code: def test_correctness_with_golden(self):
      optimizer = Adadelta(learning_rate=1.0, rho=0.8, epsilon=1e-6)
  
      x = backend.Variable(np.ones([10]))
      grads = ops.arange(0.1, 1.1, 0.1)
      first_grads = ops.full((10,), 0.01)
  
      golden = np.tile(
          [[0.9978], [0.9947], [0.9915], [0.9882], [0.9849]], (1, 10)
      )
  
      optimizer.apply_gradients(zip([first_grads], [x]))
      for i in range(5):
          self.assertAllClose(x, golden[i], rtol=5e-4, atol=5e-4)
          optimizer.apply_gradients(zip([grads], [x]))
  
file_path: keras/keras/optimizers/adadelta_test.py
imports: import numpy
  from keras import backend
  from keras import ops
  from keras import testing
  from keras.optimizers.adadelta import Adadelta
label_desc: Use image node_id 4 for calling the AdadeltaTest obj's underlying member method code with example usage: obj.test_correctness_with_golden() without return types