diff --git a/learned_optimization/research/univ_nfn/learned_opt/learned_opts.py b/learned_optimization/research/univ_nfn/learned_opt/learned_opts.py
index bec0f64..9c31a98 100644
--- a/learned_optimization/research/univ_nfn/learned_opt/learned_opts.py
+++ b/learned_optimization/research/univ_nfn/learned_opt/learned_opts.py
@@ -97,22 +97,24 @@ def make_hk_perm_spec(mlp_params):
   return perm_spec
 
 
-def make_hk_cnn_perm_spec(mlp_params):
+def make_hk_cnn_perm_spec(params):
   """Produces perm spec for a haiku cnn."""
   perm_spec = {}
-  for i in range(len(mlp_params)):
-    if i < len(mlp_params) - 1:
-      if i == 0:
-        name = 'conv2_d'
-      else:
-        name = f'conv2_d_{i}'
-      perm_spec[name] = {
-          'w': (-i, -(len(mlp_params) + i), i, i + 1),
-          'b': (i + 1,),
-      }
+  num_convs = len([k for k in params if k.startswith('conv2_d')])
+  for i in range(num_convs):
+    if i == 0:
+      conv_name = 'conv2_d'
+      ln_name = 'layer_norm'
     else:
-      name = 'linear'
-      perm_spec[name] = {'w': (i, i + 1), 'b': (i + 1,)}
+      conv_name = f'conv2_d_{i}'
+      ln_name = f'layer_norm_{i}'
+    perm_spec[conv_name] = {
+        'w': (-i, -(len(params) + i), i, i + 1),
+        'b': (i + 1,),
+    }
+    if ln_name in params:  # layernorm is optional
+      perm_spec[ln_name] = {'offset': (i + 1,), 'scale': (i + 1,)}
+  perm_spec['linear'] = {'w': (num_convs, num_convs + 1), 'b': (num_convs + 1,)}  # final linear layer
   return perm_spec
 
 
diff --git a/learned_optimization/tasks/fixed/conv.py b/learned_optimization/tasks/fixed/conv.py
index 3ffbc46..14753ae 100644
--- a/learned_optimization/tasks/fixed/conv.py
+++ b/learned_optimization/tasks/fixed/conv.py
@@ -100,6 +100,21 @@ def normalizer(self, loss):
                     1.5 * jnp.log(self.datasets.extra_info["num_classes"]))
 
 
+@gin.configurable
+def Conv_Cifar10_8_16x32_layernorm():
+  """A 3 hidden layer convnet with layernorm designed for 16x16 cifar10."""
+
+  def norm_fn(x):
+    return hk.LayerNorm(create_scale=True, create_offset=True, axis=-1)(x)
+
+  base_model_fn = _cross_entropy_pool_loss([16, 32],
+                                           jax.nn.relu,
+                                           num_classes=10,
+                                           norm_fn=norm_fn)
+  datasets = image.cifar10_datasets(batch_size=128, image_size=(8, 8))
+  return _ConvTask(base_model_fn, datasets)
+
+
 @gin.configurable
 def Conv_Cifar10_8_16x32():
   """A 3 hidden layer convnet designed for 16x16 cifar10."""