import torch
from torch.nn import functional as F
import numpy as np
from utils import PlaceHolder
def sum_except_batch(x):
return x.reshape(x.size(0), -1).sum(dim=-1)
def assert_correctly_masked(variable, node_mask):
assert (variable * (1 - node_mask.long())).abs().max().item() < 1e-4, \
'Variables not masked properly.'
def cosine_beta_schedule_discrete(timesteps, s=0.008):
""" Cosine schedule as proposed in https://openreview.net/forum?id=-NEXDKk8gZ. """
steps = timesteps + 2
x = np.linspace(0, steps, steps)
alphas_cumprod = np.cos(0.5 * np.pi * ((x / steps) + s) / (1 + s)) ** 2
alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
alphas = (alphas_cumprod[1:] / alphas_cumprod[:-1])
betas = 1 - alphas
return betas.squeeze()
def custom_beta_schedule_discrete(timesteps, average_num_nodes=30, s=0.008):
""" Cosine schedule as proposed in https://openreview.net/forum?id=-NEXDKk8gZ. """
steps = timesteps + 2
x = np.linspace(0, steps, steps)
alphas_cumprod = np.cos(0.5 * np.pi * ((x / steps) + s) / (1 + s)) ** 2
alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
alphas = (alphas_cumprod[1:] / alphas_cumprod[:-1])
betas = 1 - alphas
assert timesteps >= 100
p = 4 / 5 # 1 - 1 / num_edge_classes
num_edges = average_num_nodes * (average_num_nodes - 1) / 2
# First 100 steps: only a few updates per graph
updates_per_graph = 1.2
beta_first = updates_per_graph / (p * num_edges)
betas[betas < beta_first] = beta_first
return np.array(betas)
def check_mask_correct(variables, node_mask):
for i, variable in enumerate(variables):
if len(variable) > 0:
assert_correctly_masked(variable, node_mask)
def check_tensor_same_size(*args):
for i, arg in enumerate(args):
if i == 0:
continue
assert args[0].size() == arg.size()
def reverse_tensor(x):
return x[torch.arange(x.size(0) - 1, -1, -1)]
def sample_discrete_features(probX, probE, node_mask, step=None, add_nose=True):
''' Sample features from multinomial distribution with given probabilities (probX, probE, proby)
:param probX: bs, n, dx_out node features
:param probE: bs, n, n, de_out edge features
:param proby: bs, dy_out global features.
'''
bs, n, _ = probX.shape
# Noise X
# The masked rows should define probability distributions as well
probX[~node_mask] = 1 / probX.shape[-1]
# Flatten the probability tensor to sample with multinomial
probX = probX.reshape(bs * n, -1) # (bs * n, dx_out)
# Sample X
probX = probX + 1e-12
probX = probX / probX.sum(dim=-1, keepdim=True)
X_t = probX.multinomial(1) # (bs * n, 1)
X_t = X_t.reshape(bs, n) # (bs, n)
# Noise E
# The masked rows should define probability distributions as well
inverse_edge_mask = ~(node_mask.unsqueeze(1) * node_mask.unsqueeze(2))
diag_mask = torch.eye(n).unsqueeze(0).expand(bs, -1, -1)
probE[inverse_edge_mask] = 1 / probE.shape[-1]
probE[diag_mask.bool()] = 1 / probE.shape[-1]
probE = probE.reshape(bs * n * n, -1) # (bs * n * n, de_out)
probE = probE + 1e-12
probE = probE / probE.sum(dim=-1, keepdim=True)
# Sample E
E_t = probE.multinomial(1).reshape(bs, n, n) # (bs, n, n)
E_t = torch.triu(E_t, diagonal=1)
E_t = (E_t + torch.transpose(E_t, 1, 2))
return PlaceHolder(X=X_t, E=E_t, y=torch.zeros(bs, 0).type_as(X_t))
def compute_batched_over0_posterior_distribution(X_t, Qt, Qsb, Qtb):
""" M: X or E
Compute xt @ Qt.T * x0 @ Qsb / x0 @ Qtb @ xt.T for each possible value of x0
X_t: bs, n, dt or bs, n, n, dt
Qt: bs, d_t-1, dt
Qsb: bs, d0, d_t-1
Qtb: bs, d0, dt.
