n_nodes, z_dim].
z2_n: Tensor of shape [n_nodes, z_dim].
tau: Float. Usually in (0,1].
norm: Boolean. Whether to apply normlization.
'''
if norm:
z1_n = F.normalize(z1_n)
z2_n = F.normalize(z2_n)
exp = lambda x: torch.exp(x / tau)
refl_sim = exp(torch.mm(z1_n, z1_n.t()))
between_sim = exp(torch.mm(z1_n, z2_n.t()))
pos_sim = between_sim.diag()
intra_sim = refl_sim.sum(1) - refl_sim.diag()
inter_pos_sim = between_sim.sum(1)
loss = pos_sim / (intra_sim + inter_pos_sim)
loss = -torch.log(loss).mean()
return loss
def infoNCE_local_global(z_n, z_g, batch, tau=0.5, norm=True):
'''
Args:
z_n: Tensor of shape [n_nodes, z_dim].
z_g: Tensor of shape [n_graphs, z_dim].
tau: Float. Usually in (0,1].
norm: Boolean. Whether to apply normlization.
'''
# Not yet used in existing methods, to be implemented.
loss = 0
return loss
def NT_Xent(z1, z2, tau=0.5, norm=True):
'''
Args:
z1, z2: Tensor of shape [batch_size, z_dim]
tau: Float. Usually in (0,1].
norm: Boolean. Whether to apply normlization.
'''
batch_size, _ = z1.size()
sim_matrix = torch.einsum('ik,jk->ij', z1, z2)
if norm:
z1_abs = z1.norm(dim=1)
z2_abs = z2.norm(dim=1)
sim_matrix = sim_matrix / torch.einsum('i,j->ij', z1_abs, z2_abs)
sim_matrix = torch.exp(sim_matrix / tau)
pos_sim = sim_matrix[range(batch_size), range(batch_size)]
loss = pos_sim / (sim_matrix.sum(dim=1) - pos_sim)
loss = - torch.log(loss).mean()
return loss