diff --git a/examples/optimizers.py b/examples/optimizers.py
index 66c6225..7003869 100644
--- a/examples/optimizers.py
+++ b/examples/optimizers.py
@@ -290,6 +290,7 @@ def _update_estimator_curvature(
       sync: Union[Array, bool] = True
   ) -> EstimatorState:
     """Updates the curvature estimator state."""
+
     state = self.estimator.update_curvature_matrix_estimate(
         state=estimator_state,
         ema_old=ema_old,
@@ -316,7 +317,9 @@ def maybe_update_estimator_curvature(
       sync: Union[Array, bool] = True,
   ) -> PreconditionState:
     """Updates the curvature estimates if it is the right iteration."""
+
     ema_old = decay_old_ema * self._curvature_ema + (1.0 - decay_old_ema) * 1.0
+
     return self._maybe_update_estimator_state(
         state,
         self.should_update_estimate_curvature(state),
@@ -587,9 +590,12 @@ def _step(
       Tuple[Params, OptaxAndPreconditionState, Mapping[str, Array]],
   ]:
     """A single step of optax."""
+
+    rng_func, rng_precon = jax.random.split(rng)
+
     batch = self._batch_process_func(batch)
     func_args = kfac_jax.optimizer.make_func_args(
-        params, func_state, rng, batch,
+        params, func_state, rng_func, batch,
         has_state=self._value_func_has_state,
         has_rng=self._value_func_has_rng
     )
@@ -599,7 +605,7 @@ def _step(
       precond_state = self._preconditioner.maybe_update(
           precond_state,
           func_args,
-          rng,
+          rng_precon,
       )
       precond_state = self._preconditioner.increment_count(precond_state)
     out, grads = self._value_and_grad_func(*func_args)
@@ -666,16 +672,22 @@ def step(
       Tuple[Params, Any, Mapping[str, Array]],
   ]:
     """A step with similar interface to KFAC."""
+
+    rng_init, rng_step = self._pmap_rng_split(rng, 2)
+
     batch = next(data_iterator)
+
     if self._preconditioner is not None and state.precond_state is None:
+
       precond_state = self._pmap_init_preconditioner(
-          params, rng, batch, func_state
+          params, rng_init, batch, func_state
       )
       state = OptaxAndPreconditionState(state.optax_state, precond_state)
+
     return self._pmap_step(
         params,
         state,
-        rng,
+        rng_step,
         batch,
         func_state,
         global_step_int,
diff --git a/kfac_jax/_src/curvature_blocks.py b/kfac_jax/_src/curvature_blocks.py
index 65e0b3d..9e69727 100644
--- a/kfac_jax/_src/curvature_blocks.py
+++ b/kfac_jax/_src/curvature_blocks.py
@@ -880,7 +880,6 @@ def _multiply_matpower_unscaled(
     vector = self.parameters_list_to_single_vector(vector)
 
     if power == 1:
-
       result = jnp.matmul(state.matrix.value, vector) + identity_weight * vector
 
     elif not use_cached:
@@ -1208,22 +1207,6 @@ def _eigenvalues_unscaled(
 
     return utils.outer_product(*s)
 
-  @utils.auto_scope_method
-  def update_curvature_matrix_estimate(
-      self,
-      state: "KroneckerFactored.State",
-      estimation_data: Mapping[str, Sequence[Array]],
-      ema_old: Numeric,
-      ema_new: Numeric,
-      batch_size: Numeric,
-  ) -> "KroneckerFactored.State":
-    assert len(state.factors) == len(self.axis_groups)
-
-    # This function call will return a copy of state:
-    return self._update_curvature_matrix_estimate(
-        state, estimation_data, ema_old, ema_new, batch_size
-    )
-
   def _update_cache(  # pytype: disable=signature-mismatch  # numpy-scalars
       self,
       state: "KroneckerFactored.State",
diff --git a/kfac_jax/_src/optimizer.py b/kfac_jax/_src/optimizer.py
index f33e8b4..b17d2f3 100644
--- a/kfac_jax/_src/optimizer.py
+++ b/kfac_jax/_src/optimizer.py
@@ -1463,8 +1463,11 @@ def convert_value_and_grad_to_value_func(
   Returns:
     A function that returns only the loss value.
   """
+
   def value_func(*args, **kwargs) -> Array:
+
     out, _ = value_and_grad_func(*args, **kwargs)
+
     return out[0] if has_aux else out
 
   return value_func