"""
X_t = X_t.float()
Qt_T = Qt.transpose(-1, -2).float() # bs, N, dt
assert Qt.dim() == 3
left_term = X_t @ Qt_T
left_term = left_term.unsqueeze(dim=2) # bs, N, 1, d_t-1
right_term = Qsb.unsqueeze(1)
numerator = left_term * right_term # bs, N, d0, d_t-1
denominator = Qtb @ X_t.transpose(-1, -2) # bs, d0, N
denominator = denominator.transpose(-1, -2) # bs, N, d0
denominator = denominator.unsqueeze(-1) # bs, N, d0, 1
denominator[denominator == 0] = 1.
return numerator / denominator
def mask_distributions(true_X, true_E, pred_X, pred_E, node_mask):
# Add a small value everywhere to avoid nans
pred_X = pred_X.clamp_min(1e-18)
pred_X = pred_X / torch.sum(pred_X, dim=-1, keepdim=True)
pred_E = pred_E.clamp_min(1e-18)
pred_E = pred_E / torch.sum(pred_E, dim=-1, keepdim=True)
# Set masked rows to arbitrary distributions, so it doesn't contribute to loss
row_X = torch.ones(true_X.size(-1), dtype=true_X.dtype, device=true_X.device)
row_E = torch.zeros(true_E.size(-1), dtype=true_E.dtype, device=true_E.device).clamp_min(1e-18)
row_E[0] = 1.
diag_mask = ~torch.eye(node_mask.size(1), device=node_mask.device, dtype=torch.bool).unsqueeze(0)
true_X[~node_mask] = row_X
true_E[~(node_mask.unsqueeze(1) * node_mask.unsqueeze(2) * diag_mask), :] = row_E
pred_X[~node_mask] = row_X
pred_E[~(node_mask.unsqueeze(1) * node_mask.unsqueeze(2) * diag_mask), :] = row_E
return true_X, true_E, pred_X, pred_E
def posterior_distributions(X, X_t, Qt, Qsb, Qtb, X_dim):
bs, n, d = X.shape
X = X.float()
Qt_X_T = torch.transpose(Qt.X, -2, -1).float() # (bs, d, d)
left_term = X_t @ Qt_X_T # (bs, N, d)
right_term = X @ Qsb.X # (bs, N, d)
numerator = left_term * right_term # (bs, N, d)
denominator = X @ Qtb.X # (bs, N, d) @ (bs, d, d) = (bs, N, d)
denominator = denominator * X_t
num_X = numerator[:, :, :X_dim]
num_E = numerator[:, :, X_dim:].reshape(bs, n*n, -1)
deno_X = denominator[:, :, :X_dim]
deno_E = denominator[:, :, X_dim:].reshape(bs, n*n, -1)
# denominator = (denominator * X_t).sum(dim=-1) # (bs, N, d) * (bs, N, d) + sum = (bs, N)
denominator = denominator.unsqueeze(-1) # (bs, N, 1)
deno_X = deno_X.sum(dim=-1).unsqueeze(-1)
deno_E = deno_E.sum(dim=-1).unsqueeze(-1)
deno_X[deno_X == 0.] = 1
deno_E[deno_E == 0.] = 1
prob_X = num_X / deno_X
prob_E = num_E / deno_E
prob_E = prob_E / prob_E.sum(dim=-1, keepdim=True)
prob_X = prob_X / prob_X.sum(dim=-1, keepdim=True)
return PlaceHolder(X=prob_X, E=prob_E, y=None)
def sample_discrete_feature_noise(limit_dist, node_mask):
""" Sample from the limit distribution of the diffusion process"""
bs, n_max = node_mask.shape
x_limit = limit_dist.X[None, None, :].expand(bs, n_max, -1)
U_X = x_limit.flatten(end_dim=-2).multinomial(1).reshape(bs, n_max)
U_X = F.one_hot(U_X.long(), num_classes=x_limit.shape[-1]).float()
e_limit = limit_dist.E[None, None, None, :].expand(bs, n_max, n_max, -1)
U_E = e_limit.flatten(end_dim=-2).multinomial(1).reshape(bs, n_max, n_max)
U_E = F.one_hot(U_E.long(), num_classes=e_limit.shape[-1]).float()
U_X = U_X.to(node_mask.device)
U_E = U_E.to(node_mask.device)
# Get upper triangular part of edge noise, without main diagonal
upper_triangular_mask = torch.zeros_like(U_E)
indices = torch.triu_indices(row=U_E.size(1), col=U_E.size(2), offset=1)
upper_triangular_mask[:, indices[0], indices[1], :] = 1
U_E = U_E * upper_triangular_mask
U_E = (U_E + torch.transpose(U_E, 1, 2))
assert (U_E == torch.transpose(U_E, 1, 2)).all()
return PlaceHolder(X=U_X, E=U_E, y=None).mask(node_mask)
def index_QE(X, q_e, n_bond=5):
bs, n, n_atom = X.shape
node_indices = X.argmax(-1) # (bs, n)
exp_ind1 = node_indices[ :, :, None, None, None].expand(bs, n, n_atom, n_bond, n_bond)
exp_ind2 = node_indices[ :, :, None, None, None].expand(bs, n, n, n_bond, n_bond)
q_e = torch.gather(q_e, 1, exp_ind1)
q_e = torch.gather(q_e, 2, exp_ind2) # (bs, n, n, n_bond, n_bond)
node_mask = X.sum(-1) != 0
no_edge = (~node_mask)[:, :, None] & (~node_mask)[:, None, :]
q_e[no_edge] = torch.tensor([1, 0, 0, 0, 0]).type_as(q_e)
return q_e