code: def test_spectral_norm_train(self, model_index, key_paths):
      class FooDense(nn.Module):
          @nn.compact
          def __call__(self, x, train):
              x = nn.Dense(8)(x)
              x = nn.SpectralNorm(nn.Dense(6))(x, update_stats=train)
              x = nn.Dense(4)(x)
              return x
  
      class FooConv(nn.Module):
          @nn.compact
          def __call__(self, x, train):
              x = nn.Dense(9)(x)
              x = x.reshape((1, 3, 3))
              x = nn.SpectralNorm(nn.Conv(2, kernel_size=(2, 2)))(
                  x, update_stats=train
              )
              x = x.reshape(1, -1)
              x = nn.Dense(4)(x)
              return x
  
      class FooAttention(nn.Module):
          @nn.compact
          def __call__(self, x, train):
              a = nn.Dense(4)(x)
              b = nn.Dense(4)(x)
              x = nn.SpectralNorm(
                  nn.attention.MultiHeadDotProductAttention(4)
              )(a, b, update_stats=train)
              x = nn.Dense(4)(x)
              return x
  
      key1, key2, key3 = random.split(random.PRNGKey(0), 3)
      x = random.normal(key1, (1, 4))
      y = random.normal(key2, (1, 4))
  
      model_cls = (FooDense, FooConv, FooAttention)[model_index]
      variables = model_cls().init(key3, x, train=False)
      params, batch_stats = (
          variables["params"],
          variables["batch_stats"],
      )
      self.assertEqual(key_paths, batch_stats["SpectralNorm_0"].keys())
  
      class TrainState(train_state.TrainState):
          batch_stats: Any
  
      state = TrainState.create(
          apply_fn=model_cls().apply,
          params=params,
          batch_stats=batch_stats,
          tx=optax.adam(1e-3),
      )
  
      @jax.jit
      def train_step(state, batch):
          def loss_fn(params):
              logits, updates = state.apply_fn(
                  {"params": params, "batch_stats": state.batch_stats},
                  x=batch["image"],
                  train=True,
                  mutable=["batch_stats"],
              )
              loss = jnp.mean(
                  optax.l2_loss(
                      predictions=logits, targets=batch["label"]
                  )
              )
              return loss, updates
  
          grad_fn = jax.value_and_grad(loss_fn, has_aux=True)
          (loss, updates), grads = grad_fn(state.params)
          state = state.apply_gradients(grads=grads)
          state = state.replace(batch_stats=updates["batch_stats"])
          return state, loss
  
      prev_loss = float("inf")
      for _ in range(10):
          state, loss = train_step(state, {"image": x, "label": y})
          self.assertLess(loss, prev_loss)
          prev_loss = loss
  
imports: import copy
  import functools
  from typing import Any
  import jax
  import jax.numpy
  import numpy
  import optax
  from absl.testing import absltest, parameterized
  from jax import random
  from flax import ids
  from flax import linen
  from flax.linen import fp8_ops
  from flax.training import train_state
label_desc: Use image node_id 14 for calling the NormalizationTest obj's underlying member method code with example usage: obj.test_spectral_norm_train(model_index, key_paths) and returns: state,  loss, x, x, x, loss,  updates