code: def gmm_loss(batch, mus, sigmas, logpi, reduce=True):
      """Computes the gmm loss.
  
      Compute minus the log probability of batch under the GMM model described
      by mus, sigmas, pi. Precisely, with bs1, bs2, ... the sizes of the batch
      dimensions (several batch dimension are useful when you have both a batch
      axis and a time step axis), gs the number of mixtures and fs the number of
      features.
  
      :param batch: (bs1, bs2, *, fs) torch tensor
      :param mus: (bs1, bs2, *, gs, fs) torch tensor
      :param sigmas: (bs1, bs2, *, gs, fs) torch tensor
      :param logpi: (bs1, bs2, *, gs) torch tensor
      :param reduce: if not reduce, the mean in the following formula is omitted
  
      :returns:
      loss(batch) = - mean_{i1=0..bs1, i2=0..bs2, ...} log(
          sum_{k=1..gs} pi[i1, i2, ..., k] * N(
              batch[i1, i2, ..., :] | mus[i1, i2, ..., k, :], sigmas[i1, i2, ..., k, :]))
  
      NOTE: The loss is not reduced along the feature dimension (i.e. it should
      scale linearily with fs).
  
      Adapted from: https://github.com/ctallec/world-models
      """
      # for non-image based environment, batch's shape before unsqueeze:
      # (seq_len, batch_size, fs)
      batch = batch.unsqueeze(-2)
      normal_dist = Normal(mus, sigmas)
      g_log_probs = normal_dist.log_prob(batch)
      # According to the world model paper, the prediction of next state is a
      # factored Gaussian distribution (i.e., the covariance matrix of the multi-
      # dimensional Gaussian distribution is a diagonal matrix). Hence we can sum
      # log probability of each dimension when calculating log joint probability
      g_log_probs = logpi + torch.sum(g_log_probs, dim=-1)
      # log sum exp
      max_log_probs = torch.max(g_log_probs, dim=-1, keepdim=True)[0]
      g_log_probs = g_log_probs - max_log_probs
  
      g_probs = torch.exp(g_log_probs)
      probs = torch.sum(g_probs, dim=-1)
  
      log_prob = max_log_probs.squeeze() + torch.log(probs)
      if reduce:
          return -(torch.mean(log_prob))
      return -log_prob
  
imports: import logging
  from collections import deque
  from typing import NamedTuple
  import numpy
  import torch
  import torch.nn
  import torch.nn.functional
  from reagent.core import types
  from reagent.core.torch_utils import stack
  from torch.distributions.normal import Normal
label_desc: Use image node_id 2 for calling a global function with example usage: gmm_loss(batch, mus, sigmas, logpi, reduce) and returns: unknown, unknown