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import math
import torch
import torch.nn.functional as F
import numpy as np
class DistributionNodes:
def __init__(self, histogram):
histogram = torch.tensor(histogram).float()
histogram = histogram + 1e-3 # for numerical stability
prob = histogram / histogram.sum()
self.idx_to_n_nodes = torch.tensor(
[[(i, j) for j in range(prob.shape[1])] for i in range(prob.shape[0])]
).view(-1, 2)
self.n_nodes_to_idx = {tuple(x.tolist()): i
for i, x in enumerate(self.idx_to_n_nodes)}
self.prob = prob
self.m = torch.distributions.Categorical(self.prob.view(-1),
validate_args=True)
self.n1_given_n2 = \
[torch.distributions.Categorical(prob[:, j], validate_args=True)
for j in range(prob.shape[1])]
self.n2_given_n1 = \
[torch.distributions.Categorical(prob[i, :], validate_args=True)
for i in range(prob.shape[0])]
# entropy = -torch.sum(self.prob.view(-1) * torch.log(self.prob.view(-1) + 1e-30))
# entropy = self.m.entropy()
# print("Entropy of n_nodes: H[N]", entropy.item())
def sample(self, n_samples=1):
idx = self.m.sample((n_samples,))
num_nodes_lig, num_nodes_pocket = self.idx_to_n_nodes[idx].T
return num_nodes_lig, num_nodes_pocket
def sample_conditional(self, n1=None, n2=None):
assert (n1 is None) ^ (n2 is None), \
"Exactly one input argument must be None"
m = self.n1_given_n2 if n2 is not None else self.n2_given_n1
c = n2 if n2 is not None else n1
return torch.tensor([m[i].sample() for i in c], device=c.device)
def log_prob(self, batch_n_nodes_1, batch_n_nodes_2):
assert len(batch_n_nodes_1.size()) == 1
assert len(batch_n_nodes_2.size()) == 1
idx = torch.tensor(
[self.n_nodes_to_idx[(n1, n2)]
for n1, n2 in zip(batch_n_nodes_1.tolist(), batch_n_nodes_2.tolist())]
)
# log_probs = torch.log(self.prob.view(-1)[idx] + 1e-30)
log_probs = self.m.log_prob(idx)
return log_probs.to(batch_n_nodes_1.device)
def log_prob_n1_given_n2(self, n1, n2):
assert len(n1.size()) == 1
assert len(n2.size()) == 1
log_probs = torch.stack([self.n1_given_n2[c].log_prob(i.cpu())
for i, c in zip(n1, n2)])
return log_probs.to(n1.device)
def log_prob_n2_given_n1(self, n2, n1):
assert len(n2.size()) == 1
assert len(n1.size()) == 1
log_probs = torch.stack([self.n2_given_n1[c].log_prob(i.cpu())
for i, c in zip(n2, n1)])
return log_probs.to(n2.device)
def cosine_beta_schedule_midi(timesteps, s=0.008, nu=1.0, clip=False):
"""
Modified cosine schedule as proposed in https://arxiv.org/abs/2302.09048.
Note: we use (t/T)^\nu not (t/T + s)^\nu as written in the MiDi paper
We also divide by alphas_cumprod[0] as the original cosine schedule from
https://arxiv.org/abs/2102.09672
"""
device = nu.device if torch.is_tensor(nu) else None
x = torch.linspace(0, timesteps, timesteps + 1, device=device)
alphas_cumprod = torch.cos(0.5 * np.pi * ((x / timesteps)**nu + s) / (1 + s)) ** 2
alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
if clip:
alphas_cumprod = torch.cat([torch.tensor([1.0], device=alphas_cumprod.device), alphas_cumprod])
betas = 1 - (alphas_cumprod[1:] / alphas_cumprod[:-1])
betas = torch.clip(betas, min=0, max=0.999)
alphas = 1. - betas
alphas_cumprod = torch.cumprod(alphas, axis=0)
return alphas_cumprod
class CosineSchedule(torch.nn.Module):
"""
nu=1.0 corresponds to the standard cosine schedule
"""
def __init__(self, timesteps, nu=1.0, trainable=False, clip_alpha2_step=0.001):
super(CosineSchedule, self).__init__()
self.timesteps = timesteps
self.trainable = trainable
self.nu = nu
assert 0.0 <= clip_alpha2_step < 1.0
self.clip = clip_alpha2_step
if self.trainable:
self.nu = torch.nn.Parameter(torch.Tensor([nu]), requires_grad=True)
else:
self._alpha2 = self.alphas2
self._gamma = torch.nn.Parameter(self.gammas, requires_grad=False)
@property
def alphas2(self):
"""
Cumulative alpha squared.
