code: def log_softmax(self, dim, **kwargs):
      r"""Applies a softmax followed by a logarithm.
      While mathematically equivalent to log(softmax(x)), doing these two
      operations separately is slower, and numerically unstable. This function
      uses an alternative formulation to compute the output and gradient correctly.
      """
      # 0-d case
      if self.dim() == 0:
          assert dim == 0, "Improper dim argument"
          return self.new(torch.zeros((), device=self.device))
  
      if self.size(dim) == 1:
          return self.new(torch.zeros_like(self.data))
  
      maximum_value = self.max(dim, keepdim=True)[0]
      logits = self - maximum_value
      normalize_term = exp(logits).sum(dim, keepdim=True)
      result = logits - normalize_term.log()
      return result
  
file_path: CrypTen/crypten/common/functions/approximations.py
imports: import math
  import crypten
  import torch
  from crypten.config import cfg
label_desc: Use image node_id 15 for calling a global function with example usage: log_softmax(dim) and returns: result, self, self