code: def natural_exp_decay(
      learning_rate,
      global_step,
      decay_steps,
      decay_rate,
      staircase=False,
      name=None,
  ):
      """Applies natural exponential decay to the initial learning rate.
  
      When training a model, it is often recommended to lower the learning rate as
      the training progresses.  This function applies an exponential decay function
      to a provided initial learning rate.  It requires an `global_step` value to
      compute the decayed learning rate.  You can just pass a TensorFlow variable
      that you increment at each training step.
  
      The function returns the decayed learning rate.  It is computed as:
  
      ```python
      decayed_learning_rate = learning_rate * exp(-decay_rate * global_step /
      decay_step)
      ```
  
      or, if `staircase` is `True`, as:
  
      ```python
      decayed_learning_rate = learning_rate * exp(-decay_rate * floor(global_step /
      decay_step))
      ```
  
      Example: decay exponentially with a base of 0.96:
  
      ```python
      ...
      global_step = tf.Variable(0, trainable=False)
      learning_rate = 0.1
      decay_steps = 5
      k = 0.5
      learning_rate = tf.compat.v1.train.natural_exp_decay(learning_rate,
      global_step,
                                                 decay_steps, k)
  
      # Passing global_step to minimize() will increment it at each step.
      learning_step = (
          tf.compat.v1.train.GradientDescentOptimizer(learning_rate)
          .minimize(...my loss..., global_step=global_step)
      )
      ```
  
      Args:
        learning_rate: A scalar `float32` or `float64` `Tensor` or a Python number.
          The initial learning rate.
        global_step: A Python number. Global step to use for the decay computation.
          Must not be negative.
        decay_steps: How often to apply decay.
        decay_rate: A Python number.  The decay rate.
        staircase: Whether to apply decay in a discrete staircase, as opposed to
          continuous, fashion.
        name: String.  Optional name of the operation.  Defaults to
          'ExponentialTimeDecay'.
  
      Returns:
        A scalar `Tensor` of the same type as `learning_rate`.  The decayed
        learning rate.
  
      Raises:
        ValueError: if `global_step` is not supplied.
  
      @compatibility(eager)
      When eager execution is enabled, this function returns a function which in
      turn returns the decayed learning rate Tensor. This can be useful for changing
      the learning rate value across different invocations of optimizer functions.
      @end_compatibility
      """
      natural_exp_rate = math_ops.exp(math_ops.negative(decay_rate))
      decayed_lr = learning_rate_schedule.ExponentialDecay(
          learning_rate,
          decay_steps,
          natural_exp_rate,
          staircase=staircase,
          name=name,
      )
  
      if not context.executing_eagerly():
          decayed_lr = decayed_lr(global_step)
      else:
          decayed_lr = functools.partial(decayed_lr, global_step)
      return decayed_lr
  
file_path: tensorflow/tensorflow/python/keras/optimizer_v2/legacy_learning_rate_decay.py
imports: import functools
  from tensorflow.python.eager import context
  from tensorflow.python.framework import dtypes
  from tensorflow.python.framework import tensor_conversion
  from tensorflow.python.keras.optimizer_v2 import learning_rate_schedule
  from tensorflow.python.ops import math_ops
  from tensorflow.python.util import nest
  from tensorflow.python.util.tf_export import tf_export
label_desc: Use image node_id 4 for calling a global function with example usage: natural_exp_decay(learning_rate, global_step, decay_steps, decay_rate, staircase, name) and returns: decayed_lr