diff --git a/cirkit/layers/input/exp_family/exp_family.py b/cirkit/layers/input/exp_family/exp_family.py
index 52d9ebc5..28d9d74a 100644
--- a/cirkit/layers/input/exp_family/exp_family.py
+++ b/cirkit/layers/input/exp_family/exp_family.py
@@ -6,6 +6,7 @@
 
 from cirkit.layers.input import InputLayer
 from cirkit.reparams.leaf import ReparamIdentity
+from cirkit.reparams.reparam import Reparameterizaion
 from cirkit.utils.type_aliases import ReparamFactory
 
 
@@ -20,6 +21,9 @@ class ExpFamilyLayer(InputLayer):
     based on its implementation.
     """
 
+    params: Reparameterizaion
+    """The reparameterizaion that gives the natural parameters eta, shape (D, K, P, S)."""
+
     def __init__(  # type: ignore[misc]  # pylint: disable=too-many-arguments
         self,
         *,
diff --git a/cirkit/layers/sum.py b/cirkit/layers/sum.py
index 8f50214e..33322b37 100644
--- a/cirkit/layers/sum.py
+++ b/cirkit/layers/sum.py
@@ -5,6 +5,7 @@
 
 from cirkit.layers.layer import Layer
 from cirkit.reparams.leaf import ReparamIdentity
+from cirkit.reparams.reparam import Reparameterizaion
 from cirkit.utils.log_trick import log_func_exp
 from cirkit.utils.type_aliases import ReparamFactory
 
@@ -15,6 +16,9 @@ class SumLayer(Layer):
     TODO: currently this is only a sum for mixing, but not generic sum layer.
     """
 
+    params: Reparameterizaion
+    """The reparameterizaion that gives the parameters for sum units, shape (F, H, K)."""
+
     def __init__(  # pylint: disable=too-many-arguments
         self,
         *,
@@ -49,7 +53,6 @@ def __init__(  # pylint: disable=too-many-arguments
             reparam=reparam,
         )
 
-        # TODO: how to annotate shapes for reparams?
         # TODO: better way to handle fold_mask shape? too many None checks
         self.params = reparam(
             (num_folds, arity, num_output_units),
diff --git a/cirkit/layers/sum_product/cp.py b/cirkit/layers/sum_product/cp.py
index c351f643..389c311b 100644
--- a/cirkit/layers/sum_product/cp.py
+++ b/cirkit/layers/sum_product/cp.py
@@ -13,6 +13,14 @@
 class BaseCPLayer(SumProductLayer):
     """Candecomp Parafac (decomposition) layer."""
 
+    params_in: Optional[Reparameterizaion]
+    """The reparameterizaion that gives the parameters for sum units on input, shape as given by \
+    dim names, e.g., (F, H, I, O). Can be None to disable this part of computation."""
+
+    params_out: Optional[Reparameterizaion]
+    """The reparameterizaion that gives the parameters for sum units on output, shape as given by \
+    dim names, e.g., (F, I, O). Can be None to disable this part of computation."""
+
     def __init__(  # pylint: disable=too-many-arguments
         self,
         *,
@@ -71,7 +79,7 @@ def __init__(  # pylint: disable=too-many-arguments
             # TODO: currently we can only support this. any elegant impl?
             assert params_in_dim_name[:2] == "fh" or fold_mask is None
             # Only params_in can see the folds and need mask.
-            self.params_in: Optional[Reparameterizaion] = reparam(
+            self.params_in = reparam(
                 self._infer_shape(params_in_dim_name),
                 dim=-2,
                 mask=fold_mask.view(
@@ -88,9 +96,7 @@ def __init__(  # pylint: disable=too-many-arguments
             i, o = tuple(params_out_dim_name[-2:])
             assert i == ("r" if params_in_dim_name else "i") and o == "o"
             self._einsum_out = f"{params_out_dim_name},f{i}...->f{o}..."
-            self.params_out: Optional[Reparameterizaion] = reparam(
-                self._infer_shape(params_out_dim_name), dim=-2
-            )
+            self.params_out = reparam(self._infer_shape(params_out_dim_name), dim=-2)
         else:
             self._einsum_out = ""
             self.params_out = None
@@ -162,6 +168,13 @@ def forward(self, x: Tensor) -> Tensor:
 class CollapsedCPLayer(BaseCPLayer):
     """Candecomp Parafac (decomposition) layer, with matrix C collapsed."""
 
+    params_in: Reparameterizaion
+    """The reparameterizaion that gives the parameters for sum units on input, \
+    shape (F, H, I, O)."""
+
+    params_out: None
+    """CollapsedCPLayer does not have sum units on output."""
+
     def __init__(  # pylint: disable=too-many-arguments
         self,
         *,
@@ -197,6 +210,13 @@ def __init__(  # pylint: disable=too-many-arguments
 class UncollapsedCPLayer(BaseCPLayer):
     """Candecomp Parafac (decomposition) layer, without collapsing."""
 
+    params_in: Reparameterizaion
+    """The reparameterizaion that gives the parameters for sum units on input, \
+    shape (F, H, I, R)."""
+
+    params_out: Reparameterizaion
+    """The reparameterizaion that gives the parameters for sum units on output, shape (F, R, O)."""
+
     def __init__(  # pylint: disable=too-many-arguments
         self,
         *,
@@ -237,6 +257,12 @@ def __init__(  # pylint: disable=too-many-arguments
 class SharedCPLayer(BaseCPLayer):
     """Candecomp Parafac (decomposition) layer, with parameter sharing and matrix C collapsed."""
 
+    params_in: Reparameterizaion
+    """The reparameterizaion that gives the parameters for sum units on input, shape (H, I, O)."""
+
+    params_out: None
+    """SharedCPLayer does not have sum units on output."""
+
     def __init__(  # pylint: disable=too-many-arguments
         self,
         *,
diff --git a/cirkit/layers/sum_product/tucker.py b/cirkit/layers/sum_product/tucker.py
index 815a5599..80128b5a 100644
--- a/cirkit/layers/sum_product/tucker.py
+++ b/cirkit/layers/sum_product/tucker.py
@@ -5,6 +5,7 @@
 
 from cirkit.layers.sum_product.sum_product import SumProductLayer
 from cirkit.reparams.leaf import ReparamIdentity
+from cirkit.reparams.reparam import Reparameterizaion
 from cirkit.utils.log_trick import log_func_exp
 from cirkit.utils.type_aliases import ReparamFactory
 
@@ -14,6 +15,9 @@
 class TuckerLayer(SumProductLayer):
     """Tucker (2) layer."""
 
+    params: Reparameterizaion
+    """The reparameterizaion that gives the parameters for sum units, shape (F, I, J, O)."""
+
     def __init__(  # pylint: disable=too-many-arguments
         self,
         *,