docstr: Compute backward variable beta as well as gradients of the activation
  matrix wrt loglikelihood of forward variable.
  
  Args:
      grad: Working space memory of flattened shape [B, T, U, V+1]
      log_probs: Activatio tensor of flattented shape [B, T, U, V+1]
      T: Length of the acoustic sequence T (not padded).
      U: Length of the target sequence U (not padded).
      alphas: Working space memory for alpha of shape [B, T, U].
      betas: Working space memory for alpha of shape [B, T, U].
      labels: Ground truth label of shape [B, U]
      logll: Loglikelihood of the forward variable.
  
  Returns:
      Loglikelihood of the forward variable and inplace updates the grad tensor.
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code: def compute_betas_and_grads(
      self,
      grad: torch.Tensor,
      log_probs: torch.Tensor,
      T: int,
      U: int,
      alphas: torch.Tensor,
      betas: torch.Tensor,
      labels: torch.Tensor,
      logll: torch.Tensor,
  ):
      """
      Compute backward variable beta as well as gradients of the activation
      matrix wrt loglikelihood of forward variable.
  
      Args:
          grad: Working space memory of flattened shape [B, T, U, V+1]
          log_probs: Activatio tensor of flattented shape [B, T, U, V+1]
          T: Length of the acoustic sequence T (not padded).
          U: Length of the target sequence U (not padded).
          alphas: Working space memory for alpha of shape [B, T, U].
          betas: Working space memory for alpha of shape [B, T, U].
          labels: Ground truth label of shape [B, U]
          logll: Loglikelihood of the forward variable.
  
      Returns:
          Loglikelihood of the forward variable and inplace updates the grad tensor.
      """
  
      idx = CpuRNNT_index(
          U,
          self.maxU_,
          self.minibatch_,
          self.alphabet_size_,
          self.batch_first,
      )
      betas[idx(T - 1, U - 1)] = log_probs[idx(T - 1, U - 1) * 2]
  
      for t in range(T - 1, -1, -1):
          for u in range(U - 1, -1, -1):
              if (u == U - 1) and (t < T - 1):
                  betas[idx(t, U - 1)] = (
                      betas[idx(t + 1, U - 1)]
                      + log_probs[idx(t, U - 1) * 2]
                  )
  
              if (t == T - 1) and (u < U - 1):
                  betas[idx(T - 1, u)] = (
                      betas[idx(T - 1, u + 1)]
                      + log_probs[idx(T - 1, u) * 2 + 1]
                  )
  
              if (t < T - 1) and (u < U - 1):
                  no_emit = (
                      betas[idx(t + 1, u)] + log_probs[idx(t, u) * 2]
                  )
                  emit = (
                      betas[idx(t, u + 1)]
                      + log_probs[idx(t, u) * 2 + 1]
                  )
                  betas[idx(t, u)] = log_sum_exp(emit, no_emit)
  
      loglike = betas[0]
      # // Gradients w.r.t. log probabilities
      for t in range(T):
          for u in range(U):
              if t < T - 1:
                  g = alphas[idx(t, u)] + betas[idx(t + 1, u)]
                  grad[idx(t, u, self.blank_)] = -torch.exp(
                      log_probs[idx(t, u) * 2] + g - loglike
                  )
  
              if u < U - 1:
                  g = alphas[idx(t, u)] + betas[idx(t, u + 1)]
                  grad[idx(t, u, labels[u])] = -torch.exp(
                      math.log1p(self.fastemit_lambda_)
                      + log_probs[idx(t, u) * 2 + 1]
                      + g
                      - loglike
                  )
  
      # // gradient to the last blank transition
      grad[idx(T - 1, U - 1, self.blank_)] = -torch.exp(
          log_probs[idx(T - 1, U - 1) * 2]
          + alphas[idx(T - 1, U - 1)]
          - loglike
      )
  
      return loglike
  
imports: import math
  import multiprocessing
  from typing import Optional
  import numba
  import torch
  from torch.autograd import Function
  from espnet2.asr.transducer.rnnt_multi_blank.utils import global_constants
label_desc: Use image node_id 4 for calling the CPURNNT obj's underlying member method code with example usage: obj.compute_betas_and_grads(grad, log_probs, T, U, alphas, betas, labels, logll) and returns: loglike