class_docstr: 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``.
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code: 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),
      )
  
file_path: benchmark_VAE/src/pythae/models/pvae/pvae_model.py
imports: import warnings
  from typing import Optional
  import numpy
  import torch
  import torch.nn
  import torch.nn.functional
  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
label_desc: Use image node_id 3 for calling the PoincareVAE obj's underlying member method code with example usage: obj.loss_function(recon_x, x, z, qz_x) and returns: unknown,  recon_loss,  KLD