diff --git a/optax/_src/transform.py b/optax/_src/transform.py
index c8f92422..a4a78890 100644
--- a/optax/_src/transform.py
+++ b/optax/_src/transform.py
@@ -885,10 +885,6 @@ def update_fn(updates, state, params=None):
 
   return base.GradientTransformation(init_fn, update_fn)
 
-
-AddDecayedWeightsState = base.EmptyState
-
-
 def add_decayed_weights(
     weight_decay: Union[float, jax.Array] = 0.0,
     mask: Optional[Union[Any, Callable[[base.Params], Any]]] = None
@@ -906,10 +902,6 @@ def add_decayed_weights(
     A `GradientTransformation` object.
   """
 
-  def init_fn(params):
-    del params
-    return AddDecayedWeightsState()
-
   def update_fn(updates, state, params):
     if params is None:
       raise ValueError(base.NO_PARAMS_MSG)
@@ -921,8 +913,8 @@ def update_fn(updates, state, params):
   # E.g. it is common to skip weight decay on bias units and batch stats.
   if mask is not None:
     return wrappers.masked(
-        base.GradientTransformation(init_fn, update_fn), mask)
-  return base.GradientTransformation(init_fn, update_fn)
+        base.GradientTransformation(_init_empty_state, update_fn), mask)
+  return base.GradientTransformation(_init_empty_state, update_fn)
 
 
 class ScaleByScheduleState(NamedTuple):
@@ -982,10 +974,6 @@ def update_fn(updates, state, params=None):
   return base.GradientTransformation(init_fn, update_fn)
 
 
-class ScaleByTrustRatioState(NamedTuple):
-  """The scale and decay trust ratio transformation is stateless."""
-
-
 def scale_by_trust_ratio(
     min_norm: float = 0.0,
     trust_coefficient: float = 1.,
@@ -1005,10 +993,6 @@ def scale_by_trust_ratio(
     A `GradientTransformation` object.
   """
 
-  def init_fn(params):
-    del params
-    return ScaleByTrustRatioState()
-
   def update_fn(updates, state, params):
     if params is None:
       raise ValueError(base.NO_PARAMS_MSG)
@@ -1031,7 +1015,7 @@ def _scale_update(update, param):
     updates = jax.tree_util.tree_map(_scale_update, updates, params)
     return updates, state
 
-  return base.GradientTransformation(init_fn, update_fn)
+  return base.GradientTransformation(_init_empty_state, update_fn)
 
 
 class AddNoiseState(NamedTuple):
@@ -1131,10 +1115,6 @@ def _subtract_mean(g):
   else:
     return g
 
-
-CentralState = base.EmptyState
-
-
 def centralize() -> base.GradientTransformation:
   """Centralize gradients.
 
@@ -1145,16 +1125,12 @@ def centralize() -> base.GradientTransformation:
     A `GradientTransformation` object.
   """
 
-  def init_fn(params):
-    del params
-    return CentralState()
-
   def update_fn(updates, state, params=None):
     del params
     updates = jax.tree_util.tree_map(_subtract_mean, updates)
     return updates, state
 
-  return base.GradientTransformation(init_fn, update_fn)
+  return base.GradientTransformation(_init_empty_state, update_fn)
 
 
 class ScaleBySM3State(NamedTuple):