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import torch
import torch.nn as nn
import torch.nn.functional as F
from torch_scatter import scatter_mean
# auxiliary function for diffusion
def cosine_beta_schedule(timesteps, s=0.008):
"""
cosine schedule
as proposed in https://openreview.net/forum?id=-NEXDKk8gZ
"""
steps = timesteps + 1
x = np.linspace(0, steps, steps)
alphas_cumprod = np.cos(((x / steps) + s) / (1 + s) * np.pi * 0.5) ** 2
alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
alphas = (alphas_cumprod[1:] / alphas_cumprod[:-1])
alphas = np.clip(alphas, a_min=0.001, a_max=1.)
# Use sqrt of this, so the alpha in our paper is the alpha_sqrt from the
# Gaussian diffusion in Ho et al.
alphas = np.sqrt(alphas)
return alphas
def get_beta_schedule(beta_schedule, *, beta_start, beta_end, num_diffusion_timesteps):
def sigmoid(x):
return 1 / (np.exp(-x) + 1)
if beta_schedule == "quad":
betas = (
np.linspace(
beta_start ** 0.5,
beta_end ** 0.5,
num_diffusion_timesteps,
dtype=np.float64,
)
** 2
)
elif beta_schedule == "linear":
betas = np.linspace(
beta_start, beta_end, num_diffusion_timesteps, dtype=np.float64
)
elif beta_schedule == "const":
betas = beta_end * np.ones(num_diffusion_timesteps, dtype=np.float64)
elif beta_schedule == "jsd": # 1/T, 1/(T-1), 1/(T-2), ..., 1
betas = 1.0 / np.linspace(
num_diffusion_timesteps, 1, num_diffusion_timesteps, dtype=np.float64
)
elif beta_schedule == "sigmoid":
betas = np.linspace(-6, 6, num_diffusion_timesteps)
betas = sigmoid(betas) * (beta_end - beta_start) + beta_start
else:
raise NotImplementedError(beta_schedule)
assert betas.shape == (num_diffusion_timesteps,)
return betas
def to_torch_const(x):
x = torch.from_numpy(x).float()
x = nn.Parameter(x, requires_grad=False)
return x
def extract(coef, t, batch):
out = coef[t][batch]
return out.unsqueeze(-1)
def log_add_exp(a, b):
maximum = torch.max(a, b)
return maximum + torch.log(torch.exp(a - maximum) + torch.exp(b - maximum))
def log_categorical(log_x_start, log_prob):
return (log_x_start.exp() * log_prob).sum(dim=1)
def categorical_kl(log_prob1, log_prob2):
kl = (log_prob1.exp() * (log_prob1 - log_prob2)).sum(dim=1)
return kl
def log_sample_categorical(logits):
uniform = torch.rand_like(logits)
gumbel_noise = -torch.log(-torch.log(uniform + 1e-30) + 1e-30)
sample_index = (gumbel_noise + logits).argmax(dim=-1)
return sample_index
def index_to_log_onehot(x, num_classes):
assert x.max().item() < num_classes, f'Error: {x.max().item()} >= {num_classes}'
x_onehot = F.one_hot(x, num_classes)
# permute_order = (0, -1) + tuple(range(1, len(x.size())))
# x_onehot = x_onehot.permute(permute_order)
log_x = torch.log(x_onehot.float().clamp(min=1e-30))
return log_x
def log_1_min_a(a):
return np.log(1 - np.exp(a) + 1e-40)
def q_v_pred(log_v0, t, log_alphas_cumprod_v, log_one_minus_alphas_cumprod_v, batch):
# compute q(vt | v0)
log_cumprod_alpha_t = extract(log_alphas_cumprod_v, t, batch)
log_1_min_cumprod_alpha = extract(log_one_minus_alphas_cumprod_v, t, batch)
log_probs = log_add_exp(
log_v0 + log_cumprod_alpha_t,
log_1_min_cumprod_alpha - np.log(30)
)
return log_probs
def q_v_sample(log_v0, log_alphas_cumprod_v, log_one_minus_alphas_cumprod_v, t, batch):
log_qvt_v0 = q_v_pred(log_v0, t, log_alphas_cumprod_v, log_one_minus_alphas_cumprod_v, batch)
sample_index = log_sample_categorical(log_qvt_v0)
log_sample = index_to_log_onehot(sample_index, 30)
return sample_index, log_sample
def sample_time(num_graphs, num_timesteps, device, method='symmetric', low_ratio=0.3):
if method == 'symmetric':
