diff --git a/n3fit/src/n3fit/backends/keras_backend/MetaLayer.py b/n3fit/src/n3fit/backends/keras_backend/MetaLayer.py
index acdf01bc1d..2dc3c24105 100644
--- a/n3fit/src/n3fit/backends/keras_backend/MetaLayer.py
+++ b/n3fit/src/n3fit/backends/keras_backend/MetaLayer.py
@@ -8,7 +8,7 @@
     For instance: np_to_tensor is just a call to K.constant
 """
 
-from keras.initializers import Constant, RandomUniform, glorot_normal, glorot_uniform
+from keras.initializers import Constant, RandomUniform, glorot_normal, glorot_uniform, RandomNormal
 from keras.layers import Layer
 
 # Define in this dictionary new initializers as well as the arguments they accept (with default values if needed be)
@@ -16,6 +16,7 @@
     "random_uniform": (RandomUniform, {"minval": -0.5, "maxval": 0.5}),
     "glorot_uniform": (glorot_uniform, {}),
     "glorot_normal": (glorot_normal, {}),
+    "random_normal": (RandomNormal, {"mean": 0.0, "stddev": 0.05}),
 }
 
 
diff --git a/n3fit/src/n3fit/layers/preprocessing.py b/n3fit/src/n3fit/layers/preprocessing.py
index b716f8f398..78179db327 100644
--- a/n3fit/src/n3fit/layers/preprocessing.py
+++ b/n3fit/src/n3fit/layers/preprocessing.py
@@ -76,15 +76,15 @@ def generate_weight(self, name: str, kind: str, dictionary: dict, set_to_zero: b
             single_replica_initializer = MetaLayer.init_constant(0.0)
             trainable = False
         else:
-            minval, maxval = dictionary[kind]
+            prepro_kwargs = dictionary[kind]
             trainable = dictionary.get("trainable", True)
             # Seeds will be set in the wrapper MultiInitializer
-            single_replica_initializer = MetaLayer.select_initializer(
-                "random_uniform", minval=minval, maxval=maxval
-            )
+            single_replica_initializer = MetaLayer.select_initializer(**prepro_kwargs)
             # If we are training, constrain the weights to be within the limits
-            if trainable:
-                constraint = constraints.MinMaxWeight(minval, maxval)
+            if trainable and prepro_kwargs["ini_name"] == "random_uniform":
+                constraint = constraints.MinMaxWeight(
+                    prepro_kwargs["minval"], prepro_kwargs["maxval"]
+                )
 
         initializer = MultiInitializer(single_replica_initializer, self._replica_seeds, base_seed=0)
         # increment seeds for the next coefficient