import warnings
from typing import Optional
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from ...data.datasets import BaseDataset
from ..base.base_utils import ModelOutput
from ..nn import BaseDecoder, BaseEncoder
from ..nn.default_architectures import Encoder_SVAE_MLP, Encoder_VAE_MLP
from ..vae import VAE
from .pvae_config import PoincareVAEConfig
from .pvae_utils import PoincareBall, RiemannianNormal, WrappedNormal
[docs]class PoincareVAE(VAE):
"""Poincaré Variational Autoencoder model.
Args:
model_config (PoincareVAEConfig): The Poincaré Variational Autoencoder configuration
setting the main parameters of the model.
encoder (BaseEncoder): An instance of BaseEncoder (inheriting from `torch.nn.Module` which
plays the role of encoder. This argument allows you to use your own neural networks
architectures if desired. If None is provided, a simple Multi Layer Preception
(https://en.wikipedia.org/wiki/Multilayer_perceptron) is used. Default: None.
decoder (BaseDecoder): An instance of BaseDecoder (inheriting from `torch.nn.Module` which
plays the role of decoder. This argument allows you to use your own neural networks
architectures if desired. If None is provided, a simple Multi Layer Preception
(https://en.wikipedia.org/wiki/Multilayer_perceptron) is used. Default: None.
.. note::
For high dimensional data we advice you to provide you own network architectures. With the
provided MLP you may end up with a ``MemoryError``.
"""
def __init__(
self,
model_config: PoincareVAEConfig,
encoder: Optional[BaseEncoder] = None,
decoder: Optional[BaseDecoder] = None,
):
VAE.__init__(self, model_config=model_config, encoder=encoder, decoder=decoder)
self.model_name = "PoincareVAE"
self.latent_manifold = PoincareBall(
dim=model_config.latent_dim, c=model_config.curvature
)
if model_config.prior_distribution == "riemannian_normal":
self.prior = RiemannianNormal
else:
self.prior = WrappedNormal
if model_config.posterior_distribution == "riemannian_normal":
warnings.warn(
"Carefull, this model expects the encoder to give a one dimensional "
"`log_concentration` tensor for the Riemannian normal distribution. "
"Make sure the encoder actually outputs this."
)
self.posterior = RiemannianNormal
else:
self.posterior = WrappedNormal
if encoder is None:
if model_config.posterior_distribution == "riemannian_normal":
encoder = Encoder_SVAE_MLP(model_config)
else:
encoder = Encoder_VAE_MLP(model_config)
self.model_config.uses_default_encoder = True
else:
self.model_config.uses_default_encoder = False
self.set_encoder(encoder)
self._pz_mu = nn.Parameter(
torch.zeros(1, model_config.latent_dim), requires_grad=False
)
self._pz_logvar = nn.Parameter(torch.zeros(1, 1), requires_grad=False)
[docs] def forward(self, inputs: BaseDataset, **kwargs):
"""
The VAE model
Args:
inputs (BaseDataset): The training dataset with labels
Returns:
ModelOutput: An instance of ModelOutput containing all the relevant parameters
"""
x = inputs["data"]
encoder_output = self.encoder(x)
if self.model_config.posterior_distribution == "riemannian_normal":
mu, log_var = encoder_output.embedding, encoder_output.log_concentration
else:
mu, log_var = encoder_output.embedding, encoder_output.log_covariance
std = torch.exp(0.5 * log_var)
qz_x = self.posterior(loc=mu, scale=std, manifold=self.latent_manifold)
z = qz_x.rsample(torch.Size([1]))
recon_x = self.decoder(z.squeeze(0))["reconstruction"]
loss, recon_loss, kld = self.loss_function(recon_x, x, z, qz_x)
output = ModelOutput(
recon_loss=recon_loss,
reg_loss=kld,
loss=loss,
recon_x=recon_x,
z=z.squeeze(0),
)
return output
def loss_function(self, recon_x, x, z, qz_x):
if self.model_config.reconstruction_loss == "mse":
recon_loss = 0.5 * F.mse_loss(
recon_x.reshape(x.shape[0], -1),
x.reshape(x.shape[0], -1),
reduction="none",
).sum(dim=-1)
elif self.model_config.reconstruction_loss == "bce":
recon_loss = F.binary_cross_entropy(
recon_x.reshape(x.shape[0], -1),
x.reshape(x.shape[0], -1),
reduction="none",
).sum(dim=-1)
pz = self.prior(
loc=self._pz_mu, scale=self._pz_logvar.exp(), manifold=self.latent_manifold
)
KLD = (qz_x.log_prob(z) - pz.log_prob(z)).sum(-1).squeeze(0)
return (recon_loss + KLD).mean(dim=0), recon_loss.mean(dim=0), KLD.mean(dim=0)
[docs] def interpolate(
self,
starting_inputs: torch.Tensor,
ending_inputs: torch.Tensor,
granularity: int = 10,
):
"""This function performs a geodesic interpolation in the poincaré disk of the autoencoder
from starting inputs to ending inputs. It returns the interpolation trajectories.