time_step = torch.randint(
0, num_timesteps, size=(num_graphs // 2 + 1,), device=device)
time_step = torch.cat(
[time_step, num_timesteps - time_step - 1], dim=0)[:num_graphs]
pt = torch.ones_like(time_step).float() / num_timesteps
return time_step, pt
elif method == 'mid_symmetric':
# only use mid timesteps, i.e., [300,700]
t_min = int(num_timesteps * low_ratio)
t_max = num_timesteps - t_min
time_step = torch.randint(
t_min, t_max, size=(num_graphs // 2 + 1,), device=device)
time_step = torch.cat(
[time_step, num_timesteps - time_step - 1], dim=0)[:num_graphs]
pt = torch.ones_like(time_step).float() / (t_max - t_min)
return time_step, pt
else:
raise ValueError
def compute_v_Lt(log_v_model_prob, log_v0, log_v_true_prob, t, batch):
kl_v = categorical_kl(log_v_true_prob, log_v_model_prob) # [num_atoms, ]
decoder_nll_v = -log_categorical(log_v0, log_v_model_prob) # L0
assert kl_v.shape == decoder_nll_v.shape
mask = (t == 0).float()[batch]
loss_v = scatter_mean(mask * decoder_nll_v + (1. - mask) * kl_v, batch, dim=0)
return loss_v
# atom type diffusion process
def q_v_pred_one_timestep(log_vt_1, t, log_alphas_v, log_one_minus_alphas_v, batch):
# q(vt | vt-1)
log_alpha_t = extract(log_alphas_v, t, batch)
log_1_min_alpha_t = extract(log_one_minus_alphas_v, t, batch)
# alpha_t * vt + (1 - alpha_t) 1 / K
log_probs = log_add_exp(
log_vt_1 + log_alpha_t,
log_1_min_alpha_t - np.log(30)
)
return log_probs
# atom type generative process
def q_v_posterior(log_v0, log_vt, log_alphas_cumprod_v, log_one_minus_alphas_cumprod_v, log_alphas_v, log_one_minus_alphas_v, t, batch):
# q(vt-1 | vt, v0) = q(vt | vt-1, x0) * q(vt-1 | x0) / q(vt | x0)
t_minus_1 = t - 1
# Remove negative values, will not be used anyway for final decoder
t_minus_1 = torch.where(t_minus_1 < 0, torch.zeros_like(t_minus_1), t_minus_1)
log_qvt1_v0 = q_v_pred(log_v0, t_minus_1, log_alphas_cumprod_v, log_one_minus_alphas_cumprod_v, batch)
unnormed_logprobs = log_qvt1_v0 + q_v_pred_one_timestep(log_vt, t, log_alphas_v, log_one_minus_alphas_v, batch)
log_vt1_given_vt_v0 = unnormed_logprobs - torch.logsumexp(unnormed_logprobs, dim=-1, keepdim=True)
return log_vt1_given_vt_v0
def diffusion_loss(
ligand_pos,
ligand_pos_perturbed,
pred_ligand_pos,
pred_ligand_v,
log_ligand_v0,
log_ligand_vt,
log_alphas_cumprod_v,
log_one_minus_alphas_cumprod_v,
log_alphas_v,
log_one_minus_alphas_v,
time_step,
batch_ligand
):
## using FP32 to prevent NAN/INF and then cast back to FP16
target_pos = ligand_pos.float()
pred_pos = pred_ligand_pos.float()
per_atom_pos_mse = ((pred_pos - target_pos) ** 2).sum(-1)
loss_pos = scatter_mean(per_atom_pos_mse, batch_ligand, dim=0).mean()
logits_v = pred_ligand_v.float()
log_v_recon = F.log_softmax(logits_v, dim=-1)
log_v0 = log_ligand_v0.float()
log_vt = log_ligand_vt.float()
log_v_model_prob = q_v_posterior(
log_v_recon,
log_vt,
log_alphas_cumprod_v.float(),
log_one_minus_alphas_cumprod_v.float(),
log_alphas_v.float(),
log_one_minus_alphas_v.float(),
time_step,
batch_ligand,
)
log_v_true_prob = q_v_posterior(
log_v0,
log_vt,
log_alphas_cumprod_v.float(),
log_one_minus_alphas_cumprod_v.float(),
log_alphas_v.float(),
log_one_minus_alphas_v.float(),
time_step,
batch_ligand,
)
kl_v = compute_v_Lt(
log_v_model_prob=log_v_model_prob,
log_v0=log_v0,
log_v_true_prob=log_v_true_prob,
t=time_step,
batch=batch_ligand,
)
loss_v = kl_v.mean()
loss = loss_pos + 100 * loss_v
return (loss.to(pred_ligand_pos.dtype), loss_pos.to(pred_ligand_pos.dtype), loss_v.to(pred_ligand_pos.dtype))
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