diff --git a/tests/unit/autogram/test_engine.py b/tests/unit/autogram/test_engine.py
index 1ba8cc20..a7749b60 100644
--- a/tests/unit/autogram/test_engine.py
+++ b/tests/unit/autogram/test_engine.py
@@ -20,6 +20,7 @@
     InterModuleParamReuse,
     MIMOBranched,
     MISOBranched,
+    ModelUsingSubmoduleParamsDirectly,
     ModuleReuse,
     MultiInputMultiOutput,
     MultiInputSingleOutput,
@@ -172,6 +173,21 @@ def test_compute_gramian_with_weird_modules(
     _assert_gramian_is_equivalent_to_autograd(architecture, batch_size, batch_dim)
 
 
+@mark.xfail
+@mark.parametrize("architecture", [ModelUsingSubmoduleParamsDirectly])
+@mark.parametrize("batch_size", [1, 3, 32])
+@mark.parametrize("batch_dim", [0, None])
+def test_compute_gramian_unsupported_architectures(
+    architecture: type[ShapedModule], batch_size: int, batch_dim: int | None
+):
+    """
+    Tests compute_gramian on some architectures that are known to be unsupported. It is expected to
+    fail.
+    """
+
+    _assert_gramian_is_equivalent_to_autograd(architecture, batch_size, batch_dim)
+
+
 @mark.parametrize("batch_size", [1, 3, 16])
 @mark.parametrize(
     ["reduction", "movedim_source", "movedim_destination", "batch_dim"],
diff --git a/tests/utils/architectures.py b/tests/utils/architectures.py
index facf852c..0b26d89e 100644
--- a/tests/utils/architectures.py
+++ b/tests/utils/architectures.py
@@ -755,6 +755,23 @@ def forward(self, input: Tensor) -> Tensor:
         return self.dropout(self.conv2d(self.dropout(input)))
 
 
+class ModelUsingSubmoduleParamsDirectly(ShapedModule):
+    """
+    Model that uses its submodule's parameters directly and that does not call its submodule's
+    forward.
+    """
+
+    INPUT_SHAPES = (2,)
+    OUTPUT_SHAPES = (3,)
+
+    def __init__(self):
+        super().__init__()
+        self.linear = nn.Linear(2, 3)
+
+    def forward(self, input: Tensor) -> Tensor:
+        return input @ self.linear.weight.T + self.linear.bias
+
+
 class FreeParam(ShapedModule):
     """
     Model that contains a free (i.e. not contained in a submodule) parameter, that is used at the