Called alpha_bar in: Nichol, Alexander Quinn, and Prafulla Dhariwal.
"Improved denoising diffusion probabilistic models." PMLR, 2021.
"""
if hasattr(self, '_alpha2'):
return self._alpha2
assert isinstance(self.nu, float) or ~self.nu.isnan()
# our alpha is eqivalent to sqrt(alpha) from https://arxiv.org/abs/2102.09672, where the cosine schedule was introduced
alphas2 = cosine_beta_schedule_midi(self.timesteps, nu=self.nu, clip=False)
# avoid singularities near t=T
alphas2 = torch.cat([torch.tensor([1.0], device=alphas2.device), alphas2])
alphas2_step = alphas2[1:] / alphas2[:-1]
alphas2_step = torch.clip(alphas2_step, min=self.clip, max=1.0)
alphas2 = torch.cumprod(alphas2_step, dim=0)
return alphas2
@property
def alphas2_t_given_tminus1(self):
"""
Alphas for a single transition
"""
alphas2 = torch.cat([torch.tensor([1.0]), self.alphas2])
return alphas2[1:] / alphas2[:-1]
@property
def gammas(self):
"""
Gammas as defined in appendix B of the EDM paper
gamma_t = -(log alpha_t^2 - log sigma_t^2)
"""
if hasattr(self, '_gamma'):
return self._gamma
alphas2 = self.alphas2
sigmas2 = 1 - alphas2
gammas = -(torch.log(alphas2) - torch.log(sigmas2))
return gammas.float()
def forward(self, t):
t_int = torch.round(t * self.timesteps).long()
return self.gammas[t_int]
@staticmethod
def alpha(gamma):
""" Computes alpha given gamma. """
return torch.sqrt(torch.sigmoid(-gamma))
@staticmethod
def sigma(gamma):
""" Computes sigma given gamma. """
return torch.sqrt(torch.sigmoid(gamma))
@staticmethod
def SNR(gamma):
""" Computes signal to noise ratio (alpha^2/sigma^2) given gamma. """
return torch.exp(-gamma)
def sigma_and_alpha_t_given_s(self, gamma_t: torch.Tensor, gamma_s: torch.Tensor):
"""
Computes sigma_t_given_s, using gamma_t and gamma_s. Used during sampling.
These are defined as:
alpha_t_given_s = alpha_t / alpha_s,
sigma_t_given_s = sqrt(1 - (alpha_t_given_s)^2 ).
"""
sigma2_t_given_s = -torch.expm1(
F.softplus(gamma_s) - F.softplus(gamma_t))
# alpha_t_given_s = alpha_t / alpha_s
log_alpha2_t = F.logsigmoid(-gamma_t)
log_alpha2_s = F.logsigmoid(-gamma_s)
log_alpha2_t_given_s = log_alpha2_t - log_alpha2_s
alpha_t_given_s = torch.exp(0.5 * log_alpha2_t_given_s)
alpha_t_given_s = torch.clip(alpha_t_given_s, min=self.clip ** 0.5, max=1.0)
sigma_t_given_s = torch.sqrt(sigma2_t_given_s)
return sigma2_t_given_s, sigma_t_given_s, alpha_t_given_s
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