diff --git a/examples/training.py b/examples/training.py
index da6f9cd..5f30bbc 100644
--- a/examples/training.py
+++ b/examples/training.py
@@ -271,9 +271,10 @@ def create_optimizer(self) -> Union[
 
   def initialize_state(self):
     """Initializes all of the experiment's state variables."""
-    init_rng, preprocess_rng = jax.random.split(self.init_rng)
+    init_rng, seed_rng = jax.random.split(self.init_rng)
     init_rng = kfac_jax.utils.replicate_all_local_devices(init_rng)
-    preprocess_rng = jax.random.fold_in(preprocess_rng, jax.process_index())
+    seed_rng = jax.random.fold_in(seed_rng, jax.process_index())
+    seed = int(seed_rng[0])
 
     # Initialize and load dataset
     if self.mode == "train":
@@ -281,7 +282,7 @@ def initialize_state(self):
           datasets.dataset_as_generator(
               self._build_train_input,
               split="train",
-              seed=int(preprocess_rng[0]),
+              seed=seed,
               device_batch_size=self.train_per_device_batch_size,
           )
       )
@@ -293,12 +294,12 @@ def initialize_state(self):
       self._eval_input = dict(
           train=self._build_eval_input(
               split="train",
-              seed=int(preprocess_rng[0]),
+              seed=seed,
               device_batch_size=self.eval_per_device_batch_size
           ),
           test=self._build_eval_input(
               split="test",
-              seed=int(preprocess_rng[0]),
+              seed=seed,
               device_batch_size=self.eval_per_device_batch_size
           ),
       )
diff --git a/kfac_jax/_src/optimizer.py b/kfac_jax/_src/optimizer.py
index e028e11..5de28e0 100644
--- a/kfac_jax/_src/optimizer.py
+++ b/kfac_jax/_src/optimizer.py
@@ -121,6 +121,7 @@ def __init__(
       default_batch_size_extractor,
       pmap_axis_name: str = "kfac_axis",
       forbid_setting_attributes_after_finalize: bool = True,
+      modifiable_attribute_exceptions: Sequence[str] = (),
       include_norms_in_stats: bool = False,
   ):
     """Initializes the K-FAC optimizer with the provided settings.
@@ -266,6 +267,10 @@ def __init__(
         they have been compiled. However, if you are extending this class, and
         clearly understand the risks of modifying attributes, setting this to
         ``False`` will remove the restriction. (Default: ``True``)
+      modifiable_attribute_exceptions: Sequence of strings. Gives a list
+        of names for attributes that can be modified after finalization even
+        when ``forbid_setting_attributes_after_finalize`` is ``True``.
+        (Default: ``()``)
       include_norms_in_stats: Boolean. It True, the vector norms of the
         gradient, preconditioned gradient, and parameter update are included in
         the statistics returned by the step function. (Default: ``False``)
@@ -276,6 +281,7 @@ def __init__(
         debug=debug,
         forbid_setting_attributes_after_finalize=
         forbid_setting_attributes_after_finalize,
+        excluded_attribute_names=modifiable_attribute_exceptions,
     )
     if use_adaptive_damping and initial_damping is None:
       raise ValueError("When use_adaptive_damping is True you must provide a "