code: def test_training_works(self, strategy):
      if isinstance(strategy, tf.distribute.OneDeviceStrategy):
          strategy_scope = contextlib.nullcontext()
      else:
          strategy_scope = strategy.scope()
  
      def make_model():
          inputs = tf.keras.Input((1000,))
          dense = tf.keras.layers.Dense(
              units=1,
              use_bias=False,
              kernel_initializer=tf.initializers.ones(),
          )
          outputs = dense(inputs)
          return tf.keras.models.Model(inputs=inputs, outputs=outputs)
  
      x = tf.ones(shape=[5000, 1000])
      y = tf.zeros(shape=[5000])
      with strategy_scope:
          model = make_model()
          clip = 100.0
          noise_mult = 0.01
          acc_steps = 5
          batch_size = 10
          opt = dp_optimizer_keras_sparse.DPSparseKerasSGDOptimizer(
              l2_norm_clip=clip,
              noise_multiplier=noise_mult,
              gradient_accumulation_steps=acc_steps,
              learning_rate=0.001,
          )
          model.compile(
              loss=tf.keras.losses.MeanAbsoluteError(
                  reduction=tf.keras.losses.Reduction.NONE
              ),
              optimizer=opt,
          )
          history = model.fit(
              x=x,
              y=y,
              epochs=2,
              steps_per_epoch=500,
              batch_size=batch_size,
          )
          self.assertIn("loss", history.history)
          # total steps: 1000 (2 epochs, 500 steps/epoch)
          # accumulation steps: 5
          # expected_iterations = total steps / accumulation steps
          expected_iterations = 1000 / acc_steps  # = 200
          # The loss is |w.x - y| (where w is the dense layer weights).
          # The gradient is sign(w.x - y)x. With the choice of x, y, the gradient
          # becomes x.
          # So each gradient update is w <- w - learning_rate*1 + noise
          expected_params = 1 - 0.001 * expected_iterations
          expected_noise = (
              0.001
              * clip
              * noise_mult
              * np.sqrt(expected_iterations)
              / (acc_steps * batch_size)
          )
          self.assertEqual(opt.iterations.numpy(), expected_iterations)
          self.assertAllClose(
              np.mean(model.trainable_variables[0].numpy()),
              expected_params,  # 0.8
              # stddev = expected_noise/√1000 (since we're averaging 1000 samples)
              # we set atol to 4 stddev
              atol=4 * expected_noise / np.sqrt(1000),  # 0.0358
          )
          self.assertAllClose(
              np.std(model.trainable_variables[0].numpy()),
              expected_noise,  # 0.2828
              atol=4 * expected_noise / np.sqrt(1000),  # 0.0358
          )
  
file_path: privacy/tensorflow_privacy/privacy/optimizers/dp_optimizer_keras_sparse_distributed_test.py
imports: import contextlib
  import multiprocessing
  import os
  import sys
  from absl.testing import parameterized
  import numpy
  import tensorflow
  from tensorflow_privacy.privacy.optimizers import dp_optimizer_keras_sparse
label_desc: Use image node_id 1 for calling the DistributedTrainingTest obj's underlying member method code with example usage: obj.test_training_works(strategy) and returns: tf