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e8edb9d | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 | """Structured VAE with kinetic model decoder for DeepPTR.
The generative model factorises latent space into transcriptional (z_T) and
post-transcriptional (z_PT) factors. The decoder uses RNA kinetic equations
to map these to expected unspliced / spliced counts observed through a
negative binomial likelihood.
"""
from __future__ import annotations
import torch
import torch.nn.functional as F
from torch import Tensor, nn
from ._distributions import log_nb_positive
from ._utils import init_weights
# ---------------------------------------------------------------------------
# Encoder
# ---------------------------------------------------------------------------
class Encoder(nn.Module):
"""Amortised inference network q(z_T, z_PT | x).
Takes concatenated log1p(spliced, unspliced) and outputs mean and
log-variance for two independent Gaussian posteriors.
"""
def __init__(
self,
n_genes: int,
d_hidden: int = 128,
d_T: int = 10,
d_PT: int = 10,
n_layers: int = 3,
dropout: float = 0.1,
) -> None:
super().__init__()
n_input = 2 * n_genes # [log1p(s); log1p(u)]
layers: list[nn.Module] = []
in_dim = n_input
for _ in range(n_layers):
layers.extend(
[
nn.Linear(in_dim, d_hidden),
nn.LayerNorm(d_hidden),
nn.ReLU(),
nn.Dropout(dropout),
]
)
in_dim = d_hidden
self.shared = nn.Sequential(*layers)
# Heads for z_T
self.mu_T = nn.Linear(d_hidden, d_T)
self.logvar_T = nn.Linear(d_hidden, d_T)
# Heads for z_PT
self.mu_PT = nn.Linear(d_hidden, d_PT)
self.logvar_PT = nn.Linear(d_hidden, d_PT)
self.apply(init_weights)
def forward(
self, s: Tensor, u: Tensor
) -> tuple[Tensor, Tensor, Tensor, Tensor]:
"""Encode observations to posterior parameters.
Returns
-------
mu_T, logvar_T, mu_PT, logvar_PT : Tensor
Each shape ``(N, d_*)``.
"""
x = torch.cat([torch.log1p(s), torch.log1p(u)], dim=-1)
h = self.shared(x)
return (
self.mu_T(h),
self.logvar_T(h),
self.mu_PT(h),
self.logvar_PT(h),
)
# ---------------------------------------------------------------------------
# Kinetic Decoder
# ---------------------------------------------------------------------------
class KineticDecoder(nn.Module):
r"""Decoder mapping (z_T, z_PT) → expected counts via kinetic model.
.. math::
\alpha_g &= \text{softplus}(f_\alpha(z_T))_g \\
\gamma_g &= \text{softplus}(f_\gamma(z_{PT}))_g \\
\beta_g &= \exp(\log\beta_g) \quad (\text{gene-specific parameter}) \\
\mu^u_g &= \frac{\alpha_g / \beta_g}{\sum_g \alpha_g / \beta_g}
\cdot l_u \\
\mu^s_g &= \frac{\alpha_g / \gamma_g}{\sum_g \alpha_g / \gamma_g}
\cdot l_s
"""
def __init__(
self,
n_genes: int,
d_T: int = 10,
d_PT: int = 10,
d_hidden: int = 128,
) -> None:
super().__init__()
self.n_genes = n_genes
# alpha network: z_T → alpha (transcription rate)
self.f_alpha = nn.Sequential(
nn.Linear(d_T, d_hidden),
nn.LayerNorm(d_hidden),
nn.ReLU(),
nn.Linear(d_hidden, n_genes),
)
# gamma network: z_PT → gamma (degradation rate)
self.f_gamma = nn.Sequential(
nn.Linear(d_PT, d_hidden),
nn.LayerNorm(d_hidden),
nn.ReLU(),
nn.Linear(d_hidden, n_genes),
)
# Gene-specific splicing rate (not cell-specific)
self.log_beta = nn.Parameter(torch.zeros(n_genes))
# Inverse dispersion parameters (learnable, per-gene)
self.log_theta_s = nn.Parameter(torch.zeros(n_genes))
self.log_theta_u = nn.Parameter(torch.zeros(n_genes))
self.apply(init_weights)
# Re-init log_beta/theta after apply
nn.init.zeros_(self.log_beta)
nn.init.constant_(self.log_theta_s, 2.0) # ~exp(2)≈7.4
nn.init.constant_(self.log_theta_u, 2.0)
def forward(
self,
z_T: Tensor,
z_PT: Tensor,
l_s: Tensor,
l_u: Tensor,
) -> dict[str, Tensor]:
"""Decode latent variables to NB distribution parameters.