Args:
starting_inputs (torch.Tensor): The starting inputs in the interpolation of shape
[B x input_dim]
ending_inputs (torch.Tensor): The starting inputs in the interpolation of shape
[B x input_dim]
granularity (int): The granularity of the interpolation.
Returns:
torch.Tensor: A tensor of shape [B x granularity x input_dim] containing the
interpolation trajectories.
"""
assert starting_inputs.shape[0] == ending_inputs.shape[0], (
"The number of starting_inputs should equal the number of ending_inputs. Got "
f"{starting_inputs.shape[0]} sampler for starting_inputs and {ending_inputs.shape[0]} "
"for endinging_inputs."
)
starting_z = self.encoder(starting_inputs).embedding
ending_z = self.encoder(ending_inputs).embedding
t = torch.linspace(0, 1, granularity).to(starting_inputs.device)
inter_geo = torch.zeros(
starting_inputs.shape[0], granularity, starting_z.shape[-1]
).to(starting_z.device)
for i, t_i in enumerate(t):
z_i = self.latent_manifold.geodesic(t_i, starting_z, ending_z)
inter_geo[:, i, :] = z_i
decoded_geo = self.decoder(
inter_geo.reshape(
(starting_z.shape[0] * t.shape[0],) + (starting_z.shape[1:])
)
).reconstruction.reshape(
(
starting_inputs.shape[0],
t.shape[0],
)
+ (starting_inputs.shape[1:])
)
return decoded_geo
[docs] def get_nll(self, data, n_samples=1, batch_size=100):
"""
Function computed the estimate negative log-likelihood of the model. It uses importance
sampling method with the approximate posterior distribution. This may take a while.
Args:
data (torch.Tensor): The input data from which the log-likelihood should be estimated.
Data must be of shape [Batch x n_channels x ...]
n_samples (int): The number of importance samples to use for estimation
batch_size (int): The batchsize to use to avoid memory issues
"""
if n_samples <= batch_size:
n_full_batch = 1
else:
n_full_batch = n_samples // batch_size
n_samples = batch_size
log_p = []
for i in range(len(data)):
x = data[i].unsqueeze(0)
log_p_x = []
for j in range(n_full_batch):
x_rep = torch.cat(batch_size * [x])
encoder_output = self.encoder(x_rep)
if self.model_config.posterior_distribution == "riemannian_normal":
mu, log_var = (
encoder_output.embedding,
encoder_output.log_concentration,
)
else:
mu, log_var = (
encoder_output.embedding,
encoder_output.log_covariance,
)
std = torch.exp(0.5 * log_var)
qz_x = self.posterior(loc=mu, scale=std, manifold=self.latent_manifold)
z = qz_x.rsample(torch.Size([1]))
pz = self.prior(
loc=self._pz_mu,
scale=self._pz_logvar.exp(),
manifold=self.latent_manifold,
)
log_q_z_given_x = qz_x.log_prob(z).sum(-1).squeeze(0)
log_p_z = pz.log_prob(z).sum(-1).squeeze(0)
recon_x = self.decoder(z.squeeze(0))["reconstruction"]
if self.model_config.reconstruction_loss == "mse":
log_p_x_given_z = -0.5 * F.mse_loss(
recon_x.reshape(x_rep.shape[0], -1),
x_rep.reshape(x_rep.shape[0], -1),
reduction="none",
).sum(dim=-1) - torch.tensor(
[np.prod(self.input_dim) / 2 * np.log(np.pi * 2)]
).to(
data.device
) # decoding distribution is assumed unit variance N(mu, I)
elif self.model_config.reconstruction_loss == "bce":
log_p_x_given_z = -F.binary_cross_entropy(
recon_x.reshape(x_rep.shape[0], -1),
x_rep.reshape(x_rep.shape[0], -1),
reduction="none",
).sum(dim=-1)
log_p_x.append(log_p_x_given_z + log_p_z - log_q_z_given_x)
log_p_x = torch.cat(log_p_x)
log_p.append((torch.logsumexp(log_p_x, 0) - np.log(len(log_p_x))).item())
return np.mean(log_p)