class_docstr: Optimizer that implements the Adafactor algorithm.
  
  Adafactor is described in https://arxiv.org/abs/1804.04235.
  
  Adafactor is most similar to Adam (Kingma and Ba), the major differences are:
  
  1. For a two-dimensional AxB weight matrix, Adafactor uses only A+B auxiliary
     parameters to maintain the second-moment estimator, instead of AB.
     This is advantageous on memory-limited systems.  In addition, beta1
     (momentum) is set to zero by default, saving an additional auxiliary
     parameter per weight.  Variables with >=3 dimensions are treated as
     collections of two-dimensional matrices - factorization is over the final
     two dimensions.
  
  2. Adafactor incorporates "update-clipping" - a scale-invariant analog of
     gradient clipping.  This adds stability
  
  3. Adafactor does not require an external "learning rate".  By default, it
     incorporates a relative-update-scale schedule, corresponding to
     inverse-square-root learning-rate-decay in ADAM.  We hope this works well
     for most applications.
  
  ALGORITHM:
  
  parameter -= absolute_update_scale * clip(grad / grad_scale)
  
  where:
  
    absolute_update_scale := relative_update_scale * parameter_scale
    relative_update_scale := min((step_num + 1)**-0.5, 1e-2)
    parameter_scale := max(rms(var)), epsilon2)
    clip(x) := x / max(1.0, rms(x))
    grad_scale := tf.sqrt(v)   (v is the second-moment estimator)
  
  The second-moment estimator v is maintained in a manner similar to Adam:
  We initialize
  ```
  if var is 2-dimensional:
    v_r <- zeros([num_rows])
    v_c <- zeros([num_cols])
  if var is 0-dimensional or 1-dimensional:
    v <- zeros(shape(var))
  ```
  
  The update rule is as follows:
  ```
  decay_rate = 1 - (step_num + 1) ^ -0.8
  grad_squared = tf.square(grad) + epsilon1
  if var is 2-dimensional:
    v_r <- decay_rate * v_r + (1 - decay_rate) * reduce_mean(grad_squared, 1)
    v_c <- decay_rate * v_c + (1 - decay_rate) * reduce_mean(grad_squared, 0)
    v = outer_prod(v_r, v_c) / reduce_mean(v_r)
  if var is 0-dimensional or 1-dimensional:
    v <- decay_rate * v + (1 - decay_rate) * grad_squared
  ```
  
  For variables with >=3 dimensions, we factorize the second-moment accumulator
  over the final 2 dimensions.  See the code for details.
  
  
  Several parts of this algorithm are configurable from the initializer.
  
    multiply_by_parameter_scale:  If True, then compute absolute_update_scale
      as described above.  If False, let absolute_update_scale be the externally
      supplied learning_rate.
    learning_rate: represents relative_update_scale if
      multiply_by_parameter_scale==True, or absolute_update_scale if
      multiply_by_parameter_scale==False.
    decay_rate: Decay rate of the second moment estimator (varies by step_num).
      This should be set to a function such that:
      1-1/(step_num + 1) <= decay_rate(step_num) < 1.0
    beta1: enables momentum, as in Adam.  Uses extra memory if nonzero.
    clipping_threshold: should be >=1.0 or None for no update clipping
    factored: whether to factor the second-moment estimator.  True means
      less memory usage.
docstr: Estimate the scale of the parameters from the current values.
  
  We include a minimum value of 0.001 to give it a chance to escape 0
  if it was zero-initialized.
  
  Instead of using the value, we could impute the scale from the shape,
  as initializers do.
  
  Args:
    var: a variable or Tensor.
  Returns:
    a Scalar
docstr_tok: ["Estimate","the","scale","of","the","parameters","from","the","current","values",".","We","include","a","minimum","value","of","0.001","to","give","it","a","chance","to","escape","0","if","it","was","zero-initialized",".","Instead","of","using","the","value",",","we","could","impute","the","scale","from","the","shape",",","as","initializers","do",".","Args",":","var",":","a","variable","or","Tensor",".","Returns",":","a","Scalar"]
code: def _parameter_scale(self, var):
      """Estimate the scale of the parameters from the current values.
  
      We include a minimum value of 0.001 to give it a chance to escape 0
      if it was zero-initialized.
  
      Instead of using the value, we could impute the scale from the shape,
      as initializers do.
  
      Args:
        var: a variable or Tensor.
      Returns:
        a Scalar
      """
      return tf.maximum(reduce_rms(var), self._epsilon2)
  
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  from tensor2tensor.layers import common_layers
  from tensor2tensor.utils import quantization
  import tensorflow.compat.v1
label_desc: Use image node_id 7 for calling the AdafactorOptimizer obj's underlying member method code with example usage: obj._parameter_scale(var) and returns: tf