Parameters
----------
z_T : (N, d_T)
z_PT : (N, d_PT)
l_s : (N,) library size for spliced
l_u : (N,) library size for unspliced
Returns
-------
dict with keys: mu_s, mu_u, theta_s, theta_u, alpha, gamma, beta
"""
alpha = F.softplus(self.f_alpha(z_T)) # (N, G), positive
gamma = F.softplus(self.f_gamma(z_PT)) # (N, G), positive
beta = self.log_beta.exp() # (G,), positive
eps = 1e-8
# Expected proportions from kinetic model
rho_u = alpha / (beta.unsqueeze(0) + eps) # (N, G)
rho_s = alpha / (gamma + eps) # (N, G)
# Normalize to proportions (sum to 1 across genes)
rho_u = rho_u / (rho_u.sum(dim=-1, keepdim=True) + eps)
rho_s = rho_s / (rho_s.sum(dim=-1, keepdim=True) + eps)
# Scale by library size
mu_u = rho_u * l_u.unsqueeze(-1) # (N, G)
mu_s = rho_s * l_s.unsqueeze(-1) # (N, G)
theta_s = self.log_theta_s.exp()
theta_u = self.log_theta_u.exp()
return {
"mu_s": mu_s,
"mu_u": mu_u,
"theta_s": theta_s,
"theta_u": theta_u,
"alpha": alpha,
"gamma": gamma,
"beta": beta,
}
# ---------------------------------------------------------------------------
# Full VAE
# ---------------------------------------------------------------------------
class DeepPTR(nn.Module):
"""Structured VAE for mRNA degradation rate estimation.
Combines an amortised encoder with a kinetic-model-constrained decoder
and a negative binomial observation model.
"""
def __init__(
self,
n_genes: int,
d_T: int = 10,
d_PT: int = 10,
d_hidden: int = 128,
n_enc_layers: int = 3,
dropout: float = 0.1,
) -> None:
super().__init__()
self.n_genes = n_genes
self.d_T = d_T
self.d_PT = d_PT
self.encoder = Encoder(
n_genes=n_genes,
d_hidden=d_hidden,
d_T=d_T,
d_PT=d_PT,
n_layers=n_enc_layers,
dropout=dropout,
)
self.decoder = KineticDecoder(
n_genes=n_genes,
d_T=d_T,
d_PT=d_PT,
d_hidden=d_hidden,
)
# -- helpers --
@staticmethod
def reparameterize(mu: Tensor, logvar: Tensor) -> Tensor:
"""Sample z = mu + eps * std with reparameterization trick."""
std = (0.5 * logvar).exp()
return mu + std * torch.randn_like(std)
@staticmethod
def kl_divergence(mu: Tensor, logvar: Tensor) -> Tensor:
"""KL(q(z) || N(0,I)), summed over latent dims, mean over batch."""
return -0.5 * (1 + logvar - mu.pow(2) - logvar.exp()).sum(dim=-1).mean()
# -- forward --
def forward(
self,
s: Tensor,
u: Tensor,
l_s: Tensor,
l_u: Tensor,
kl_weight: float = 1.0,
) -> dict[str, Tensor]:
"""Full forward pass: encode → sample → decode → loss.
Parameters
----------
s : (N, G) spliced counts
u : (N, G) unspliced counts
l_s : (N,) spliced library size
l_u : (N,) unspliced library size
kl_weight : float annealing coefficient for KL term
Returns
-------
dict
``loss``, ``recon_loss``, ``kl_loss``, and decoder outputs.
"""
mu_T, logvar_T, mu_PT, logvar_PT = self.encoder(s, u)
z_T = self.reparameterize(mu_T, logvar_T)
z_PT = self.reparameterize(mu_PT, logvar_PT)
dec = self.decoder(z_T, z_PT, l_s, l_u)
# Reconstruction: sum NB log-likelihood over genes, mean over batch
ll_s = log_nb_positive(s, dec["mu_s"], dec["theta_s"]).sum(dim=-1).mean()
ll_u = log_nb_positive(u, dec["mu_u"], dec["theta_u"]).sum(dim=-1).mean()
recon_loss = -(ll_s + ll_u)
kl_T = self.kl_divergence(mu_T, logvar_T)
kl_PT = self.kl_divergence(mu_PT, logvar_PT)
kl_loss = kl_T + kl_PT
loss = recon_loss + kl_weight * kl_loss
return {
"loss": loss,
"recon_loss": recon_loss,
"kl_loss": kl_loss,
"kl_T": kl_T,
"kl_PT": kl_PT,
"mu_T": mu_T,
"logvar_T": logvar_T,
"mu_PT": mu_PT,
"logvar_PT": logvar_PT,
**dec,
}
@torch.no_grad()
def get_latent(
self, s: Tensor, u: Tensor
) -> tuple[Tensor, Tensor, Tensor, Tensor]:
"""Return posterior means for z_T and z_PT (no sampling)."""
mu_T, logvar_T, mu_PT, logvar_PT = self.encoder(s, u)
return mu_T, logvar_T, mu_PT, logvar_PT
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