diff --git a/keras_core/initializers/random_initializers_test.py b/keras_core/initializers/random_initializers_test.py
index 38ab70bcc..a2ad291d0 100644
--- a/keras_core/initializers/random_initializers_test.py
+++ b/keras_core/initializers/random_initializers_test.py
@@ -19,7 +19,7 @@ class InitializersTest(testing.TestCase):
         self.assertEqual(initializer.stddev, stddev)
         self.assertEqual(initializer.seed, seed)
         self.assertEqual(values.shape, shape)
-        self.test_load_external_config(initializer, external_config)
+        self.assert_idempotent_config(initializer, external_config)
 
     def test_random_uniform(self):
         shape = (5, 5)
@@ -35,11 +35,11 @@ class InitializersTest(testing.TestCase):
         self.assertEqual(initializer.maxval, maxval)
         self.assertEqual(initializer.seed, seed)
         self.assertEqual(values.shape, shape)
-        self.test_load_external_config(initializer, external_config)
+        self.assert_idempotent_config(initializer, external_config)
         values = values.numpy()
         self.assertGreaterEqual(np.min(values), minval)
         self.assertLess(np.max(values), maxval)
 
-    def test_load_external_config(self, initializer, config):
+    def assert_idempotent_config(self, initializer, config):
         initializer = initializer.from_config(config)
         self.assertEqual(initializer.get_config(), config)
diff --git a/keras_core/metrics/metric_test.py b/keras_core/metrics/metric_test.py
index 878928c09..19a02fa68 100644
--- a/keras_core/metrics/metric_test.py
+++ b/keras_core/metrics/metric_test.py
@@ -11,10 +11,10 @@ class ExampleMetric(Metric):
     def __init__(self, name="mean_square_error", dtype=None):
         super().__init__(name=name, dtype=dtype)
         self.sum = self.add_variable(
-            name="sum", initializer=initializers.Zeros()
+            name="sum", shape=(), initializer=initializers.Zeros()
         )
         self.total = self.add_variable(
-            name="total", initializer=initializers.Zeros(), dtype="int32"
+            name="total", shape=(), initializer=initializers.Zeros(), dtype="int32"
         )
 
     def update_state(self, y_true, y_pred):
diff --git a/keras_core/metrics/regression_metrics.py b/keras_core/metrics/regression_metrics.py
index ffcbee696..e64a85ab0 100644
--- a/keras_core/metrics/regression_metrics.py
+++ b/keras_core/metrics/regression_metrics.py
@@ -7,10 +7,10 @@ class MeanSquareError(Metric):
     def __init__(self, name="mean_square_error", dtype=None):
         super().__init__(name=name, dtype=dtype)
         self.sum = self.add_variable(
-            name="sum", initializer=initializers.Zeros()
+            name="sum", shape=(), initializer=initializers.Zeros()
         )
         self.total = self.add_variable(
-            name="total", initializer=initializers.Zeros()
+            name="total", shape=(), initializer=initializers.Zeros()
         )
 
     def update_state(self, y_true, y_pred):
diff --git a/keras_core/operations/numpy.py b/keras_core/operations/numpy.py
index a027ddcc6..904134bd8 100644
--- a/keras_core/operations/numpy.py
+++ b/keras_core/operations/numpy.py
@@ -996,6 +996,20 @@ def square(x):
     return backend.execute("square", x)
 
 
+class Sqrt(Operation):
+    def call(self, x):
+        return backend.execute("sqrt", x)
+
+    def compute_output_spec(self, x):
+        return KerasTensor(x.shape, dtype=x.dtype)
+
+
+def sqrt(x):
+    if any_symbolic_tensors((x,)):
+        return Sqrt().symbolic_call(x)
+    return backend.execute("sqrt", x)
+
+
 class Squeeze(Operation):
     def __init__(self, axis=None):
         super().__init__()
diff --git a/keras_core/regularizers/regularizers.py b/keras_core/regularizers/regularizers.py
index 03cd8847d..a0d28edac 100644
--- a/keras_core/regularizers/regularizers.py
+++ b/keras_core/regularizers/regularizers.py
@@ -345,6 +345,6 @@ def validate_float_arg(value, name):
     return float(value)
 
 
-def l2_normalize(x):
-    l2_norm = ops.sqrt(ops.sum(ops.square(x)))
+def l2_normalize(x, axis=0):
+    l2_norm = ops.sqrt(ops.sum(ops.square(x), axis=axis))
     return x / l2_norm