code: def test_autodiff(self, get, same_inputs, phi):
      x1 = jnp.cos(random.normal(random.PRNGKey(1), (3, 1, 2, 3)))
      if same_inputs is None:
          x2 = None
      elif same_inputs is True:
          x2 = x1
      else:
          x2 = jnp.cos(random.normal(random.PRNGKey(2), (4, 1, 2, 3)))
  
      name = phi.__name__
      if name == "LeakyRelu":
          phi = phi(0.1)
      elif name == "ElementwiseNumerical":
          phi = phi(fn=jnp.cos, deg=25)
      else:
          phi = phi()
  
      _, _, kernel_fn = stax.serial(
          stax.Dense(1, 2.0, 0.01), phi, stax.Dense(1, 2.0, 0.01), phi
      )
  
      def k(x1, x2):
          return kernel_fn(x1, x2, get)
  
      dx1 = random.normal(random.PRNGKey(3), x1.shape) * 0.01
      if x2 is None:
          dx2 = None
      else:
          dx2 = random.normal(random.PRNGKey(4), x2.shape) * 0.01
  
      def dk(x1, x2):
          return jvp(k, (x1, x2), (dx1, dx2))[1]
  
      def d2k(x1, x2):
          return jvp(dk, (x1, x2), (dx1, dx2))[1]
  
      _dk = dk(x1, x2)
      _d2k = d2k(x1, x2)
  
      if same_inputs is not False and get == "ntk" and "Relu" in name:
          tol = 8e-3
      else:
          tol = 2e-3 if name == "ElementwiseNumerical" else 1e-4
  
      def assert_close(x, y, tol=3e-5):
          if default_backend() == "tpu":
              # TODO(romann): understand why TPUs have high errors.
              tol = 0.21
          self.assertLess(
              jnp.max(jnp.abs(x - y))
              / (jnp.mean(jnp.abs(x)) + jnp.mean(jnp.abs(y))),
              tol,
          )
  
      # k(x + dx) ~ k(x) + dk(x) dx + dx^T d2k(x) dx
      assert_close(
          k(x1 + dx1, None if same_inputs is None else x2 + dx2),
          k(x1, x2) + _dk + _d2k / 2,
          tol=tol,
      )
  
      # d/dx1
      k_fwd_0 = jacfwd(k)(x1, x2)
      k_rev_0 = jacrev(k)(x1, x2)
      assert_close(k_fwd_0, k_rev_0)
  
      if same_inputs is not None:
          # d/dx2
          k_fwd_1 = jacfwd(k, 1)(x1, x2)
          k_rev_1 = jacrev(k, 1)(x1, x2)
          assert_close(k_fwd_1, k_rev_1)
  
          # dk(x2, x1)/dx2 = dk(x1, x2)/dx1
          k_fwd_01 = jacfwd(k, 1)(x2, x1)
          k_rev_01 = jacrev(k, 1)(x2, x1)
          assert_close(
              jnp.moveaxis(k_fwd_0, (0, 2, 4), (1, 3, 5)), k_fwd_01
          )
          assert_close(
              jnp.moveaxis(k_rev_0, (0, 2, 4), (1, 3, 5)), k_rev_01
          )
  
          # dk(x2, x1)/dx1 = dk(x1, x2)/dx2
          k_fwd_10 = jacfwd(k)(x2, x1)
          k_rev_10 = jacrev(k)(x2, x1)
          assert_close(
              jnp.moveaxis(k_fwd_1, (0, 2, 4), (1, 3, 5)), k_fwd_10
          )
          assert_close(
              jnp.moveaxis(k_rev_1, (0, 2, 4), (1, 3, 5)), k_rev_10
          )
  
imports: import itertools
  import random
  from absl.testing import absltest
  from jax import config
  from jax import default_backend
  from jax import grad, jacfwd, jacrev, jit, jvp, value_and_grad
  from jax import random
  import jax.numpy
  import neural_tangents
  from neural_tangents import stax
  from neural_tangents._src.empirical import _DEFAULT_TESTING_NTK_IMPLEMENTATION
  from tests import test_utils
label_desc: Use image node_id 1 for calling the AutodiffTest obj's underlying member method code with example usage: obj.test_autodiff(get, same_inputs, phi) and returns: kernel_fn, jvp, jvp