diff --git a/pymc/pytensorf.py b/pymc/pytensorf.py
index f1d69c9282..572241e49a 100644
--- a/pymc/pytensorf.py
+++ b/pymc/pytensorf.py
@@ -567,10 +567,8 @@ def __init__(self, f):
     def __call__(self, state):
         return self.f(**state)
 
-    def __getattr__(self, item):
-        """Allow access to the original function attributes."""
-        # This is only reached if `__getattribute__` fails.
-        return getattr(self.f, item)
+    def dprint(self, **kwrags):
+        return self.f.dprint(**kwrags)
 
 
 class CallableTensor:
diff --git a/tests/test_pytensorf.py b/tests/test_pytensorf.py
index f7efd5f6d4..de7f7f1cbe 100644
--- a/tests/test_pytensorf.py
+++ b/tests/test_pytensorf.py
@@ -746,7 +746,7 @@ def test_hessian_sign_change_warning(func):
     assert equal_computations([res_neg], [-res])
 
 
-def test_point_func():
+def test_point_func(capsys):
     x, y = pt.vectors("x", "y")
     outs = x * 2 + y**2
     f = compile([x, y], outs)
@@ -758,3 +758,30 @@ def test_point_func():
     dprint_res = point_f.dprint(file="str")
     expected_dprint_res = point_f.f.dprint(file="str")
     assert dprint_res == expected_dprint_res
+
+    point_f.dprint(print_shape=True)
+    captured = capsys.readouterr()
+
+    # The shape=(?,) arises because the inputs are dvector. This checks that the dprint works, and the print_shape
+    # kwargs was correctly forwarded
+    assert "shape=(?,)" in captured.out
+
+
+def test_pickle_point_func():
+    """
+    Regression test for https://github.com/pymc-devs/pymc/issues/7857
+    """
+    import cloudpickle
+
+    x, y = pt.vectors("x", "y")
+    outs = x * 2 + y**2
+    f = compile([x, y], outs)
+
+    point_f = PointFunc(f)
+    point_f_pickled = cloudpickle.dumps(point_f)
+    point_f_unpickled = cloudpickle.loads(point_f_pickled)
+
+    # Check that the function survived the round-trip
+    np.testing.assert_allclose(
+        point_f_unpickled({"y": [3], "x": [2]}), point_f({"y": [3], "x": [2]})
+    )