diff --git a/tests/test_modules.py b/tests/test_modules.py
index b8f7c4f9f..beaea6e12 100644
--- a/tests/test_modules.py
+++ b/tests/test_modules.py
@@ -155,9 +155,8 @@ def test_linear8bitlt_no_fp16_weights(device, threshold):
         b1 = torch.randn(16, 8, 32, device=device, dtype=torch.float16)
         o1 = mlp(b1)
         assert o1.dtype == torch.float16
-        if threshold > 0:
+        if threshold > 0 and device not in ("cpu", "xpu"):
             assert mlp.fc1.state.idx is not None
-        if threshold > 0:
             assert mlp.fc2.state.idx is not None
 
     mlp = MLP8bit(32, 64, threshold=threshold, has_fp16_weights=False).half().to(device)
@@ -166,9 +165,8 @@ def test_linear8bitlt_no_fp16_weights(device, threshold):
         b1 = torch.randn(16, 8, 32, device=device, dtype=torch.float16)
         o1 = mlp(b1)
         assert o1.dtype == torch.float16
-        if threshold > 0:
+        if threshold > 0 and device not in ("cpu", "xpu"):
             assert mlp.fc1.state.idx is not None
-        if threshold > 0:
             assert mlp.fc2.state.idx is not None
     assert mlp.fc1.weight.dtype == torch.int8
     assert mlp.fc2.weight.dtype == torch.int8
@@ -188,9 +186,8 @@ def test_linear8bitlt_no_fp16_weights(device, threshold):
         b1 = torch.randn(16, 8, 32, device=device, dtype=torch.float16)
         o1 = mlp(b1)
         assert o1.dtype == torch.float16
-        if threshold > 0:
+        if threshold > 0 and device not in ("cpu", "xpu"):
             assert mlp.fc1.state.idx is not None
-        if threshold > 0:
             assert mlp.fc2.state.idx is not None
     assert mlp.fc1.weight.dtype == torch.int8
     assert mlp.fc2.weight.dtype == torch.int8
@@ -210,9 +207,8 @@ def test_linear8bitlt_no_fp16_weights(device, threshold):
         b1 = torch.randn(16, 8, 32, device=device, dtype=torch.float16)
         o1 = mlp(b1)
         assert o1.dtype == torch.float16
-        if threshold > 0:
+        if threshold > 0 and device not in ("cpu", "xpu"):
             assert mlp.fc1.state.idx is not None
-        if threshold > 0:
             assert mlp.fc2.state.idx is not None
 
     assert mlp.fc1.weight.dtype == torch.int8