diff --git a/tests/test_add.py b/tests/test_add.py
index 1c98d91..d1ea0f8 100644
--- a/tests/test_add.py
+++ b/tests/test_add.py
@@ -4,13 +4,10 @@
 
 from tests.utils import Payload, empty_strided, randint_strided, randn_strided
 
-_INT_DTYPES = (
-    torch.int16,
-    torch.uint16,
-    torch.int32,
-    torch.uint32,
-    torch.int64,
-    torch.uint64,
+_INT_DTYPES = (torch.int16, torch.int32, torch.int64)
+
+_UINT_DTYPES = tuple(
+    filter(None, (getattr(torch, f"uint{bits}", None) for bits in (16, 32, 64)))
 )
 
 
@@ -38,18 +35,13 @@
         (torch.float32, 1e-7, 1e-7),
         (torch.float16, 1e-3, 1e-3),
         (torch.bfloat16, 1e-2, 5e-3),
-        (torch.int16, 0, 0),
-        (torch.uint16, 0, 0),
-        (torch.int32, 0, 0),
-        (torch.uint32, 0, 0),
-        (torch.int64, 0, 0),
-        (torch.uint64, 0, 0),
-    ),
+    )
+    + tuple((dtype, 0, 0) for dtype in _INT_DTYPES + _UINT_DTYPES),
 )
 def test_add(
     shape, input_strides, other_strides, out_strides, dtype, device, rtol, atol
 ):
-    if dtype in _INT_DTYPES:
+    if dtype in _INT_DTYPES or dtype in _UINT_DTYPES:
         input = randint_strided(
             0, 100, shape, input_strides, dtype=dtype, device=device
         )
@@ -72,10 +64,10 @@ def _add(input, other, out):
 
 
 def _torch_add(input, other, out):
-    if input.dtype in (torch.uint16, torch.uint32, torch.uint64):
+    if input.dtype in _UINT_DTYPES:
         input = input.to(torch.int64)
 
-    if other.dtype in (torch.uint16, torch.uint32, torch.uint64):
+    if other.dtype in _UINT_DTYPES:
         other = other.to(torch.int64)
 
     res = torch.add(input, other)
diff --git a/tests/test_rms_norm.py b/tests/test_rms_norm.py
index f447091..d6d4dff 100644
--- a/tests/test_rms_norm.py
+++ b/tests/test_rms_norm.py
@@ -59,4 +59,19 @@ def _rms_norm(input, weight, *, eps=1e-6, out=None):
 
 
 def _torch_rms_norm(input, weight, *, eps=1e-6, out=None):
-    return torch.nn.functional.rms_norm(input, input.shape[-1:], weight=weight, eps=eps)
+    # Fallback for `torch<2.3`: `rms_norm = (x / sqrt(mean(x^2) + eps)) * weight`.
+    def _fallback(input, _normalized_shape, weight, *, eps=1e-6):
+        rms = torch.sqrt(torch.mean(input * input, dim=-1, keepdim=True) + eps)
+
+        return (input / rms) * weight
+
+    rms_norm_fn = getattr(torch.nn.functional, "rms_norm", _fallback)
+
+    result = rms_norm_fn(input, input.shape[-1:], weight=weight, eps=eps)
+
+    if out is not None:
+        out.copy_(result)
+    else:
+        out = result
+
+    return out