diff --git a/lab/autograd/__init__.py b/lab/autograd/__init__.py
index bcf6936..ddec35b 100644
--- a/lab/autograd/__init__.py
+++ b/lab/autograd/__init__.py
@@ -12,6 +12,8 @@
 
 from plum import clear_all_cache as _clear_all_cache
 
+import autograd  # Load `autograd` to load all new types.
+
 # noinspection PyUnresolvedReferences
 from .generic import *
 from .linear_algebra import *
diff --git a/lab/jax/__init__.py b/lab/jax/__init__.py
index 81fdbdd..9f5474f 100644
--- a/lab/jax/__init__.py
+++ b/lab/jax/__init__.py
@@ -12,6 +12,8 @@
 
 from plum import clear_all_cache as _clear_all_cache
 
+import jax  # Load `jax` to load all new types.
+
 # noinspection PyUnresolvedReferences
 from .generic import *
 from .linear_algebra import *
diff --git a/lab/tensorflow/__init__.py b/lab/tensorflow/__init__.py
index 153f639..717533c 100644
--- a/lab/tensorflow/__init__.py
+++ b/lab/tensorflow/__init__.py
@@ -12,7 +12,7 @@
 
 from plum import clear_all_cache as _clear_all_cache
 
-import tensorflow as tf
+import tensorflow as tf  # Load `tensorflow` to load all new types.
 
 # noinspection PyUnresolvedReferences
 from .generic import *
diff --git a/lab/torch/__init__.py b/lab/torch/__init__.py
index 9fd9029..ea99be9 100644
--- a/lab/torch/__init__.py
+++ b/lab/torch/__init__.py
@@ -12,6 +12,8 @@
 
 from plum import clear_all_cache as _clear_all_cache
 
+import torch  # Load `torch` to load all new types.
+
 # noinspection PyUnresolvedReferences
 from .generic import *
 from .linear_algebra import *
diff --git a/lab/types.py b/lab/types.py
index 927ceb6..f0784d8 100644
--- a/lab/types.py
+++ b/lab/types.py
@@ -83,12 +83,11 @@ def _module_attr(module, attr):
 _ag_tensor = ModuleType("autograd.tracer", "Box")
 
 # Define JAX module types.
-if (
-    sys.version_info.minor > 7
-):  # jax>0.4 deprecated python-3.7 support, rely on older jax versions
-    _jax_tensor = ModuleType("jaxlib.xla_extension", "ArrayImpl")
-else:
+if sys.version_info.minor <= 7:
+    # `jax` 0.4 deprecated Python 3.7 support. Rely on older JAX versions.
     _jax_tensor = ModuleType("jax.interpreters.xla", "DeviceArray")
+else:
+    _jax_tensor = ModuleType("jaxlib.xla_extension", "ArrayImpl")
 _jax_tracer = ModuleType("jax.core", "Tracer")
 _jax_dtype = ModuleType("jax._src.numpy.lax_numpy", "_ScalarMeta")
 _jax_device = ModuleType("jaxlib.xla_extension", "Device")
@@ -156,31 +155,34 @@ def _module_attr(module, attr):
 _torch_lookup_cache = {}
 
 
+def _name_to_numpy_dtype(name):
+    # We will want to get types from `np`, but the built-in types should be just
+    # those.
+    if name in {"int", "long"}:
+        return int
+    elif name == "bool":
+        return bool
+    elif name == "unicode":
+        return str
+    else:
+        return getattr(np, name)
+
+
 def _torch_lookup(dtype):
     if not _torch_lookup_cache:
         # Cache is empty. Fill it.
 
-        def _from_np(name):
-            # We will want to get types from `np`, but the built-in types should be just
-            # those.
-            if name in {"int", "long"}:
-                return int
-            elif name == "bool":
-                return bool
-            elif name == "unicode":
-                return str
-            else:
-                return getattr(np, name)
-
         # `bool` can occur but isn't in `__all__`.
         for name in np.core.numerictypes.__all__ + ["bool"]:
+            _from_np = _name_to_numpy_dtype(name)
+
             # Check that it is a type.
-            if not isinstance(_from_np(name), type):
+            if not isinstance(_from_np, type):
                 continue
 
             # Attempt to get the PyTorch equivalent.
             try:
-                _torch_lookup_cache[_module_attr("torch", name)] = _from_np(name)
+                _torch_lookup_cache[_module_attr("torch", name)] = _from_np
             except AttributeError:
                 # Could not find the PyTorch equivalent. That's okay.
                 pass
@@ -355,12 +357,7 @@ def dtype_int(dtype: DType):
     name = list(convert(dtype, NPDType).__name__)
     while name and name[0] not in set([str(i) for i in range(10)]):
         name.pop(0)
-    name_int = "int" + "".join(name)
-    if name_int == "int":
-        dtype_int = int
-    else:
-        dtype_int = getattr(np, name_int)
-    return _convert_back(dtype_int, dtype)
+    return _convert_back(_name_to_numpy_dtype("int" + "".join(name)), dtype)
 
 
 @dispatch